f((R)over-bar,L(X))-gravity in the context of dark energy with power law expansion and energy conditions

The objective of this work is to generate a general formalismf ( R & macr;, of L(X))- gravity in the context of dark energy under the framework of K -essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where is the familiar Ricci scalar, is the DBI type non-canonical Lagrangian with , R & macr; L(X) X = 1/2 g(mu nu)& nabla;(mu)phi & nabla;(nu)phi and phi is the K-essence scalar field. The emergent gravity metric ((G) over bar mu y) and the well known gravitational metric (g(mu v)) are not conformally equivalent. We have constructed a modified field equation using the metric formalism in f((R) over bar, L(X))-gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric, which is of Friedmann-Lemaitre-Robertson-Walker (FLRW) type. The solution of the modified Friedmann equations have been deduced for the specific choicef (R) over bar, L(X)) , which is of Starobinsky-type, using the power law expansion method. The consistency of the model with the accelerating phase of the universe has been shown when we restrict ourselves to consider the value of the dark energy density as , which in phi(2) = 8/9 = 0.888 < 1 indicates that the present universe is dark-energy dominated. Graphical plots for the energy density (rho), pressure (p), and equation of state parameter (w) with respect to (w.r.t.) time (t) based on parametric values are interestingly consistent with the dark energy domination theory, and hence the accelerating features. We also highlight the corresponding energy conditions and constraints of the f ((R) over bar, L(X)) theory with a basic example.

Automated summary

The work aims to generate a general formalism of L(X)-gravity in the context of dark energy under the framework of K-essence emergent geometry with the DBI variety of action. The modified field equation has been constructed using the metric formalism in f(R), L(X)-gravity, incorporating the Friedmann equations of the FLRW type. The solution of the modified Friedmann equations for a specific choice of f(R), L(X) is consistent with the dark energy domination theory and the accelerating features.