Asymptotic solution for expanding universe with matter-dominated evolution

Abstract

We applied the theory of regularly varying (RV) functions to the analysis of the cosmological parameters for the [Formula: see text]CDM model with the matter-dominated evolution. Carroll et al. proved in 1992 that for this type of universe with the curvature [Formula: see text], the expression [Formula: see text] ([Formula: see text] is the Hubble parameter) depends solely on the density parameter [Formula: see text]. Using this result, we infer for such universe the complete asymptotics of all main cosmological parameters. More specifically, the following is derived. If the limit [Formula: see text] does exist and [Formula: see text], then the cosmological constant [Formula: see text] is equal to [Formula: see text]. If [Formula: see text], then for the expansion scale factor [Formula: see text] of a flat universe, we have [Formula: see text]. On the other hand, if the limit [Formula: see text] does not exist, then [Formula: see text] bounces between two power functions and therefore has infinitely many flexion points. Hence, the deceleration parameter in this case changes the sign infinitely many times.