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 to 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 the gravity and the $k$-essence scalar field.

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References in corpus (5)

• The Raychaudhuri equations: a brief review
• On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
• Early dark energy in $k$-essence
• Focusing of geodesic congruences in an accelerated expanding Universe
• The Hawking temperature in the context of dark energy for Kerr-Newman and Kerr-Newman-AdS backgrounds