Effects of Nonlinear Inhomogeneity on the Cosmic Expansion with Numerical Relativity

Area of Science:

• Cosmology
• Astrophysics
• General Relativity

Background:

• The Einstein-de Sitter model provides a baseline for a homogeneous and isotropic universe.
• Understanding deviations from this model is key to comprehending cosmic evolution.
• Perturbation theory is a standard tool for analyzing early universe structures.

Purpose of the Study:

• To construct and analyze a fully relativistic numerical model of an inhomogeneous universe.
• To quantify the departure of the expansion rate from the homogeneous Einstein-de Sitter model.
• To investigate the behavior and impact of the backreaction term (Q_{D}) on cosmic expansion.

Main Methods:

• Developed a three-dimensional, fully relativistic numerical simulation.
• Used initial data perturbing the Einstein-de Sitter model.
• Compared local quantities with linear perturbation theory predictions.
• Analyzed the behavior of the backreaction term Q_{D}.

Main Results:

• Collapsing perturbations reach their turnaround point earlier than predicted by the spherical top-hat collapse model.
• Local expansion rate deviations can reach 28% at an underdensity for an initial density contrast of 10^{-2}.
• The backreaction term Q_{D} exhibits a 1/a scaling for small perturbations.
• For larger amplitudes, Q_{D} is negative and grows linearly, contributing to deceleration, but remains small in magnitude.

Conclusions:

• Inhomogeneous pressureless fluid models show significant early deviations from homogeneous models.
• The backreaction term plays a decelerating role in cosmic expansion, with its magnitude dependent on perturbation amplitude.
• Numerical simulations are crucial for accurately modeling complex cosmological scenarios and understanding backreaction effects.