The document summarizes research presented by Vesselin Gueorguiev and André Maeder at the 14th International Conference on Gravitation, Astrophysics and Cosmology. The research applies the Scale-Invariant Vacuum Theory (SIVT) to address issues in cosmology, galaxy dynamics, and dwarf spheroidal galaxies. Key findings include that SIVT provides equations for cosmology without needing dark matter, can explain fast growth of density fluctuations, and describes dwarf spheroidal galaxies in a way that both challenges ΛCDM and MOND. The theory draws on scale invariance as a possible explanation for dark matter and dark energy effects.

1. Gueorguiev & Maeder 2
The 14th Interna6onal Conference on Gravita6on, Astrophysics and Cosmology (ICGAC14),
Na6onal Central University, Jhongli, Taiwan, 17 – 21 August 2020
in collabora*on with
André Maeder, Geneva Observatory, Switzerland
Vesselin G. Gueorguiev
Institute for Advanced Physical Studies, Sofia, Bulgaria
& Ronin Institute for Independent Scholarship, NJ, USA
Fotosearch Royalty Free Stock Photography (h/ps://www.fotosearch.com)
Scale-Invariant Vacuum Theory (SIVT)– Applica:ons:
The Growth of the Density Fluctua:ons in the SIVT
Physics of the Dark Universe 25 (2019) 100315 [arXiv:1811.03495]
Scale-invariant dynamics of galaxies,
MOND, dark ma,er, and the dwarf spheroidals
Monthly No6ces of the Royal Astronomical Society 492, 2698 (2020) [arXiv:2001.04978]
The 14th Interna:onal Conference on Gravita:on, Astrophysics and Cosmology (ICGAC14),
Na:onal Central University, Jhongli, Taiwan, 17 – 21 August 2020

2. Gueorguiev & Maeder VGG talk at ICGAC14 via zoom on 18 August 2020 3
Key Results!
 Equa6ons for Cosmology within the Scale-Invariant Vacuum Theory (SIVT)
 The Growth of the Density Perturba6on within the SIVT
 SIVT Descrip6on of the Dwarf Spheroidals - failure of ΛCDM and MOND!
’Integrable Weyl Geometry

3. Gueorguiev & Maeder VGG talk at ICGAC14 via zoom on 18 August 2020 4
Canuto et al 1977
Alike in GR, vacuum proper6es do not depend on the material content
Within SIVT:
The empty space!
If l =const.=1
 usual equa6ons.
The cosmological
equa:ons :
If dR/dt > 0, addi6onal accelera6on
opposed to gravity.
No need of unknown Dark Stu9!
COSMOLOGY
Maeder (2017)
λ∝1/t
-
L
3
The Ield equa6on with the R-W metric
√3
Λ

4. Gueorguiev & Maeder VGG talk at ICGAC14 via zoom on 18 August 2020 5
SIVT vs. ΛCDM (k=0)
Maeder, 2017aThe Astrophysical Journal, 834:194 (16pp), 2017

5. Gueorguiev & Maeder ICGAC14 via Zoom on 18 August 2020 6
Equa6ons of con6nuity, of Euler, and Poisson within the SIVT:
Applied to a density perturba6on d they give:
The 6me deriva6ve
of the Irst one and
the divergence of
the second eqs.,
with p=0, lead to:
n
Euler h-order of δ.
Maeder &
Gueorguiev, 2018
The Growth of the Density Perturba6on
Physics of the Dark Universe 25 (2019) 100315; arXiv:1811.03495 [astro-ph.CO]
(t)= 1/t

6. n-dependence of the growth
-1
-2
-3
-4
-5
logd
3.0 2.5 2.0 1.5 1.0 0.5
log (1+z)
EdS model
Different values of n
n = 5, 3, 2, 1
Dotted lines:
initial z=3000 and
z=500 for n=2.
Ωm=0.10, ini6al value δ = 10−5
at z = 1376
Gueorguiev & Maeder ICGAC14 via Zoom on 18 August 2020 7

7. FAST GROWTH OF THE DENSITY FLUCTUATIONS
(short free-fall 6me, addi6onal infall velocity)
DARK MATTER NEEDS NOT TO BE PRESENT!
Gueorguiev & Maeder ICGAC14 via Zoom on 18 August 2020 8

8. Gueorguiev & Maeder VGG talk at ICGAC14 via zoom on 18 August 2020 9
k2
= 10-10.85
Lelli et al. (2017)

9. Gueorguiev & Maeder VGG talk at ICGAC14 via zoom on 18 August 2020 10
The geodesics: curve whose tangent vector um
=dxm
/ds is transported by
parallel displacement along the curve. Dirac, 1973
From an ac:on: Bouvier & Maeder, 1978
k(t) = 1/tPoten6al F=GM/r
is scale invariant
The ra6o of the 2 terms is
GM
THE WEAK FIELD APPROXIMATION for SIVT
x = k v r2

10. Gueorguiev & Maeder VGG talk at ICGAC14 via zoom on 18 August 2020 11
x = k v r2
GM
k= 1/t= H
x
At any 6me,
Using v = (r gobs)1/2
 x =
Consider 2 gravit. systems 1 and 2 at the same t and r,
gobs - gbar__________
gbar
2nd
degree equa6on
Calling gobs,2  g and gbar,2  gN
for system 2, system 1 is a reference
gbarx
H (r gobs)1/2
~
k2
is the lower limit of g for gN  0, this limit is the same everywhere
If gN >> k2
, then g  gN
If gN  0 , then g  k2
thus k2
≥ min [gN]
for any r
TOWARDS the RAR
Explicit scale invariance!

11. Gueorguiev & Maeder VGG talk at ICGAC14 via zoom on 18 August 2020 12
For gN >> 10-10
, g  gN+ (gN k2
)1/2
k2
= 10-10.85

12.  SIV paradigm is a minimal generalization of the Einstein GR,
 Provides New framework for Cosmology & Gravity,
 Density perturbations can grow fast enough!
 No need of Dark Matter!
 Explains the Dwarf Spheroidal, unlike MOND!
 Scale invariance might explain dark matter effects!
 New perspective on dark energy and the CC problem?
 Universe 2020, 6(8), 108; https://doi.org/10.3390/universe6080108
Thank You!
Conclusion:
Revisiting the Cosmological Constant Problem within Quantum Cosmology in Universe 2020, 6(8), 108;
https://doi.org/10.3390/universe6080108

13. The Growth of the Density Fluctuations in the SIV theory
Physics of the Dark Universe 25 (2019) 100315, https://arxiv.org/abs/1811.03495
Scale-invariant dynamics of galaxies, MOND, dark matter, and the dwarf spheroidals,
Monthly Notices of the Royal Astronomical Society
NNRAS 492, 2698 (2020), https://arxiv.org/abs/2001.04978
The Scale-Invariant Vacuum (SIV) Theory: A Possible Origin of Dark Matter and Dark
Energy, Universe 2020, 6, 46; https://doi.org/10.3390/universe6030046
Revisiting the Cosmological Constant Problem within Quantum Cosmology,
Universe 2020, 6, 108; https://doi.org/10.3390/universe6080108
Special Issue "Nature and Origin of Dark Matter and Dark Energy"
https://www.mdpi.com/si/41677
References: