Abstract
This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting f(ˉR,ˉT) gravity within the framework of a nonstandard theory, called K-essence theory, where ˉR represents the Ricci scalar and ˉT 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 (ˉGμν) associated with the K-essence. This metric is distinct from the usual gravitational metric (gμν). 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(ˉR,ˉT) 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(ˉR,ˉT)≡f(ˉR)+λˉT, where λ represents a parameter within the model. We have found a relationship between ω and time for different kinds of f(ˉR) by treating the kinetic energy of the K-essence scalar field (˙ϕ2) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on ˙ϕ2. 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.
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