Thermodynamics of a Non-canonical $f(\bar{R},\bar{T})$ gravity

TL;DR

This paper investigates the thermodynamic properties of a modified $f(ar{R},ar{T})$ gravity theory based on K-essence and DBI Lagrangian, analyzing the generalized second law and entropy evolution in different cosmological scenarios.

Contribution

It introduces a novel thermodynamic analysis of $f(ar{R},ar{T})$ gravity with non-canonical K-essence, developing modified laws and exploring entropy behavior during cosmic evolution.

Findings

Modified GSLT can be violated during initial universe phases.

Entropy can be negative or positive depending on curvature and epoch.

Entropy saturation suggests possible heat death of the universe.

Abstract

This work comprises a study of the thermodynamic behavior of modified $f(\bar{R},\bar{T})$ gravity, which had been developed based on a non-canonical theory known as K-essence theory. In this development, we use the Dirac-Born-Infeld (DBI) type of non-standard Lagrangian. We develop a modified first law and generalized second law of thermodynamics (GSLT) within the modified $f(\bar{R},\bar{T})$ gravity, where we consider the background metric to be the usual Friedmann-Lema$\hat{\text{i}}$tre-Robertson-Walker (FLRW) type. A graphical analysis of surface gravity has been performed for the modified FLRW metric via the $f(\bar{R},\bar{T})$ theory, which is different from the usual FLRW gravity through the usual $f(R,T)$ gravity. Exponential and power law scale factors are used to analyze cosmic surface gravity. Through the investigation of the modified GSLT, using the relation of scale factor with the scalar field, we have seen that during the initial phase of the universe, the entropy's rate of change may be either negative or positive, contingent upon the value of the curvature constant. The negativity of the entropy change indicates that the modified GSLT is not feasible in that particular area for a particular curvature constant. These traits suggest that during the inflationary period, entropy might have been either negative or positive. It has also been seen that entropy saturates every curvature value at different time ranges, which indicates the heat death of the universe.