Solutions of Friedmann's Equations and Cosmological Consequences

TL;DR

This paper analyzes solutions to Friedmann's equations in cosmology, revealing how nonlinear matter influences dark energy and universe expansion, especially near the phantom divide line, with implications for understanding cosmic evolution.

Contribution

It provides new insights into solving Friedmann equations and derives a universal formula for the asymptotic growth rate of the universe's scale factor in Chaplygin fluid models.

Findings

Linear matter contributes to dark energy near the phantom divide line.

Derived a universal formula for exponential growth rate of the scale factor.

Insights into the impact of nonlinear matter on cosmic evolution.

Abstract

The Einstein equations of general relativity reduce, when the spacetime metric is of the Friedmann--Lemaitre--Robertson--Walker type governing an isotropic and homogeneous universe, to the Friedmann equations, which is a set of nonlinear ordinary differential equations, determining the law of evolution of the spatial scale factor, in terms of the Hubble ``constant''. It is a challenging task, not always possible, to solve these equations. In this talk, we present some insights from solving and analyzing the Friedmann equations and their implications to evolutionary cosmology. In particular, in the Chaplygin fluid universe, we derive a universal formula for the asymptotic exponential growth rate of the scale factor which indicates that, as far as there is a tiny presence of nonlinear (exotic) matter, linear (conventional) matter makes contribution to the dark energy, which becomes significant near the phantom divide line. Joint work with Shouxin Chen, Gary W. Gibbons, and Yijun Li.