1. Dynamics of spherical voids in Friedmann-Lemaitre Universes
Roland Triay
CPT

2. Challenge for Structures Formation Theories
(our) Motivation
Challenge for Structures Formation Theories
Voids are non linear structures
N. Benhamidouche, B. Torresani, R. Triay (1999) - traveling wavelets
b) « vacuum gravitational repulsion »
e.g., Schwarzschild solution of Einstein Eq. with Cosmological constant
c) -Effect for a single void embedded in a Friedmann universe
-Effect in the cosmological expansion of voids : Fliche &Triay (2007)
Full relativistic treatment : Maeda & Triay (in progress)
Phase Space, Marseille (2009)

3. Status of L - (Geometry)
S. Sternberg, Einstein Memorial Lecture (Jerusalem 2006)
The gravitational field and its sources are characterized by
Schwarzschild solution - Newton approximation
Phase Space, Marseille (2009)

4. Status of L- Geometry) Dimensional analysis of EE
Phase Space, Marseille (2009)

5. Modeling gravitational structures
(Modified) Newton law
With L : Gravitation becomes repulsive at “large” scale
No L-effect in Solar neighborhood
Small effect in the outerpart of the Galaxy
Intervenes at the edge of LSC
Homogeneity scale
Phase Space, Marseille (2009)

6. Reference Coordinates
(Hubble-Friedmann Expansion)
(defined as a reciprocal mapping of a quadrature) not decreasing
Phase Space, Marseille (2009)

7. Euler-Newton-Poisson
(in the Reference Frame)
Newton-Friedmann model :
Vacuum model :
Phase Space, Marseille (2009)

8. Spherical Voids S NF V
Covariant formulation of Euler-Poisson eq. syst.
J.M. Souriau, (French) C.R. Acad. Sci., p.751 (1970)
C. Duval, H.P. Kunzle, Rep. Math. Phys. 13,351 (1978)
Phase Space, Marseille (2009)

9. Magnification & Expansion Rate
Phase Space, Marseille (2009)

10. Corrective factor to Hubble expansion
Phase Space, Marseille (2009)

11. Magnification & Expansion Rate
Phase Space, Marseille (2009)

12. Phase Space, Marseille (2009)
Formation date
Phase Space, Marseille (2009)

13. Observational Signature of Ko
“The Local Void is Really Empty”
R. Brent Tully etal.,IAU Symposium, Volume 244, p arXiv: v2
“Is a spatially closed universe possible ?” R. Triay
IJTP 42,6,1187 (2003)
Phase Space, Marseille (2009)