Exact solutions, finite time singularities and non-singular universe models from a variety of $\Lambda(t)$ cosmologies

TL;DR

This paper explores various time-dependent cosmological models with a dynamic cosmological constant, providing exact solutions and analyzing their singular behaviors, including conditions for avoiding future singularities in flat FLRW universes.

Contribution

It offers a comprehensive analysis of exact solutions in $\Lambda(t)$ cosmologies, highlighting models with different expansion behaviors and conditions to prevent future singularities.

Findings

Several models admit exact solutions with diverse universe evolutions.

Many models exhibit finite-time past or future singularities.

Certain models can avoid future singularities under specific restrictions.

Abstract

Cosmological models with time dependent $\Lambda$ (read as $\Lambda (t)$) have been investigated widely in the literature. Models that solve background dynamics analytically, are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of $\Lambda (t)$ models focusing on their evolutions and singular behaviour. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power law expansion, oscillating, and the singularity free universe as well. However, we also noticed that a large number of models in this series permits past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.