Variable cosmological term $\Lambda(t)$

TL;DR

This paper explores models of a time-varying cosmological term 5(t)5 using scalar fields in FRW cosmology, deriving exact solutions and analyzing different evolution scenarios for 5(t).

Contribution

It introduces a framework where the scalar potential adapts to a dynamic 5(t), extending the cosmological constant concept to time-dependent cases with exact solutions.

Findings

Derived exact solutions for 5(t) in scalar field cosmology.

Analyzed different evolution scenarios of 5(t).

Extended the scalar field potential to incorporate time dependence.

Abstract

We present the case of time-varying cosmological term $\Lambda(t)$. The main idea arises by proposing that as in the cosmological constant case, the scalar potential is identified as $ V(\phi)=2\Lambda$, with $\Lambda$ a constant, this identification should be kept even when the cosmological term has a temporal dependence, i.e., $ V(\phi(t))=2\Lambda(t)$. We Use the Lagrangian formalism for a scalar field $\phi$ with standard kinetic energy and arbitrary potential $V(\phi)$ and apply this model to the Friedmann-Robertson-Walker (FRW)cosmology. Exact solutions of the field equations are obtained by a special ansatz to solve the Einstein-Klein-Gordon equation and a particular potential for the scalar field and barotropic perfect fluid. We present the evolution on this cosmological term with different scenarios.