Cosmological effects on f(R̄,T̄) gravity through a non-standard theory

Abstract

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting [Formula: see text] gravity within the framework of a nonstandard theory, called K-essence theory, where [Formula: see text] represents the Ricci scalar and [Formula: see text] denotes the trace of the energy–momentum tensor associated with the K-essence geometry. The Dirac–Born–Infeld (DBI) nonstandard Lagrangian has been employed to generate the emergent gravity metric [Formula: see text] associated with the K-essence. This metric is distinct from the usual gravitational metric [Formula: see text]. It has been shown that under a flat Friedmann–Lemaître–Robertson–Walker (FLRW) background gravitational metric, the modified field equations and the Friedmann equations of the [Formula: see text] gravity are distinct from the usual ones. In order to get the equation of state (EoS) parameter [Formula: see text], we have solved the Friedmann equations by taking into account the function [Formula: see text], where [Formula: see text] represents a parameter within the model. We have found a relationship between [Formula: see text] and time for different kinds of [Formula: see text] by treating the kinetic energy of the K-essence scalar field ([Formula: see text]) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on [Formula: see text]. By presenting graphical representations of the EoS parameter with time, we show that our model is consistent with the data of SNIa[Formula: see text][Formula: see text][Formula: see text]BAO[Formula: see text][Formula: see text][Formula: see text][Formula: see text] within a certain temporal interval.