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

Abstract

We investigate how the Raychaudhuri equation behaves in the k‐essence geometry. As far as we are concerned, both the early and current epochs of the universe are relevant to the k‐essence theory. Here, we have studied the k‐essence geometry using the Dirac‐Born‐Infeld (DBI) variety of non‐standard action. The corresponding k‐essence emergent spacetime is not conformally equivalent to the usual gravitational metric. We assume that the background gravitational metric is of the Friedmann‐Lemaitre‐Robertson‐Walker (FLRW) type in this case. We have found that both the conditional singular and non‐singular cosmological models of the universe through the modified Raychaudhuri equation are possible where we have used the spacetime as the flat k‐essence emergent FLRW‐type. We have also addressed the Focusing theorem and conditional caustic universe construction. These conditional effects are caused by the additional interactions that arise as a result of the coupling that exists between gravity and the k‐essence scalar field.

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].…”

Geodesic Structure of Generalized Vaidya Spacetime through the K-Essence

“…This feature may mitigate the cosmic microwave background (CMB) disruptions on large angular scales [58][59][60]. In this specific situation, Manna and coworkers [8,10,[37][38][39][61][62][63][64][65][66] 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 Refs.…”

“…[73][74][75], 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 [8,10,45,[61][62][63][64], as well as from a purely gravitational perspective [37][38][39]65,66].…”