Asymptotic Solution For Expanding Universe With Matter-Dominated Evolution

We applied the theory of regularly varying (RV) functions to the analysis of the cosmological parameters for the ACDM model with the matter-dominated evolution. Carroll et ad. proved in 1992 that for this type of universe with the curvature k = 0, -1, the expression H(t)t (H(t) is the Hubble parameter) depends solely on the density parameter Omega(t). 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 omega = lim(t ->infinity)Omega(t) does exist and omega not equal 0, then the cosmological constant Lambda is equal to 0. If omega = 0, then for the expansion scale factor alpha(t) of a flat universe, we have alpha(t)similar to e(root Lambda/3t).On the other hand, if the limit lim(t ->infinity)Omega(t) does not exist, then alpha(t) 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.