-gravity in the context of dark energy with power law expansion and energy conditions*G.M. and A.P. acknowledge the DSTB, Government of West Bengal, India for financial support through the Grants No.: 322(Sanc.)/ST/P/S&T/16G-3/2018 dated 06.03.2019. S.R. is thankful to the authority of IUCAA, Pune for providing Visiting Associateship under which a part of this work has been done. (1st February 2023) - Manna, Goutam; Panda, Arijit; Karmakar, Aninda; Ray, Saibal; Islam, Md. Rabiul
Abstract: The objective of this work is to generate a general formalism of 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, and ϕ is the K- essence scalar field. The emergent gravity metric ( ) and the well known gravitational metric ( ) are not conformally equivalent. We have constructed a modified field equation using the metric formalism in -gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric, which is of Friedmann-Lemaître-Robertson-Walker (FLRW) type. The solution of the modified Friedmann equations have been deduced for the specific choice of, 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 indicates that the present universe is dark-energy dominated. Graphical plots for the energy density ( ρ ), pressure ( p ), and equation of state parameter ( ) 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 theory with a basic example.