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

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting f (R ̄ , T ̄) gravity within the framework of a nonstandard theory, called K-essence theory, where R ̄ represents the Ricci scalar and T ̄ 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 ( G ̄ μ ν) associated with the K-essence. This metric is distinct from the usual gravitational metric (g μ ν). 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 f (R ̄ , T ̄) gravity are distinct from the usual ones. In order to get the equation of state (EoS) parameter ω , we have solved the Friedmann equations by taking into account the function f (R ̄ , T ̄) ≡ f (R ̄) + λ T ̄ , where λ represents a parameter within the model. We have found a relationship between ω and time for different kinds of f (R ̄) by treating the kinetic energy of the K-essence scalar field ( ϕ ̇ 2 ) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on ϕ ̇ 2 . By presenting graphical representations of the EoS parameter with time, we show that our model is consistent with the data of SNIa + BAO + H (z) within a certain temporal interval. [ABSTRACT FROM AUTHOR]