Analysis with observational constraints in $ \Lambda $-cosmology in $f(R,T)$ gravity

TL;DR

This paper derives an exact cosmological solution within $f(R,T)$ gravity, analyzing its dynamics, observational constraints, and distinguishing features from other dark energy models, showing good agreement with data.

Contribution

The paper presents a new exact solution in $f(R,T)$ gravity with observational constraints and diagnostic analyses to differentiate it from other dark energy models.

Findings

Model is consistent with structure formation.

Constraints on $H_0$ and $n$ from observational data.

Model aligns well with multiple cosmological observations.

Abstract

An exact cosmological solution of Einstein field equations (EFEs) is derived for a dynamical vacuum energy in $f(R,T)$ gravity for Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time. A parametrization of the Hubble parameter is used to find a deterministic solution of EFE. The cosmological dynamics of our model is discussed in detail. We have analyzed the time evolution of physical parameters and obtained their bounds analytically. Moreover, the behavior of these parameters are shown graphically in terms of redshift $`z'$. Our model is consistent with the formation of structure in the Universe. The role of the $f(R,T)$ coupling constant $\lambda$ is discussed in the evolution of the equation of state parameter. The statefinder and Om diagnostic analysis is used to distinguish our model with other dark energy models. The maximum likelihood analysis has been reviewed to obtain the constraints on the Hubble parameter $H_0$ and the model parameter $n$ by taking into account the observational Hubble data set $H(z)$, the Union 2.1 compilation data set $SNeIa$, the Baryon Acoustic Oscillation data $BAO$, and the joint data set $H(z)$ + $ SNeIa$ and $H(z)$ + $SNeIa$ + $BAO $. It is demonstrated that the model is in good agreement with various observations.