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

Abstract

AbstractWe 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.