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Running head: CLOSED 2-BRANES AS DM/DE CANDIDATES 1
Clusters of microscopic closed 2-brane entities as a possible candidate for dark matter & dark
energy
Hari Kumar Nair
Toronto, CANADA
Email: harismind@gmail.com
CLOSED 2-BRANES AS DM/DE CANDIDATES 2
Abstract
The existence of closed 2-branei
, bubble-like entities are within the realm of possibility of String
Theory. It is proposed that quantum fluctuations are continuously creating such microscopic
bubble-like entities, which I call repellons. Repellons are called thus since they would be
gravitationally repulsive (have negative gravitational mass) with respect to normal matter in our
universe. Repellons will be physically imperceptible and will manifest only as a gravitationally
repulsive force field. Although repellons are repelled by normal matter, they are mutually
gravitationally attractive. Since they are repelled by normal matter, there is a continuous transit
of outward going repellons from large bodies such as planets and stars. These repellons
eventually accumulate in regions of space that are free of any attractive gravity or where the
gravitational effects of nearby bodies cancel each other (such as Lagrange points). With the
stellar, planetary and intra-galactic dynamics a good portion of the repellons generated within
galaxies find their way to its outer peripheries and get deposited in the galactic halos. These
repellon deposits in the galactic halos cause a soft gravity ‘hill’ wrapping around the galaxy. The
gravity hills keep the peripheral stars in the galaxy within it and account for the observed higher
velocity of these stars, which is attributed to dark matter. The continuous generation of repellons
in the intergalactic spaces causes the galaxies to move further apart accounting for the observed
accelerated expansion of the universe, a phenomenon attributed to dark energy. This paper,
besides presenting much supporting evidence also proposes a variety of doable tests that can
confirm/falsify the repellon theory.
Keywords: Dark Matter, Dark Energy, Quantum Fluctuations, String Theory, Repulsive
Gravity, Antigravity, Negative Mass.
CLOSED 2-BRANES AS DM/DE CANDIDATES 3
Introduction
Clusters of microscopic closed 2-brane entities as a possible candidate for dark
matter & dark energy
We know that there is some repulsive energy that is causing the galaxies to be pushed
apart from each other. The effect has been observed and verified, although its cause remains
undetected. We have currently no explanation for this energy, which—for want of a better term—
has been named dark energy. The observations of this effect also indicate that dark energy
contributes around 69% of the total energy in the observable universe.
It has been observed that the stars at the peripheral regions of galaxies have been moving
much faster than the rate suggested by the galaxy’s mass. Scientists conclude that this can only
be due to the galaxy containing much more matter than what was apparent. This unseen matter
was given the name dark matter. It was calculated that as much as 85% of the total mass of a
galaxy came from this dark matter. dark matter was also thought to have a role behind other
observed phenomena such as gravitational lensing, CMB, etc.
Dark energy and dark matter together constitute almost 95% of the mass of the universe;
far more than all visible matter. In other words, the universe must be awash with this stuff, yet it
has not been directly observed.
We know nothing more than what has been mentioned above. Despite the best efforts of
scientists, neither dark matter nor dark energy has been directly observed. Expensive and highly
sensitive detectors (like the LUX detector) have failed to find any evidence of dark matter on
Earth.
CLOSED 2-BRANES AS DM/DE CANDIDATES 4
There are numerous hypotheses and suggestions to explain the effects of both dark matter
and dark energy, but none have been verified to be true. What is proposed here is also one such
hypothesis.
In this paper, I propose that clusters of microscopic closed 2-branes could be responsible
for the observed phenomena attributed to dark matter and dark energy. Some doable experiments
are also proposed to either confirm or falsify the hypothesis.
Closed 2-brane, also known as a repellon
At the core of this hypothesis is my proposition that clusters of microscopic closed 2-
branes are being continuously generated by quantum fluctuations. I propose that these closed 2-
branes are responsible for the phenomena that have been attributed to dark matter and dark
energy. Since I prefer to call these closed 2-branes by the less wordy term, repellons, this term
will be used henceforth in this paper to refer to closed 2-branes. In this paper, I have also used
the term ‘bubble-like closed 2-dimensional universe,’ to refer to closed 2-brane or repellon.
CLOSED 2-BRANES AS DM/DE CANDIDATES 5
Contents
Abstract............................................................................................................................... 2
Introduction......................................................................................................................... 3
1. What are repellons (closed 2-branes)?................................................................ 6
2. A logical argument for repellons......................................................................... 6
3. Properties of repellons ........................................................................................ 8
4. Creation of repellons......................................................................................... 12
5. Repellons as dark matter................................................................................... 13
6. Repellons as dark energy .................................................................................. 16
7. Supporting evidence for a theory of gravitationally repulsive dark matter ...... 16
8. Experiments proposed to confirm/falsify the repellon theory of DM/DE ........ 21
9. A brief history of my idea................................................................................. 24
10. A short bio of the author ................................................................................... 26
11. One last request................................................................................................. 27
End Notes:................................................................................................................. 28
CLOSED 2-BRANES AS DM/DE CANDIDATES 6
1. What are repellons (closed 2-branes)?
A 2-brane, per my understanding, is a plane that has only two spatial dimensions. It is
analogous to a simple geometric plane that has only two spatial dimensions, i.e., length and
breadth, but zero thickness. A closed 2-brane is analogous to a bubble-like spherical shell, with a
shell thickness of zero. We shall call this closed 2-brane, a repellon.
The bounded ‘inside’ (3-dimensional space) of the repellon, is forever separated from the
outside 3-dimensional space by its bubble-like 2-dimensional ‘skin.’ Since our universe is
fundamentally defined by its spatial 3-dimensionalityii
, the repellon (together with the 3-
dimensional space it contains) does not form part of our universe even if the repellon is
technically within our universe.
2. A logical argument for repellons.
# Statement Explanation
1 “A universe is defined as a set of all
points, such that there exists an
unbroken path that connects each point
with every other point and which does
not pass through a region of a different
spatial dimension. Two points can be
said to lie in the same universe if there
exists an unbroken path, however long
(not necessarily straight) that connects
them, and which does not pass through
a region that has a different spatial
dimension.”
The most fundamental characteristic of our universe is that
it has three spatial dimensions. The statement merely
defines a universe based on this principle.
2 “A spatially 2-dimensional universe can
physically exist.”
Spatially 2-dimensional (planar) entities are extensively
used in various branches of mathematics. Although these
are abstract entities in mathematics, their physical
existence cannot be ruled out. However, various accepted
ideas in physics implicitly assume the physical existence
of two-dimensional spaces. Examples are string theory
and the holographic principle.
3 “A (bubble-like) closed 2-dimensional
universe can physically exist.”
This follows from #2. A closed 2-dimensional universe is
a 2-dimensional universe that closes in on itself, like the
surface of a sphere. Although the sphere is a
3-dimensional space, its surface is 2-
dimensional. However, statement #3
refers to an absolute 2-dimensional space
whose thickness is zero.
CLOSED 2-BRANES AS DM/DE CANDIDATES 7
# Statement Explanation
4 “The bubble-like closed 2-dimensional
space will have an ‘inside’ that is 3-
dimensional as well an ‘outside’ that is
2-dimensional.”
This is also straightforward. Even though the bubble is a
closed 2-dimensional space, it will have a 3-dimensional
‘inside,’ which is of limited volume defined by the volume
of the bubble and 3-dimensional ‘outside,’ whose volume
is unlimited (provided, it is not encased in another larger
bubble).
5 “The 3-dimensional ‘outside’ space, the
bubble-like closed 2-dimensional space,
and the 3-dimensional ‘inside’ space
will be three distinct universes.”
This follows from the definition of a universe in #1.
Although the ‘inside,’ and ‘outside,’ of the bubble are
spatially 3-dimensional, there cannot exist a path that
connects a point in the ‘inside’ to a point in the ‘outside,’
that does not pass through the 2-dimensional bubble.
Hence, the ‘inside,’ the bubble, and the ‘outside’ are three
distinct universes.
6 “The bubble-like closed 2-dimensional
universe will be positively curved
(spatially) with respect to the ‘outside.’”
This follows from the definition of ‘curvature’ as
illustrated in the figure:
7 “Normal matter in our universe curves
space negatively (gravity well).
Negative curvature of space manifests
as attractive gravity.”
From General Relativity. GR talks about space-time rather
than space. However, a curvature of space-time
necessitates a curvature of space.
8 “Since the bubble-like closed 2-
dimensional universe causes a positive
curvature on the ‘outside’ 3-
dimensional universe, its manifested
gravity would be repulsive with respect
to matter of the ‘outside’ universe.”
Logically follows from #6 and #7.
9 “Since the bubble-like closed 2-
dimensional universe is gravitationally
repulsive with respect to normal matter
of the ‘outside’ universe, the closed 2-
dimensional universe has negative
gravitational mass with respect to
matter of the ‘outside’ universe.”
Follows from #8. Also, we know that the force of
gravitation F, between two bodies of masses m1 & m2
separated by a distance d, per Newton’s equation is
𝐹 =
𝑚1 𝑚2
𝑑2
When both bodies have positive (normal case) mass, the
gravitational Force F is positive, representing attractive
gravity.
For F to be negative (representing repulsive gravity), m1 &
m2 should be of opposite sign. Hence if one mass (say, m1)
is positive, the other (m2) should be negative mass.
When both masses are negative, the force of gravity
becomes positive and therefore attractive.
10 “The photons and other elementary
particles (making up all matter) created
in a 3-dimensional universe are 3-
dimensional in nature.”
This follows from #1. Also, the wave nature of elementary
particles suggest they are 3-dimensional entities.
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# Statement Explanation
11 “It is not possible for any elementary
particle to crossover from the ‘inside’ of
the closed 2-dimensional universe to the
‘outside,’ and vice-versa.”
This too follows from #1 and also #10. Since the ‘inside’
and ‘outside’ (both 3-d) are separated by a space of a
different spatial dimension (2-d), there cannot be a transit
of any elementary particle between the ‘inside’ and
‘outside.’
12 “The closed 2-dimensional universe is
completely imperceptible to the
‘outside,’ except through its
gravitational influence.”
Follows from #11. Since even photos cannot pass between
the ‘inside,’ and ‘outside,’ the closed 2-dimensional
universe will be imperceptible to the ‘outside.’
13 “So, a closed 2-dimensional universe
within a 3-dimensional space is:
1. imperceptible,
2. gravitationally repulsive,
3. has negative gravitational mass
with respect to the ‘outside’ 3-
dimensional universe.
Hence the only way a closed 2-
dimensional universe can manifest in
the ‘outside’ 3-dimensional universe is
as a gravitationally repulsive force-
field.”
The closed 2-dimensional universe (together with its
‘inside’ 3-d universe) is the closed 2-brane. Since this
entity is gravitationally repulsive with respect to the
‘outside’ 3-d universe (the universe we live in), this entity
is called a repellon.
3. Properties of repellons
1. Since repellons are not a part of our universe, they do not occupy any physical
volume in our universe. Hence, they are invisible and almost imperceptible to
anything of our universe, including our instruments however powerful or sensitive
they may be.
2. We know that normal matter causes a negative curvature (or a gravity well) on our
universe’s space-time. However, repellons would cause a positive curvatureiii
(a
gravity hill) on our universe’s (the ‘outside’) space-time. Due to this, repellons
CLOSED 2-BRANES AS DM/DE CANDIDATES 9
would be gravitationally repulsive with respect to matter in our universe. Hence,
the only way repellons can be ‘sensed’ is through their repulsive gravitational
influence on normal matter.
3. Whatever positive mass that the repellon contains would be gravitationally
negative (and of the same magnitude) with respect to our universe. It must be
emphasized that I am not proposing any new form of matter in this paper and
hence does not require any revision of the standard model. Matter trapped inside
repellons is just normal matter.
4. Since repellons do not occupy any space in our universe, they manifest as naked
repulsive force fields in our universe. The size of this force field is directly
proportional to the mass of the matter contained within the repellons.
5. Since repellons are gravitationally repulsive, the mass of the repellon is
gravitationally negative with respect to our universe. However, it must be
CLOSED 2-BRANES AS DM/DE CANDIDATES 10
emphasized that the inertial mass of repellons is positiveiv
like normal matter.
6. Although repellons are repelled by normal matter, the gravitational force between
two repellons is attractive.
The force of gravitation F, between two bodies of masses m1 & m2
separated by a distance d, per Newton’s equation is
𝐹 =
𝑚1 𝑚2
𝑑2
When both bodies have a positive (normal case) mass, the gravitational
Force F is positive, representing attractive gravity.
When one of the bodies have a negative mass, (discussed earlier), we see
the force F, between them becoming negative. That is, the force of gravity
becomes repulsive as explained earlier.
When both masses are negative, the force of gravity becomes positive and
therefore attractive.
7. Theoretically, repellons can exist in a vast range of sizesv
. However, the larger
they are, the exponentially rarer they become.
8. Since repellons are mutually attractive but are repelled by normal matter, they can
accumulate and form large clusters in regions of the universe beyond the
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gravitational fields of normal matter or in regions where competing fields cancel
each other out (like Lagrange points).
9. Microscopic repellons do not interact with normal matter in our universe in any
way except by being gravitationally repelled.
10. Since these repellons are extremely small and since gravity is the weakest force,
their associated repulsive force fields easily pass through normal matter without
the slightest hindrance. However, in the rare instance of the formation of a larger
repellon, say the size of a golf ball, such repellons (their repulsive force fields)
can be trapped in suitable containers.
11. We know that large bodies like stars and galaxies, due to their attractive gravity,
will bend light towards them. That is, the phenomenon called gravitational lensing
by which such bodies act as gigantic convex lenses in space. Singular repellons
that are massive enough will also exhibit such behavior, though with a slight
difference. They will act as large concave lenses, bending light away from them.
However, gigantic clusters composed entirely of microscopic repellons may not
exhibit such detectable lensing.
12. Theoretically, nesting of repellons is possible. That is, a repellon may have
another repellon within it, which may contain still another and so on.
However, if there are multiple nesting levels of repellons, the equivalent mass of
all the nested repellons is the negative of the numerical sum of the magnitudes of
the masses of all the nested repellons. That is, in the figure below, D (green) is a
repellon within another repellon, C (red). And C resides within yet another
repellon, B (blue), which is in our universe. The figures within the arrow
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represent the mass of the repellons experienced by its immediate superuniverse
(higher level repellon or our universe).
D has 10 units of positive mass. To C, the mass of D is -10 units (note the
negative sign). C has another 20 units of positive mass within it. But to B, the
mass of C is -30 units. Finally, to our universe, the mass of all its nested
subuniverses is -60 units.
Multiple nested universes, though possible, are only of academic interest.
4. Creation of repellons
Repellons can be created in two ways:
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1. It is proposed that microscopic repellons are continuously created by quantum
fluctuations just like elementary particle pairs are created. The bulk of the
repellons are created this way. However, unlike the particle pairs, the repellons
have a much longer life, since they don’t have an anti-particle that can annihilate
it. Strictly speaking, repellons are not particles, but repulsive force fields.
2. It is also put forward that repellons may have been created along with matter
during the Big Bang as well. However, these repellons went through a similar
inflationary phase and drove the expansion during the birth of the universe,
preventing the universe’s collapse under its gravity. Such primordial repellons are
of galactic (and even larger) scales and today may inhabit the heart of the voids
and supervoids in our universe. However, it must be emphasized that the sum of
all mass contained in the microscopic repellons by far outweigh the sum of all
mass contained in the large scale repellons.
5. Repellons as dark matter
1. As explained earlier, microscopic repellons are continuously created by quantum
fluctuations just like elementary particle pairs are created. However, unlike the
particle pairs, the repellons have a much longer life, since they don’t have an anti-
particle that can annihilate it.
2. Since these repellons are extremely small and since gravity is the weakest force,
their associated repulsive force fields easily pass through normal matter without
the slightest hindrance.
3. Microscopic repellons do not interact with normal matter in our universe in any
way except by being gravitationally repelled.
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4. As soon as they are created, if they are near a massive body like a planet or a star,
they get repelled outwards. With the stellar, planetary and galactic dynamics a
good portion find their way to the outer peripheries of galaxies where they are met
by the repellons that are already there. These growing deposits of repellons create
a soft gravity hill (like the circular hills around a crater) at the outer peripheries
(galactic halos) of the galaxies.
5. This soft shell of repellons at the periphery is what keeps the galaxy together and
the outer stars from flying off. The gravity hill created at the periphery acts
somewhat like the greater banking angles on highways, necessary at the outer end
of turns to allow for greater vehicular speeds.
6. Thus, the observed phenomena of higher galaxy rotation curves attributed to dark
matter can be explained by repellons, since repulsive fields caused by enormous
deposits of repellons cause the peripheral stars to speed up.
7. Other observed phenomena/discrepancies such as velocity dispersions, galaxy
clusters, gravitational lensing, CMB & structure formation that are attributed to
the presence of dark matter may also be explained by repellons since repellons
provide the gravitational correction and the fact that repellons are unaffected by
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radiation. This needs to be further explored.
8. Within galaxies, these repellons will get deposited in gravitationally neutral
spaces such as stable Lagrange points.
9. There is likely to be a gradation of repellons in the halos of galaxies. A shell of
smaller repellons in the inner halo and as we move further away from the galaxy,
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the repellons are likely to be larger. The size of the repellons gradually increases
as we go outwards until a certain point after which the repellon size gradually
decreases to microscopic levels in the vast intergalactic space.
6. Repellons as dark energy
The vast intergalactic spaces are also perfect spawning grounds for the continuously
generated microscopic repellons. Quantum fluctuations in these cosmic regions cause the
steady creation of repellons. At large scales, the continuously growing mass of repellons
has the effect of pushing away galaxies and accelerating the expansion of the universe. A
soft and continuously growing repulsive force field due to these repellons, continue to
drive the expansion.
7. Supporting evidence for a theory of gravitationally repulsive dark matter
1. Dark matter in galactic halos:
The abundance of dark matter in galactic halos has been strongly suspected by
scientists. A gravitationally repulsive dark matter (repellons) hypothesis would
CLOSED 2-BRANES AS DM/DE CANDIDATES 17
perfectly fit the abundance of dark matter in galactic halos compared to the
interior of galaxies. As explained earlier, the stellar dynamics and galactic
churning would cause the repellons continuously generated in the interiors of
galaxies to be repelled by normal matter and eventually get deposited in the
galactic halos.
2. Outward movement of dark matter from the center of galaxies:
Recently it was reported that scientists had found evidence that dark matter “can
be heated up and pushed out”vi
from the centers of star-forming galaxies. It
appears that the “dark matter heating” is an assumption that the scientists have
made based on the observed outward movement. The observed outward
movement of dark matter is a natural consequence of gravitationally repulsive
dark matter (repellons) following star forming. Star-forming, which is a form of
matter compactification, would cause the repellons in the vicinity to be repelled
and pushed out.
3. Voids & Supervoids:
The observations of enormous voids in space support the existence of repellons.
These voids cannot be explained by any of the current conventional theories in
Astrophysics. They are extremely large regions of seemingly empty space. They
are the largest structures in the universe. Some are more than 300 million light-
years across. Examples of these voids are the Local Void, Bootes Void, Northern
& Southern Local Supervoid, Capricornus void and something called the Eridanus
supervoid, which, if exists, is suspected to be more than 500 million light-years
across. Voids can be explained as the large-scale clumping of gigantic primordial
CLOSED 2-BRANES AS DM/DE CANDIDATES 18
repellons. Vast accumulations repellons could also explain the puzzling region of
empty space in the nebula NGC 1999.
4. Hot gases in the peripheries of Galaxies and Galactic Clusters:
The presence of vast quantities of hot gases that envelope galaxies and galactic
clusters can be explained when considering thick shells of repellons bounding
these massive structures. The hot gases are observed as halos around galaxies.
They could be remnants of stars that strayed into the shell due to their high
velocity and momentum. As a star penetrates the shell of repellons due to its high
momentum, the repulsive gravity between the star and the bulk of surrounding
repellons gradually neutralizes the attractive gravity that holds the star together.
Due to this, it begins to lose its mass in the form of its hot gases escaping its
declining gravitational pull.
The constant repulsive force between the repellons and the rapidly shrinking star
push the star back within the bounds of the galaxy. Sometimes the star does not
survive its passage through the shell of repellons and gets completely dissolved
into a big blob of gas. The hot gas that is released also gets eventually pushed
back into the galactic space, where it spreads and forms part of the galactic halo.
5. The absence of (or failure to detect) dark matter on Earth:
There have been numerous theories proposing dark matter to be some kind of
exotic particles. Scientists have called them WIMPS, MACHOS, Axions and so
on and built extremely sensitive detectors in the hope of detecting a particle that is
supposed to be more than five times as abundant as normal matter. They have
failed till now. If dark matter were gravitationally repulsive repellons, it is futile
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to look for them on Earth using such detectors since, (a) repellons do not manifest
in our universe as a physical particle but rather as a repulsive force field, hence
any detector, however sensitive will not be able to find them, (b) microscopic
repellons generated by quantum fluctuations are repelled by the Earth’s
gravitational field as soon as they are created.
6. Kordylewski dust clouds at L4 & L5 Lagrange points of the Earth-Moon system:
I refer to the recent discovery of Kordylewski dust clouds in the stable L4 and L5
Lagrange points of the Earth-Moon system.
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Each of these dust clouds is more than nine times the size of the earth. It should
be noted that no gas has been detected to provide any hydrostatic equilibrium; it
appears to be just dust suspended in empty space. The very fact that such large
amounts of dust haven’t coalesced and compactified (and become large rocks)
under their gravity despite being around for millions of years, points to some
repulsive force that’s keeping them apart. I suspect that this is the work of the
accumulated repellons and that the dust is embedded on their repulsive force
fields.
7. ANITA & IceCube detections of strange upgoing particles in Antarctica:
Recently, strange upgoing particlesvii
were detected shooting out of the Antarctic
ice. This may have nothing to do with repellons. However, if the repellons’
repulsive force fields do have some kind of interactions with particles of normal
matter, it may account for the generation of these strange particles as the repellons
stream upwards due to the Earth repelling them.
8. Gravitational anomalies in the Hudson Bay (Canada) and the Indian Ocean:
As mentioned before, repellons can come in different sizes dependent on the mass
of the matter trapped within the closed 2-brane. Our universe could be littered
with primordial repellons that are of widely varying sizes. Some of these
repellons could even be trapped within the crust of the Earth, their force fields too
large to pass through the intermolecular space of the crust. If so, they would cause
a measurable dip in gravity on the surface of those locations where they abound.
Two such possible locations are the Hudson Bay region of Canada and the Indian
Ocean Geoid Low. Although there are alternate theories explaining such
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gravitational anomalies, they have not yet been proven. Repellons are merely
another possible explanation.
8. Experiments proposed to confirm/falsify the repellon theory of DM/DE
1. As explained earlier massive repellons, if they exist, should cause the concave
bending of light from sources in the background.
That is, a suitably massive repellon in the foreground should bend the light from a
star in the background, away from it. They will act as large concave lenses,
CLOSED 2-BRANES AS DM/DE CANDIDATES 22
bending light away from them. However, clusters of microscopic repellons—even
if the cluster occupies stellar volumes—may not cause much noticeable difference
if the central, singular repellon is not massive enough. Perhaps a void/supervoid
(if they contain star-size repellons) could be examined telescopically to see if they
cause concave bending of light from any background stars. This is a test that can
be done quite easily. While a positive result would confirm the existence of
repellons, a negative result does not falsify it since the void under study could be
composed of smaller sized repellons.
2. The above telescopic examination can also be performed on the various stable
Lagrange points on our solar system. Stable Lagrange points of the Earth-Moon
system, Earth-Sun system, Jupiter-Sun system, etc., can all be examined to see if
any exhibit concave lensing of background starlight.
3. I would also propose a costlier but more definitive test to conclusively
confirm/falsify the existence of repellons. I propose a special probe to be sent to
either L4 or L5 Lagrange points of the Earth-Moon system with a mechanism to
entrap an area of empty space in the heart of L4/L5. When the probe returns to
earth, if there is a measurable loss of weight then repellons must exist. If it is
found that there is no evidence of any negative mass stuff, then my hypothesis is
wrong. On the contrary, if the presence of repellons is confirmed, there will be
enormous benefits to humanity. Mining this vast and almost endless supply of
gravitationally repulsive repellons can have such tremendous impact on
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architecture, transportation, aviation, etc.
4. I propose some gravitational surveys to be performed in the Hudson Bay area of
Canada with the express intent to identify a specific location that can be mined to
see whether repellons are present. The other location that needs to be studied for
potential deposits of trapped repellons under the sea bed is the Indian Ocean
Geoid Low (IOGL), south of Sri Lanka. IOGL is a vast area that exhibits
unexplained low gravity.
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9. A brief history of my idea
I had first published the same idea with some small differences in 2012. I then called it
‘The Perforated Universe Hypothesis.’ Instead of using the term repellons, I had then called these
closed 2-branes as ‘spatial perforations.’
My original hypothesis was a bit too ambitious. It tried to explain not just dark matter &
dark energy but also went much further. Perhaps that may not have been a good idea.
• I had posted an article on Medium explaining my integrated DM/DE hypothesis on
November 25th, 2014. You may find it here: https://medium.com/@harikumar_23993/a-
different-look-at-dark-matter-and-dark-energy-32018a92d7d1
• You can find the original paper on Scribd (also posted in July 2012) at
https://www.scribd.com/document/100044584/The-Perforated-Universe-Revision-Evidence
• I had also sent emails to some scientists working in the field explaining my hypothesis. You
may find the text of my email in my blog post, posted on June 18, 2014, here. It also contains
some more supporting evidence: https://www.urbanyogi.guru/2014/06/on-dark-matter.html
• A PowerPoint presentation on my DM/DE idea dated March 19, 2012. Since it contains a lot
of other (related) ideas as well, perhaps it would be better if you start from slide 31 onwards:
https://www.scribd.com/document/85901916/The-Perforated-Universe
• My blog post (dated July 13, 2012) containing both the video and the Scribd paper can be
found at:
https://www.urbanyogi.guru/2012/07/this-new-evolutionary-model-of-universe.html
CLOSED 2-BRANES AS DM/DE CANDIDATES 25
Then, last year (2018) on December 5th, a paper was published on arXiv by an Oxford
scientist named Jamie Farnes, which had attracted much attention. Reading the paper & articles
on it, I was startled to note the striking similarities between his paper and mine that I published
in July 2012. I had posted my DM/DE hypothesis on Scribd, blogged about it on my BlogSpot
page a couple of times, created two YouTube videos, published PowerPoint presentations, wrote
an article on Medium on it, had online discussions with other scientists, emailed several
scientists working on DM/DE. My papers on Scribd have been viewed over 50,000 times and my
YouTube videos, generated about 11,000 hits. They’re all still available for scrutiny. Links are
given at the end of this post.
As soon as I read the phys.org report (https://phys.org/news/2018-12-universe-theory-
percent-cosmos.html) on Dr. Farnes’ paper, I wrote a blog post (noting the striking similarities)
that you can find at https://www.urbanyogi.guru/2018/12/startling-similarities-between-my.html.
Besides emailing to Dr. Farnes, I had also tweeted to him, phys.org and a few others.
The similarities are as below:
My
hypothesis
Dr. Farnes’
theory
Proposes an integrated model of both dark energy and dark matter Yes Yes
Proposes Gravitational Repulsion as the driving force that causes the observed effects Yes Yes
Proposes the continuous generation of this gravitationally repulsive substance Yes Yes
Proposes the presence of dark matter in halos, which hold together the galaxies Yes Yes
As can be seen from above, the similarities cover the gist of Farnes’ theory. However,
there are some differences as well. They are:
1. The mechanism behind the negative mass (and consequently, repulsive gravity) of
Farnes’ ‘dark fluid’ and my repellons are fundamentally different. He provides
CLOSED 2-BRANES AS DM/DE CANDIDATES 26
negative mass to his ‘dark fluid,’ by “modifying Einstein’s theory of general
relativity.” My repellons do not require any modification of Einstein’s equations.
2. His ‘dark fluid,’ has both negative gravitational mass as well as negative inertial
mass. However, repellons have negative gravitational mass, but its inertial mass
remains positive. I think negative inertial mass is an impossibility.
On December 9th
, 2018, I had also published a more detailed paper in Medium titled,
“Similarities and differences between Jamie Farnes’ paper on a unified theory of dark matter and
dark energy published on December 5th, 2018 and my paper on the same topic published six
years earlier. Also, a proposal of a test to falsify/confirm my hypothesis.” It can be found here:
https://medium.com/@harikumar_23993/similarities-and-differences-between-jamie-farnes-
paper-on-a-unified-theory-of-dark-matter-and-35a67b31a802
In that paper, I had also proposed some experiments (repeated here along with a few new
ones) to falsify/confirm my repellon hypothesis.
10. A short bio of the author
From this paper, the reader would have guessed that I am not a scientist. That is true. I
have a degree in Electrical Engineering. I work for a government organization in Toronto,
Canada and currently on the verge of retirement. I have a passion for science, especially
Astrophysics, Quantum Mechanics, etc. and follow all the latest developments in those fields.
I am also a writer. In 2015, I self-published a science fiction novel, “The Intersection
Man,” in which one of my characters, a scientist, puts forward this exact hypothesis. I explain
this in detail in the novel. In the book, this paves the way to the artificial creation of something I
labeled, Gravitationally Repulsive Medium (GRM). The GRM thus created, causes a revolution
CLOSED 2-BRANES AS DM/DE CANDIDATES 27
in almost all facets of human life, from architecture to aviation and even medicine. Think of
floating habitats, tethered cities rising to the thermosphere.
The success of “The Intersection Man,” motivated me to write the sequel, which was
published as a single novel (including the first part and two more major sections) in September
2017. However, this time, I changed the title to “Intersection Man” (without the definite article
“the”). In the book, I go much further and even propose where exactly on Earth, this GRM can
be found. I provide my reasons as well. More details of my novel, including reviews, Facebook
page, links to Amazon (ebook & paperback) can be found at https://www.milkywaybooks.com/
11. One last request
My sincere gratitude to you for having read this far. If you think this idea would not work
and there are problems with it, I really would like to hear from you with your detailed criticisms.
But please be gentle and respectful.
I know there are no complicated equations or charts in this paper (that was one of the
reasons a scientist cited for not reading my paper when I emailed to him in 2014). But I think I
have elaborated my idea as clearly as possible.
I am also of the strong conviction that while mathematics is indeed the language of the
universe, math is not its soul. The very fact that mathematics can be used to build models of
reality that conflict with each other and also many different mathematical models can be built to
explain a single observed phenomenon hints at its limitations. I decry the tendency of modern
scientists to completely rely on complex mathematical models to explain the observed
phenomenon. I think the universe at its most elemental levels is fundamentally simple. Keeping
that in mind, I have tried to explain my hypothesis using the simplest of logic. After all, logic is
CLOSED 2-BRANES AS DM/DE CANDIDATES 28
the foundation of mathematics, hence perhaps there is a hidden mathematical dimension of my
hypothesis that an astute and trained physicist/mathematician can uncover.
Once again, thank you for reading,
Hari Kumar Nair
End Notes:
i
The science in this paper may not conform to current understandings of physics, especially
String Theory, Quantum Fluctuations etc. Hence, my definition of a closed 2-brane may deviate from that
in String Theory. I define a 2-brane as a plane that has only two spatial dimensions. It is analogous to a
simple geometric plane that has only two spatial dimensions, i.e. length and breadth, but zero thickness. A
closed 2-brane is analogous to a bubble-like spherical shell, with a shell thickness of zero.
ii
A universe can be defined as a set of all points, such that there exists an unbroken path that
connects each point with every other point and which does not pass through a region of a different spatial
dimension. Two points can be said to lie in the same universe if there exists an unbroken path, however
long (not necessarily straight) that connects them, and which does not pass through a region that has a
different spatial dimension.
Thus, points at the two ends of the universe separated by billions of light-years (with no hope of light ever
reaching from one point to the other considering the expanding universe) can still be part of the same
universe. Yet, a space that is right at the tip of our nose, but fully enclosed in a closed 2-dimensional
membrane (bubble-like, closed 2-brane), will not be a part of our universe. Universes within our own can
come in a wide range of sizes right from a universe smaller than an atom to universes of galactic
proportions.
CLOSED 2-BRANES AS DM/DE CANDIDATES 29
iii
The underlying physics of how a repellon acquires its repulsive gravity is explained in the
following illustrations:
CLOSED 2-BRANES AS DM/DE CANDIDATES 30
CLOSED 2-BRANES AS DM/DE CANDIDATES 31
iv
I don’t think it is ever possible for anything to have negative inertial mass. I assume, this whole
confusion arose from the erroneous interpretation of the famous equation F=ma. The equation F = m × a
is certainly true, but with a small change. It should rightfully be F = |m|× a. That is, only the magnitude of
mass is applicable here.
I am aware of a recent discovery (https://news.wsu.edu/2017/04/10/negative-mass-created-at-
wsu/) at Washington State University that sensationally reported the creation of ‘negative mass’
Rubidium atoms that appear to exhibit negative inertial mass properties. But if you read their report
carefully, it says, “Now when the rubidium rushes out fast enough, it behaves as if it has negative mass.”
“Behaves as if.” Thus, this is not true negative mass, but merely an illusion of it created by manipulating
the spin of the rubidium atoms. It is somewhat like throwing a fast spinning top on the floor and seeing it
moving towards you rather than away.
v
Here, size refers only to size of the manifested repulsive force field. Whenever we talk about the
size of a repellon, it always refers to the manifested repulsive force field.
vi
https://scitechdaily.com/scientists-find-evidence-that-dark-matter-can-be-heated-up-and-moved/
vii
https://www.sciencemag.org/news/2018/09/oddball-particles-tunneling-through-earth-could-
point-new-physics
❖

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Clusters of microscopic closed 2-brane entities as a possible candidate for dark matter & dark energy

  • 1. Running head: CLOSED 2-BRANES AS DM/DE CANDIDATES 1 Clusters of microscopic closed 2-brane entities as a possible candidate for dark matter & dark energy Hari Kumar Nair Toronto, CANADA Email: harismind@gmail.com
  • 2. CLOSED 2-BRANES AS DM/DE CANDIDATES 2 Abstract The existence of closed 2-branei , bubble-like entities are within the realm of possibility of String Theory. It is proposed that quantum fluctuations are continuously creating such microscopic bubble-like entities, which I call repellons. Repellons are called thus since they would be gravitationally repulsive (have negative gravitational mass) with respect to normal matter in our universe. Repellons will be physically imperceptible and will manifest only as a gravitationally repulsive force field. Although repellons are repelled by normal matter, they are mutually gravitationally attractive. Since they are repelled by normal matter, there is a continuous transit of outward going repellons from large bodies such as planets and stars. These repellons eventually accumulate in regions of space that are free of any attractive gravity or where the gravitational effects of nearby bodies cancel each other (such as Lagrange points). With the stellar, planetary and intra-galactic dynamics a good portion of the repellons generated within galaxies find their way to its outer peripheries and get deposited in the galactic halos. These repellon deposits in the galactic halos cause a soft gravity ‘hill’ wrapping around the galaxy. The gravity hills keep the peripheral stars in the galaxy within it and account for the observed higher velocity of these stars, which is attributed to dark matter. The continuous generation of repellons in the intergalactic spaces causes the galaxies to move further apart accounting for the observed accelerated expansion of the universe, a phenomenon attributed to dark energy. This paper, besides presenting much supporting evidence also proposes a variety of doable tests that can confirm/falsify the repellon theory. Keywords: Dark Matter, Dark Energy, Quantum Fluctuations, String Theory, Repulsive Gravity, Antigravity, Negative Mass.
  • 3. CLOSED 2-BRANES AS DM/DE CANDIDATES 3 Introduction Clusters of microscopic closed 2-brane entities as a possible candidate for dark matter & dark energy We know that there is some repulsive energy that is causing the galaxies to be pushed apart from each other. The effect has been observed and verified, although its cause remains undetected. We have currently no explanation for this energy, which—for want of a better term— has been named dark energy. The observations of this effect also indicate that dark energy contributes around 69% of the total energy in the observable universe. It has been observed that the stars at the peripheral regions of galaxies have been moving much faster than the rate suggested by the galaxy’s mass. Scientists conclude that this can only be due to the galaxy containing much more matter than what was apparent. This unseen matter was given the name dark matter. It was calculated that as much as 85% of the total mass of a galaxy came from this dark matter. dark matter was also thought to have a role behind other observed phenomena such as gravitational lensing, CMB, etc. Dark energy and dark matter together constitute almost 95% of the mass of the universe; far more than all visible matter. In other words, the universe must be awash with this stuff, yet it has not been directly observed. We know nothing more than what has been mentioned above. Despite the best efforts of scientists, neither dark matter nor dark energy has been directly observed. Expensive and highly sensitive detectors (like the LUX detector) have failed to find any evidence of dark matter on Earth.
  • 4. CLOSED 2-BRANES AS DM/DE CANDIDATES 4 There are numerous hypotheses and suggestions to explain the effects of both dark matter and dark energy, but none have been verified to be true. What is proposed here is also one such hypothesis. In this paper, I propose that clusters of microscopic closed 2-branes could be responsible for the observed phenomena attributed to dark matter and dark energy. Some doable experiments are also proposed to either confirm or falsify the hypothesis. Closed 2-brane, also known as a repellon At the core of this hypothesis is my proposition that clusters of microscopic closed 2- branes are being continuously generated by quantum fluctuations. I propose that these closed 2- branes are responsible for the phenomena that have been attributed to dark matter and dark energy. Since I prefer to call these closed 2-branes by the less wordy term, repellons, this term will be used henceforth in this paper to refer to closed 2-branes. In this paper, I have also used the term ‘bubble-like closed 2-dimensional universe,’ to refer to closed 2-brane or repellon.
  • 5. CLOSED 2-BRANES AS DM/DE CANDIDATES 5 Contents Abstract............................................................................................................................... 2 Introduction......................................................................................................................... 3 1. What are repellons (closed 2-branes)?................................................................ 6 2. A logical argument for repellons......................................................................... 6 3. Properties of repellons ........................................................................................ 8 4. Creation of repellons......................................................................................... 12 5. Repellons as dark matter................................................................................... 13 6. Repellons as dark energy .................................................................................. 16 7. Supporting evidence for a theory of gravitationally repulsive dark matter ...... 16 8. Experiments proposed to confirm/falsify the repellon theory of DM/DE ........ 21 9. A brief history of my idea................................................................................. 24 10. A short bio of the author ................................................................................... 26 11. One last request................................................................................................. 27 End Notes:................................................................................................................. 28
  • 6. CLOSED 2-BRANES AS DM/DE CANDIDATES 6 1. What are repellons (closed 2-branes)? A 2-brane, per my understanding, is a plane that has only two spatial dimensions. It is analogous to a simple geometric plane that has only two spatial dimensions, i.e., length and breadth, but zero thickness. A closed 2-brane is analogous to a bubble-like spherical shell, with a shell thickness of zero. We shall call this closed 2-brane, a repellon. The bounded ‘inside’ (3-dimensional space) of the repellon, is forever separated from the outside 3-dimensional space by its bubble-like 2-dimensional ‘skin.’ Since our universe is fundamentally defined by its spatial 3-dimensionalityii , the repellon (together with the 3- dimensional space it contains) does not form part of our universe even if the repellon is technically within our universe. 2. A logical argument for repellons. # Statement Explanation 1 “A universe is defined as a set of all points, such that there exists an unbroken path that connects each point with every other point and which does not pass through a region of a different spatial dimension. Two points can be said to lie in the same universe if there exists an unbroken path, however long (not necessarily straight) that connects them, and which does not pass through a region that has a different spatial dimension.” The most fundamental characteristic of our universe is that it has three spatial dimensions. The statement merely defines a universe based on this principle. 2 “A spatially 2-dimensional universe can physically exist.” Spatially 2-dimensional (planar) entities are extensively used in various branches of mathematics. Although these are abstract entities in mathematics, their physical existence cannot be ruled out. However, various accepted ideas in physics implicitly assume the physical existence of two-dimensional spaces. Examples are string theory and the holographic principle. 3 “A (bubble-like) closed 2-dimensional universe can physically exist.” This follows from #2. A closed 2-dimensional universe is a 2-dimensional universe that closes in on itself, like the surface of a sphere. Although the sphere is a 3-dimensional space, its surface is 2- dimensional. However, statement #3 refers to an absolute 2-dimensional space whose thickness is zero.
  • 7. CLOSED 2-BRANES AS DM/DE CANDIDATES 7 # Statement Explanation 4 “The bubble-like closed 2-dimensional space will have an ‘inside’ that is 3- dimensional as well an ‘outside’ that is 2-dimensional.” This is also straightforward. Even though the bubble is a closed 2-dimensional space, it will have a 3-dimensional ‘inside,’ which is of limited volume defined by the volume of the bubble and 3-dimensional ‘outside,’ whose volume is unlimited (provided, it is not encased in another larger bubble). 5 “The 3-dimensional ‘outside’ space, the bubble-like closed 2-dimensional space, and the 3-dimensional ‘inside’ space will be three distinct universes.” This follows from the definition of a universe in #1. Although the ‘inside,’ and ‘outside,’ of the bubble are spatially 3-dimensional, there cannot exist a path that connects a point in the ‘inside’ to a point in the ‘outside,’ that does not pass through the 2-dimensional bubble. Hence, the ‘inside,’ the bubble, and the ‘outside’ are three distinct universes. 6 “The bubble-like closed 2-dimensional universe will be positively curved (spatially) with respect to the ‘outside.’” This follows from the definition of ‘curvature’ as illustrated in the figure: 7 “Normal matter in our universe curves space negatively (gravity well). Negative curvature of space manifests as attractive gravity.” From General Relativity. GR talks about space-time rather than space. However, a curvature of space-time necessitates a curvature of space. 8 “Since the bubble-like closed 2- dimensional universe causes a positive curvature on the ‘outside’ 3- dimensional universe, its manifested gravity would be repulsive with respect to matter of the ‘outside’ universe.” Logically follows from #6 and #7. 9 “Since the bubble-like closed 2- dimensional universe is gravitationally repulsive with respect to normal matter of the ‘outside’ universe, the closed 2- dimensional universe has negative gravitational mass with respect to matter of the ‘outside’ universe.” Follows from #8. Also, we know that the force of gravitation F, between two bodies of masses m1 & m2 separated by a distance d, per Newton’s equation is 𝐹 = 𝑚1 𝑚2 𝑑2 When both bodies have positive (normal case) mass, the gravitational Force F is positive, representing attractive gravity. For F to be negative (representing repulsive gravity), m1 & m2 should be of opposite sign. Hence if one mass (say, m1) is positive, the other (m2) should be negative mass. When both masses are negative, the force of gravity becomes positive and therefore attractive. 10 “The photons and other elementary particles (making up all matter) created in a 3-dimensional universe are 3- dimensional in nature.” This follows from #1. Also, the wave nature of elementary particles suggest they are 3-dimensional entities.
  • 8. CLOSED 2-BRANES AS DM/DE CANDIDATES 8 # Statement Explanation 11 “It is not possible for any elementary particle to crossover from the ‘inside’ of the closed 2-dimensional universe to the ‘outside,’ and vice-versa.” This too follows from #1 and also #10. Since the ‘inside’ and ‘outside’ (both 3-d) are separated by a space of a different spatial dimension (2-d), there cannot be a transit of any elementary particle between the ‘inside’ and ‘outside.’ 12 “The closed 2-dimensional universe is completely imperceptible to the ‘outside,’ except through its gravitational influence.” Follows from #11. Since even photos cannot pass between the ‘inside,’ and ‘outside,’ the closed 2-dimensional universe will be imperceptible to the ‘outside.’ 13 “So, a closed 2-dimensional universe within a 3-dimensional space is: 1. imperceptible, 2. gravitationally repulsive, 3. has negative gravitational mass with respect to the ‘outside’ 3- dimensional universe. Hence the only way a closed 2- dimensional universe can manifest in the ‘outside’ 3-dimensional universe is as a gravitationally repulsive force- field.” The closed 2-dimensional universe (together with its ‘inside’ 3-d universe) is the closed 2-brane. Since this entity is gravitationally repulsive with respect to the ‘outside’ 3-d universe (the universe we live in), this entity is called a repellon. 3. Properties of repellons 1. Since repellons are not a part of our universe, they do not occupy any physical volume in our universe. Hence, they are invisible and almost imperceptible to anything of our universe, including our instruments however powerful or sensitive they may be. 2. We know that normal matter causes a negative curvature (or a gravity well) on our universe’s space-time. However, repellons would cause a positive curvatureiii (a gravity hill) on our universe’s (the ‘outside’) space-time. Due to this, repellons
  • 9. CLOSED 2-BRANES AS DM/DE CANDIDATES 9 would be gravitationally repulsive with respect to matter in our universe. Hence, the only way repellons can be ‘sensed’ is through their repulsive gravitational influence on normal matter. 3. Whatever positive mass that the repellon contains would be gravitationally negative (and of the same magnitude) with respect to our universe. It must be emphasized that I am not proposing any new form of matter in this paper and hence does not require any revision of the standard model. Matter trapped inside repellons is just normal matter. 4. Since repellons do not occupy any space in our universe, they manifest as naked repulsive force fields in our universe. The size of this force field is directly proportional to the mass of the matter contained within the repellons. 5. Since repellons are gravitationally repulsive, the mass of the repellon is gravitationally negative with respect to our universe. However, it must be
  • 10. CLOSED 2-BRANES AS DM/DE CANDIDATES 10 emphasized that the inertial mass of repellons is positiveiv like normal matter. 6. Although repellons are repelled by normal matter, the gravitational force between two repellons is attractive. The force of gravitation F, between two bodies of masses m1 & m2 separated by a distance d, per Newton’s equation is 𝐹 = 𝑚1 𝑚2 𝑑2 When both bodies have a positive (normal case) mass, the gravitational Force F is positive, representing attractive gravity. When one of the bodies have a negative mass, (discussed earlier), we see the force F, between them becoming negative. That is, the force of gravity becomes repulsive as explained earlier. When both masses are negative, the force of gravity becomes positive and therefore attractive. 7. Theoretically, repellons can exist in a vast range of sizesv . However, the larger they are, the exponentially rarer they become. 8. Since repellons are mutually attractive but are repelled by normal matter, they can accumulate and form large clusters in regions of the universe beyond the
  • 11. CLOSED 2-BRANES AS DM/DE CANDIDATES 11 gravitational fields of normal matter or in regions where competing fields cancel each other out (like Lagrange points). 9. Microscopic repellons do not interact with normal matter in our universe in any way except by being gravitationally repelled. 10. Since these repellons are extremely small and since gravity is the weakest force, their associated repulsive force fields easily pass through normal matter without the slightest hindrance. However, in the rare instance of the formation of a larger repellon, say the size of a golf ball, such repellons (their repulsive force fields) can be trapped in suitable containers. 11. We know that large bodies like stars and galaxies, due to their attractive gravity, will bend light towards them. That is, the phenomenon called gravitational lensing by which such bodies act as gigantic convex lenses in space. Singular repellons that are massive enough will also exhibit such behavior, though with a slight difference. They will act as large concave lenses, bending light away from them. However, gigantic clusters composed entirely of microscopic repellons may not exhibit such detectable lensing. 12. Theoretically, nesting of repellons is possible. That is, a repellon may have another repellon within it, which may contain still another and so on. However, if there are multiple nesting levels of repellons, the equivalent mass of all the nested repellons is the negative of the numerical sum of the magnitudes of the masses of all the nested repellons. That is, in the figure below, D (green) is a repellon within another repellon, C (red). And C resides within yet another repellon, B (blue), which is in our universe. The figures within the arrow
  • 12. CLOSED 2-BRANES AS DM/DE CANDIDATES 12 represent the mass of the repellons experienced by its immediate superuniverse (higher level repellon or our universe). D has 10 units of positive mass. To C, the mass of D is -10 units (note the negative sign). C has another 20 units of positive mass within it. But to B, the mass of C is -30 units. Finally, to our universe, the mass of all its nested subuniverses is -60 units. Multiple nested universes, though possible, are only of academic interest. 4. Creation of repellons Repellons can be created in two ways:
  • 13. CLOSED 2-BRANES AS DM/DE CANDIDATES 13 1. It is proposed that microscopic repellons are continuously created by quantum fluctuations just like elementary particle pairs are created. The bulk of the repellons are created this way. However, unlike the particle pairs, the repellons have a much longer life, since they don’t have an anti-particle that can annihilate it. Strictly speaking, repellons are not particles, but repulsive force fields. 2. It is also put forward that repellons may have been created along with matter during the Big Bang as well. However, these repellons went through a similar inflationary phase and drove the expansion during the birth of the universe, preventing the universe’s collapse under its gravity. Such primordial repellons are of galactic (and even larger) scales and today may inhabit the heart of the voids and supervoids in our universe. However, it must be emphasized that the sum of all mass contained in the microscopic repellons by far outweigh the sum of all mass contained in the large scale repellons. 5. Repellons as dark matter 1. As explained earlier, microscopic repellons are continuously created by quantum fluctuations just like elementary particle pairs are created. However, unlike the particle pairs, the repellons have a much longer life, since they don’t have an anti- particle that can annihilate it. 2. Since these repellons are extremely small and since gravity is the weakest force, their associated repulsive force fields easily pass through normal matter without the slightest hindrance. 3. Microscopic repellons do not interact with normal matter in our universe in any way except by being gravitationally repelled.
  • 14. CLOSED 2-BRANES AS DM/DE CANDIDATES 14 4. As soon as they are created, if they are near a massive body like a planet or a star, they get repelled outwards. With the stellar, planetary and galactic dynamics a good portion find their way to the outer peripheries of galaxies where they are met by the repellons that are already there. These growing deposits of repellons create a soft gravity hill (like the circular hills around a crater) at the outer peripheries (galactic halos) of the galaxies. 5. This soft shell of repellons at the periphery is what keeps the galaxy together and the outer stars from flying off. The gravity hill created at the periphery acts somewhat like the greater banking angles on highways, necessary at the outer end of turns to allow for greater vehicular speeds. 6. Thus, the observed phenomena of higher galaxy rotation curves attributed to dark matter can be explained by repellons, since repulsive fields caused by enormous deposits of repellons cause the peripheral stars to speed up. 7. Other observed phenomena/discrepancies such as velocity dispersions, galaxy clusters, gravitational lensing, CMB & structure formation that are attributed to the presence of dark matter may also be explained by repellons since repellons provide the gravitational correction and the fact that repellons are unaffected by
  • 15. CLOSED 2-BRANES AS DM/DE CANDIDATES 15 radiation. This needs to be further explored. 8. Within galaxies, these repellons will get deposited in gravitationally neutral spaces such as stable Lagrange points. 9. There is likely to be a gradation of repellons in the halos of galaxies. A shell of smaller repellons in the inner halo and as we move further away from the galaxy,
  • 16. CLOSED 2-BRANES AS DM/DE CANDIDATES 16 the repellons are likely to be larger. The size of the repellons gradually increases as we go outwards until a certain point after which the repellon size gradually decreases to microscopic levels in the vast intergalactic space. 6. Repellons as dark energy The vast intergalactic spaces are also perfect spawning grounds for the continuously generated microscopic repellons. Quantum fluctuations in these cosmic regions cause the steady creation of repellons. At large scales, the continuously growing mass of repellons has the effect of pushing away galaxies and accelerating the expansion of the universe. A soft and continuously growing repulsive force field due to these repellons, continue to drive the expansion. 7. Supporting evidence for a theory of gravitationally repulsive dark matter 1. Dark matter in galactic halos: The abundance of dark matter in galactic halos has been strongly suspected by scientists. A gravitationally repulsive dark matter (repellons) hypothesis would
  • 17. CLOSED 2-BRANES AS DM/DE CANDIDATES 17 perfectly fit the abundance of dark matter in galactic halos compared to the interior of galaxies. As explained earlier, the stellar dynamics and galactic churning would cause the repellons continuously generated in the interiors of galaxies to be repelled by normal matter and eventually get deposited in the galactic halos. 2. Outward movement of dark matter from the center of galaxies: Recently it was reported that scientists had found evidence that dark matter “can be heated up and pushed out”vi from the centers of star-forming galaxies. It appears that the “dark matter heating” is an assumption that the scientists have made based on the observed outward movement. The observed outward movement of dark matter is a natural consequence of gravitationally repulsive dark matter (repellons) following star forming. Star-forming, which is a form of matter compactification, would cause the repellons in the vicinity to be repelled and pushed out. 3. Voids & Supervoids: The observations of enormous voids in space support the existence of repellons. These voids cannot be explained by any of the current conventional theories in Astrophysics. They are extremely large regions of seemingly empty space. They are the largest structures in the universe. Some are more than 300 million light- years across. Examples of these voids are the Local Void, Bootes Void, Northern & Southern Local Supervoid, Capricornus void and something called the Eridanus supervoid, which, if exists, is suspected to be more than 500 million light-years across. Voids can be explained as the large-scale clumping of gigantic primordial
  • 18. CLOSED 2-BRANES AS DM/DE CANDIDATES 18 repellons. Vast accumulations repellons could also explain the puzzling region of empty space in the nebula NGC 1999. 4. Hot gases in the peripheries of Galaxies and Galactic Clusters: The presence of vast quantities of hot gases that envelope galaxies and galactic clusters can be explained when considering thick shells of repellons bounding these massive structures. The hot gases are observed as halos around galaxies. They could be remnants of stars that strayed into the shell due to their high velocity and momentum. As a star penetrates the shell of repellons due to its high momentum, the repulsive gravity between the star and the bulk of surrounding repellons gradually neutralizes the attractive gravity that holds the star together. Due to this, it begins to lose its mass in the form of its hot gases escaping its declining gravitational pull. The constant repulsive force between the repellons and the rapidly shrinking star push the star back within the bounds of the galaxy. Sometimes the star does not survive its passage through the shell of repellons and gets completely dissolved into a big blob of gas. The hot gas that is released also gets eventually pushed back into the galactic space, where it spreads and forms part of the galactic halo. 5. The absence of (or failure to detect) dark matter on Earth: There have been numerous theories proposing dark matter to be some kind of exotic particles. Scientists have called them WIMPS, MACHOS, Axions and so on and built extremely sensitive detectors in the hope of detecting a particle that is supposed to be more than five times as abundant as normal matter. They have failed till now. If dark matter were gravitationally repulsive repellons, it is futile
  • 19. CLOSED 2-BRANES AS DM/DE CANDIDATES 19 to look for them on Earth using such detectors since, (a) repellons do not manifest in our universe as a physical particle but rather as a repulsive force field, hence any detector, however sensitive will not be able to find them, (b) microscopic repellons generated by quantum fluctuations are repelled by the Earth’s gravitational field as soon as they are created. 6. Kordylewski dust clouds at L4 & L5 Lagrange points of the Earth-Moon system: I refer to the recent discovery of Kordylewski dust clouds in the stable L4 and L5 Lagrange points of the Earth-Moon system.
  • 20. CLOSED 2-BRANES AS DM/DE CANDIDATES 20 Each of these dust clouds is more than nine times the size of the earth. It should be noted that no gas has been detected to provide any hydrostatic equilibrium; it appears to be just dust suspended in empty space. The very fact that such large amounts of dust haven’t coalesced and compactified (and become large rocks) under their gravity despite being around for millions of years, points to some repulsive force that’s keeping them apart. I suspect that this is the work of the accumulated repellons and that the dust is embedded on their repulsive force fields. 7. ANITA & IceCube detections of strange upgoing particles in Antarctica: Recently, strange upgoing particlesvii were detected shooting out of the Antarctic ice. This may have nothing to do with repellons. However, if the repellons’ repulsive force fields do have some kind of interactions with particles of normal matter, it may account for the generation of these strange particles as the repellons stream upwards due to the Earth repelling them. 8. Gravitational anomalies in the Hudson Bay (Canada) and the Indian Ocean: As mentioned before, repellons can come in different sizes dependent on the mass of the matter trapped within the closed 2-brane. Our universe could be littered with primordial repellons that are of widely varying sizes. Some of these repellons could even be trapped within the crust of the Earth, their force fields too large to pass through the intermolecular space of the crust. If so, they would cause a measurable dip in gravity on the surface of those locations where they abound. Two such possible locations are the Hudson Bay region of Canada and the Indian Ocean Geoid Low. Although there are alternate theories explaining such
  • 21. CLOSED 2-BRANES AS DM/DE CANDIDATES 21 gravitational anomalies, they have not yet been proven. Repellons are merely another possible explanation. 8. Experiments proposed to confirm/falsify the repellon theory of DM/DE 1. As explained earlier massive repellons, if they exist, should cause the concave bending of light from sources in the background. That is, a suitably massive repellon in the foreground should bend the light from a star in the background, away from it. They will act as large concave lenses,
  • 22. CLOSED 2-BRANES AS DM/DE CANDIDATES 22 bending light away from them. However, clusters of microscopic repellons—even if the cluster occupies stellar volumes—may not cause much noticeable difference if the central, singular repellon is not massive enough. Perhaps a void/supervoid (if they contain star-size repellons) could be examined telescopically to see if they cause concave bending of light from any background stars. This is a test that can be done quite easily. While a positive result would confirm the existence of repellons, a negative result does not falsify it since the void under study could be composed of smaller sized repellons. 2. The above telescopic examination can also be performed on the various stable Lagrange points on our solar system. Stable Lagrange points of the Earth-Moon system, Earth-Sun system, Jupiter-Sun system, etc., can all be examined to see if any exhibit concave lensing of background starlight. 3. I would also propose a costlier but more definitive test to conclusively confirm/falsify the existence of repellons. I propose a special probe to be sent to either L4 or L5 Lagrange points of the Earth-Moon system with a mechanism to entrap an area of empty space in the heart of L4/L5. When the probe returns to earth, if there is a measurable loss of weight then repellons must exist. If it is found that there is no evidence of any negative mass stuff, then my hypothesis is wrong. On the contrary, if the presence of repellons is confirmed, there will be enormous benefits to humanity. Mining this vast and almost endless supply of gravitationally repulsive repellons can have such tremendous impact on
  • 23. CLOSED 2-BRANES AS DM/DE CANDIDATES 23 architecture, transportation, aviation, etc. 4. I propose some gravitational surveys to be performed in the Hudson Bay area of Canada with the express intent to identify a specific location that can be mined to see whether repellons are present. The other location that needs to be studied for potential deposits of trapped repellons under the sea bed is the Indian Ocean Geoid Low (IOGL), south of Sri Lanka. IOGL is a vast area that exhibits unexplained low gravity.
  • 24. CLOSED 2-BRANES AS DM/DE CANDIDATES 24 9. A brief history of my idea I had first published the same idea with some small differences in 2012. I then called it ‘The Perforated Universe Hypothesis.’ Instead of using the term repellons, I had then called these closed 2-branes as ‘spatial perforations.’ My original hypothesis was a bit too ambitious. It tried to explain not just dark matter & dark energy but also went much further. Perhaps that may not have been a good idea. • I had posted an article on Medium explaining my integrated DM/DE hypothesis on November 25th, 2014. You may find it here: https://medium.com/@harikumar_23993/a- different-look-at-dark-matter-and-dark-energy-32018a92d7d1 • You can find the original paper on Scribd (also posted in July 2012) at https://www.scribd.com/document/100044584/The-Perforated-Universe-Revision-Evidence • I had also sent emails to some scientists working in the field explaining my hypothesis. You may find the text of my email in my blog post, posted on June 18, 2014, here. It also contains some more supporting evidence: https://www.urbanyogi.guru/2014/06/on-dark-matter.html • A PowerPoint presentation on my DM/DE idea dated March 19, 2012. Since it contains a lot of other (related) ideas as well, perhaps it would be better if you start from slide 31 onwards: https://www.scribd.com/document/85901916/The-Perforated-Universe • My blog post (dated July 13, 2012) containing both the video and the Scribd paper can be found at: https://www.urbanyogi.guru/2012/07/this-new-evolutionary-model-of-universe.html
  • 25. CLOSED 2-BRANES AS DM/DE CANDIDATES 25 Then, last year (2018) on December 5th, a paper was published on arXiv by an Oxford scientist named Jamie Farnes, which had attracted much attention. Reading the paper & articles on it, I was startled to note the striking similarities between his paper and mine that I published in July 2012. I had posted my DM/DE hypothesis on Scribd, blogged about it on my BlogSpot page a couple of times, created two YouTube videos, published PowerPoint presentations, wrote an article on Medium on it, had online discussions with other scientists, emailed several scientists working on DM/DE. My papers on Scribd have been viewed over 50,000 times and my YouTube videos, generated about 11,000 hits. They’re all still available for scrutiny. Links are given at the end of this post. As soon as I read the phys.org report (https://phys.org/news/2018-12-universe-theory- percent-cosmos.html) on Dr. Farnes’ paper, I wrote a blog post (noting the striking similarities) that you can find at https://www.urbanyogi.guru/2018/12/startling-similarities-between-my.html. Besides emailing to Dr. Farnes, I had also tweeted to him, phys.org and a few others. The similarities are as below: My hypothesis Dr. Farnes’ theory Proposes an integrated model of both dark energy and dark matter Yes Yes Proposes Gravitational Repulsion as the driving force that causes the observed effects Yes Yes Proposes the continuous generation of this gravitationally repulsive substance Yes Yes Proposes the presence of dark matter in halos, which hold together the galaxies Yes Yes As can be seen from above, the similarities cover the gist of Farnes’ theory. However, there are some differences as well. They are: 1. The mechanism behind the negative mass (and consequently, repulsive gravity) of Farnes’ ‘dark fluid’ and my repellons are fundamentally different. He provides
  • 26. CLOSED 2-BRANES AS DM/DE CANDIDATES 26 negative mass to his ‘dark fluid,’ by “modifying Einstein’s theory of general relativity.” My repellons do not require any modification of Einstein’s equations. 2. His ‘dark fluid,’ has both negative gravitational mass as well as negative inertial mass. However, repellons have negative gravitational mass, but its inertial mass remains positive. I think negative inertial mass is an impossibility. On December 9th , 2018, I had also published a more detailed paper in Medium titled, “Similarities and differences between Jamie Farnes’ paper on a unified theory of dark matter and dark energy published on December 5th, 2018 and my paper on the same topic published six years earlier. Also, a proposal of a test to falsify/confirm my hypothesis.” It can be found here: https://medium.com/@harikumar_23993/similarities-and-differences-between-jamie-farnes- paper-on-a-unified-theory-of-dark-matter-and-35a67b31a802 In that paper, I had also proposed some experiments (repeated here along with a few new ones) to falsify/confirm my repellon hypothesis. 10. A short bio of the author From this paper, the reader would have guessed that I am not a scientist. That is true. I have a degree in Electrical Engineering. I work for a government organization in Toronto, Canada and currently on the verge of retirement. I have a passion for science, especially Astrophysics, Quantum Mechanics, etc. and follow all the latest developments in those fields. I am also a writer. In 2015, I self-published a science fiction novel, “The Intersection Man,” in which one of my characters, a scientist, puts forward this exact hypothesis. I explain this in detail in the novel. In the book, this paves the way to the artificial creation of something I labeled, Gravitationally Repulsive Medium (GRM). The GRM thus created, causes a revolution
  • 27. CLOSED 2-BRANES AS DM/DE CANDIDATES 27 in almost all facets of human life, from architecture to aviation and even medicine. Think of floating habitats, tethered cities rising to the thermosphere. The success of “The Intersection Man,” motivated me to write the sequel, which was published as a single novel (including the first part and two more major sections) in September 2017. However, this time, I changed the title to “Intersection Man” (without the definite article “the”). In the book, I go much further and even propose where exactly on Earth, this GRM can be found. I provide my reasons as well. More details of my novel, including reviews, Facebook page, links to Amazon (ebook & paperback) can be found at https://www.milkywaybooks.com/ 11. One last request My sincere gratitude to you for having read this far. If you think this idea would not work and there are problems with it, I really would like to hear from you with your detailed criticisms. But please be gentle and respectful. I know there are no complicated equations or charts in this paper (that was one of the reasons a scientist cited for not reading my paper when I emailed to him in 2014). But I think I have elaborated my idea as clearly as possible. I am also of the strong conviction that while mathematics is indeed the language of the universe, math is not its soul. The very fact that mathematics can be used to build models of reality that conflict with each other and also many different mathematical models can be built to explain a single observed phenomenon hints at its limitations. I decry the tendency of modern scientists to completely rely on complex mathematical models to explain the observed phenomenon. I think the universe at its most elemental levels is fundamentally simple. Keeping that in mind, I have tried to explain my hypothesis using the simplest of logic. After all, logic is
  • 28. CLOSED 2-BRANES AS DM/DE CANDIDATES 28 the foundation of mathematics, hence perhaps there is a hidden mathematical dimension of my hypothesis that an astute and trained physicist/mathematician can uncover. Once again, thank you for reading, Hari Kumar Nair End Notes: i The science in this paper may not conform to current understandings of physics, especially String Theory, Quantum Fluctuations etc. Hence, my definition of a closed 2-brane may deviate from that in String Theory. I define a 2-brane as a plane that has only two spatial dimensions. It is analogous to a simple geometric plane that has only two spatial dimensions, i.e. length and breadth, but zero thickness. A closed 2-brane is analogous to a bubble-like spherical shell, with a shell thickness of zero. ii A universe can be defined as a set of all points, such that there exists an unbroken path that connects each point with every other point and which does not pass through a region of a different spatial dimension. Two points can be said to lie in the same universe if there exists an unbroken path, however long (not necessarily straight) that connects them, and which does not pass through a region that has a different spatial dimension. Thus, points at the two ends of the universe separated by billions of light-years (with no hope of light ever reaching from one point to the other considering the expanding universe) can still be part of the same universe. Yet, a space that is right at the tip of our nose, but fully enclosed in a closed 2-dimensional membrane (bubble-like, closed 2-brane), will not be a part of our universe. Universes within our own can come in a wide range of sizes right from a universe smaller than an atom to universes of galactic proportions.
  • 29. CLOSED 2-BRANES AS DM/DE CANDIDATES 29 iii The underlying physics of how a repellon acquires its repulsive gravity is explained in the following illustrations:
  • 30. CLOSED 2-BRANES AS DM/DE CANDIDATES 30
  • 31. CLOSED 2-BRANES AS DM/DE CANDIDATES 31 iv I don’t think it is ever possible for anything to have negative inertial mass. I assume, this whole confusion arose from the erroneous interpretation of the famous equation F=ma. The equation F = m × a is certainly true, but with a small change. It should rightfully be F = |m|× a. That is, only the magnitude of mass is applicable here. I am aware of a recent discovery (https://news.wsu.edu/2017/04/10/negative-mass-created-at- wsu/) at Washington State University that sensationally reported the creation of ‘negative mass’ Rubidium atoms that appear to exhibit negative inertial mass properties. But if you read their report carefully, it says, “Now when the rubidium rushes out fast enough, it behaves as if it has negative mass.” “Behaves as if.” Thus, this is not true negative mass, but merely an illusion of it created by manipulating the spin of the rubidium atoms. It is somewhat like throwing a fast spinning top on the floor and seeing it moving towards you rather than away. v Here, size refers only to size of the manifested repulsive force field. Whenever we talk about the size of a repellon, it always refers to the manifested repulsive force field. vi https://scitechdaily.com/scientists-find-evidence-that-dark-matter-can-be-heated-up-and-moved/ vii https://www.sciencemag.org/news/2018/09/oddball-particles-tunneling-through-earth-could- point-new-physics ❖