Olber's paradox states that if the universe is infinite and contains an infinite number of stars, each emitting the same amount of light, then the night sky should be uniformly bright, which it is not. Considering an expanding, finite universe explains why the night sky is dark - there is a finite number of stars with finite lifetimes, and the light from distant stars has not had time to reach us due to the universe's finite age. Distant stars are also redshifted into obscurity due to the universe's expansion.

1. E4.1
Olber’s paradox
Why is the night sky dark?
or
Why isn't the night sky as uniformly bright
as the surface of the Sun?
Newton’s model of the universe assumed that the universe
was infinite (in space and time) uniform and static.
If the Universe has infinitely many stars, then it should be
uniformly bright in all directions.

2. E4.1
Olber’s paradox
If the Universe is eternal and
infinite and if it has an infinite
number of stars, then the night sky
should be bright.
Very distant stars contribute with
very little light to an observer on
Earth but there are many of them.
So if there is an infinite number of
stars, each one emitting a certain
amount of light, the total energy
received must be infinite, making
the night sky infinitely bright, which
it is not.

3. E4.2
Olber’s paradox
If we consider the Universe finite and expanding, the
radiation received will be small and finite mainly for 2 reasons:
There is a finite number of stars and each has a finite
lifetime (they don’t radiate forever)
and
Because of the finite age of the Universe, stars that are far
away have not yet had time for their light to reach us.
Also,
The Universe is expanding, so distant stars are red-shifted
into obscurity (contain less energy).

4. E4.3-4.7
THE BIG BANG
MODEL

5. E4.3
Doppler effect
In astronomy, the Doppler effect was originally studied in the
visible part of the electromagnetic spectrum. Today, the
Doppler shift, as it is also known, applies to electromagnetic
waves in all portions of the spectrum.
Also, because of the inverse
relationship between frequency
and wavelength, we can
describe the Doppler shift in
terms of wavelength. Radiation
is redshifted when its
wavelength increases, and is
blueshifted when its wavelength
decreases.

6. E4.3
Doppler effect
In astronomy, the Doppler effect was originally studied in
the visible part of the electromagnetic spectrum. Today, the
Doppler shift, as it is also known, applies to electromagnetic
waves in all portions of the spectrum.
Astronomers
use Doppler shifts
to calculate
precisely how fast
stars and other
astronomical
objects move
toward or away
from Earth.

7. E4.4
Doppler effect
Why is Doppler effect so
important?
In 1920’s Edwin Hubble and Milton Humanson realised
that the spectra of distant galaxies showed a redshift, which
means that they are moving away from Earth. So, if galaxies
are moving away from each other then it they may have
been much closer together in the past
Matter was concentrated in one point and some
“explosion” may have thrown the matter apart.

8. E4.5
Background radiation
In 1960 two physicists, Dicke and Peebles, realising that
there was more He than it could be produced by stars,
proposed that in the beginning of the Universe it was at a
sufficiently high temperature to produce He by fusion.
In this process a great amount of highly energetic radiation
was produced. However, as the Universe expanded and
cooled, the energy of that radiation decreased as well
(wavelength increased). It was predicted that the actual
photons would have an maximum λ corresponding to a black
body spectrum of 3K.
So, we would be looking for microwave radiation.

9. E4.5
Background radiation
Shortly after this
prediction, Penzias and
Wilson were working with
a microwave aerial and
found that no matter in
what direction they
pointed the aerial it
picked up a steady,
continuous background
radiation.

10. E4.5
Background radiation
In every direction, there is a very low energy and very
uniform radiation that we see filling the Universe. This is called
the 3 Degree Kelvin Background Radiation, or the Cosmic
Background Radiation, or the Microwave Background.
These names come about
because this radiation is
essentially a black body with
temperature slightly less
than 3 degrees Kelvin
(about 2.76 K), which peaks
in the microwave portion of
the spectrum.

11. E4.6
Background radiation
Why is the background radiation an
evidence for the Big Bang?
The cosmic background radiation (sometimes called the
CBR), is the afterglow of the big bang, cooled to a faint
whisper in the microwave spectrum by the expansion of the
Universe for 15 billion years (which causes the radiation
originally produced in the big bang to redshift to longer
wavelengths).

12. E4.6
Big Bang
The Big Bang Model is a broadly accepted theory for the
origin and evolution of our universe.
It postulates that 12 to 14 billion years ago, the portion of
the universe we can see today was only a few millimetres
across.
It has since expanded from this hot dense state into the
vast and much cooler cosmos we currently inhabit.
We can see remnants of this hot dense matter as the now
very cold cosmic microwave background radiation which still
pervades the universe and is visible to microwave detectors as
a uniform glow across the entire sky.

13. E4.6
Big Bang
The singular point at which space, time, matter
and energy were created. The Universe has been
expanding ever since.
Main evidence:
Expansion of the Universe – the Universe is expanding
(redshift)  it was once smaller  it must have started
expanding sometime  “explosion”
Background radiation  evidence of an hot Universe that
cooled as it expanded
He abundance  He produced by stars is little  there is
no other explanation for the abundance of He in the Universe
than the Big Bang model.

14. E4.8
Fate of the Universe
Universe
Closed Open Flat
Enough matter  Not enough matter Critical density 
density is not enough to density is such that Universe will only
allow an infinite gravity is too weak start to contract
expansion  gravity will to stop the Universe after an infinite
stop the Universe expanding forever amount of time
expansion and cause it
to contract (Big Crunch)

15. E4.9
Critical density
The density of the Universe that separates a universe that
will expand forever (open universe) and one that will re-
colapse (closed universe).
A universe with a density equal to the critical density is
called flat and it will expand forever at a slowing rate.
So, how do we measure the density of the
Universe?

16. E4.9
Critical density
If we take in account all the matter (stars) that we can see
then the total mass would not be enough to keep the galaxies
orbiting about a cluster centre.
So, there must be some matter that can not be seen – dark
matter. This dark matter cannot be seen because it is too cold
to irradiate.
According to the present theories dark matter consists in
MACHO’s and WIMPS

17. E4.11
Massive compact halo objects – brown and
MACHO’s black dwarfs or similar cold objects and
even black holes.
Non-barionic weakly interacting massive
WIMP’s particles (neutrinos among other particles
predicted by physics of elementary
particles)
It seems that there is also what is called “dark energy”…

18. E4.11