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

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)

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)

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

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)

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

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

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)

Magnification & Expansion Rate Phase Space, Marseille (2009)

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

Magnification & Expansion Rate Phase Space, Marseille (2009)

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

Observational Signature of Ko “The Local Void is Really Empty” R. Brent Tully etal.,IAU Symposium, Volume 244, p. 146-1512007 arXiv:0705.4139v2 “Is a spatially closed universe possible ?” R. Triay IJTP 42,6,1187 (2003) Phase Space, Marseille (2009)