Kaluza-Klein cosmological model in $f(R,T)$ gravity with $\Lambda(T)$

TL;DR

This paper explores Kaluza-Klein cosmological models within $f(R,T)$ gravity, deriving exact solutions for power law and exponential expansion, and finds that the exponential model closely resembles the $ ext{Lambda}$CDM universe.

Contribution

It introduces exact solutions for Kaluza-Klein cosmology in $f(R,T)$ gravity with a specific functional form, highlighting the evolving cosmological constant and its relation to universe acceleration.

Findings

Exponential expansion model mimics $ ext{Lambda}$CDM behavior.

Derived exact solutions for power law and exponential expansion.

Discussed physical and dynamical properties of the models.

Abstract

A class of Kaluza-Klein cosmological models in $f(R,T)$ theory of gravity have been investigated. In the work, we have considered the functional $f(R,T)$ to be in the form $f(R,T)=f(R)+f(T)$ with $f(R)=\lambda R$ and $f(T)=\lambda T$. Such a choice of the functional $f(R,T)$ leads to an evolving effective cosmological constant $\Lambda$ which depends on the stress energy tensor. The source of the matter field is taken to be a perfect cosmic fluid. The exact solutions of the field equations are obtained by considering a constant deceleration parameter which leads two different aspects of the volumetric expansion namely a power law and an exponential volumetric expansion. Keeping an eye on the accelerating nature of the universe in the present epoch, the dynamics and physical behaviour of the models have been discussed. From statefinder diagnostic pair we found that the model with exponential volumetric expansion behaves more like a $\Lambda$CDM model.