Spherically Symmetric Non Linear Structures

Abstract

We present an analytical method to extract observational predictions about non linear evolution of perturbations in a Tolman Universe. We assume no a priori profile for them. We solve perturbatively a Hamilton - Jacobi equation for a timelike geodesic and obtain the null one as a limiting case in two situations: for an observer located in the center of symmetry and for a non - centered one. In the first case we find expressions to evaluate the density contrast and the number count and luminosity distance vs redshift relationships up to second order in the perturbations. In the second situation we calculate the CMBR anisotropies at large angular scales produced by the density contrast and by the asymmetry of the observer's location, up to first order in the perturbations. We develope our argument in such a way that the formulae are valid for any shape of the primordial spectrum.

27 pages, uses RevTex. Modified in response to referee's Comments (submitted to PRD)

References in corpus (4)

• Loop Corrections in Non-Linear Cosmological Perturbation Theory
• On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. I. Theory
• Dipole Anisotropy from an Entropy Gradient
• On the microwave background anisotropy produced by big voids in open universes

Cited by in corpus (8)

• Stochastic Gravity: Theory and Applications
• Stochastic Gravity: Theory and Applications
• Mapping Luminosity-Redshift Relationship to LTB Cosmology
• Stochastic dynamics of correlations in quantum field theory: From Schwinger-Dyson to Boltzmann-Langevin equation
• Stochastic Gravity
• Stochastic Gravity: A Primer with Applications
• Influence Action and decoherence of hydrodynamic modes
• New variables for the Lema\^ıtre-Tolman-Bondi dust solutions