-gravity in the context of dark energy with power law expansion and energy conditions*

Abstract

The motto of this work is to generate a general formalism of $f(\bar{R}, L(X))-$gravity in the context of dark energy under the framework of the {\bf K-}essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where $\bar{R}$ is the familiar Ricci scalar, $L(X)$ is the DBI type non-canonical Lagrangian with $X={1\over 2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi$ and $\phi$ is the {\bf K-}essence scalar field. The emergent gravity metric $\G_{\mu\nu}$ and the well known gravitational metric $g_{\mu\nu}$ are not conformally equivalent. We have constructed a modified field equation using the metric formalism in $f(\bar{R}, L(X))$-gravity incorporating the corresponding Friedmann equations in the framework of the background gravitational metric which is of Friedmann-Lema{\^i}tre-Robertson-Walker (FLRW) type. The solution of modified Friedmann equations have been deduced for the specific choice of $f(\bar{R}, L(X))$, which is of Starobinsky-type, using 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 $\dot\phi^{2}=\frac{8}{9}=0.888 <1$, which indicates that the present Universe is dark energy dominated. Graphical plots for the energy density ($\rho$), pressure ($p$) and equation of state parameter ($\o$) w.r.t. time ($t$) based on parametric values are interestingly consistent with the dark energy domination and hence accelerating features. We also put some light on the corresponding energy conditions and constraints of the $f(\bar{R}, L(X))$ theory with one basic example.

Raychaudhuri Equation in K‐essence Geometry: Conditional Singular and Non‐Singular Cosmological Models

“…Considering the background gravitational metric to be flat Friedmann‐Lemaitre‐Robertson‐Walker (FLRW), then from Equation () we have the corresponding emergent gravity line element as [ 63–65 ] $$$$\begin{align} dS^{2}=(1-\dot{\phi }^{2})dt^{2}-a^{2}(t)\sum _{i=1}^{3} (dx^{i})^{2}, \end{align}$$$$where $$a(t)$$ is scale factor and from the EOM () we have the relationship between the Hubble parameter ($$H(t)$$) and the k ‐essence scalar field [ 63–65 ] as $$$$\begin{align} \frac{\dot{a}}{a}=H(t)=-\frac{\ddot{\phi }}{\dot{\phi }(1-\dot{\phi }^{2})}. \end{align}$$$$…”

Evaporation of Dynamical Horizon with the Hawking Temperature in the K‐essence Emergent Vaidya Spacetime

“…Notably, the authors of refs. [75][76][77] have used the K-essence emergent gravity metric (Equation 8) or (Equation 12)(below) in cosmology, where they have assumed that the underlying metric is of the Friedmann-Lemaître-Robertson-Walker (FLRW) type.…”

Geodesic structure of generalized Vaidya spacetime through the K-essence

“…This feature may mitigate the cosmic microwave background (CMB) disruptions on large angular scales [56][57][58]. In this specific situation, Manna et al [8,10,[36][37][38][62][63][64][65][66][67] have developed a fascinating emergent gravity metric referred to as Ḡµν . This metric possesses distinct attributes in contrast to the standard gravitational metric g µν and is derived from the notions of the Dirac-Born-Infeld (DBI) type action, as outlined in the works [70][71][72][73].…”

“…[59][60][61], have examined the empirical evidence supporting the concept of K-essence with a DBI-type non-canonical Lagrangian, along with other modified theories. Furthermore, it has been noted that the K-essence theory may be applied in a model that combines dark energy and dark matter [8,10,47,[62][63][64][65], as well as from a purely gravitational perspective [36-38, 66, 67]. This article is organized as follows: In section 2, we provided a concise explanation of the K-essence geometry and its connection to the conventional generalized Vaidya spacetime, which leads to the construction of a new generalized K-essence Vaidya spacetime.…”