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 (37)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• Essentials of k-essence
• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• The Cosmic Triangle: Revealing the State of the Universe
• Early Dark Energy Can Resolve The Hubble Tension
• Purely kinetic k-essence as unified dark matter
• k-Essence, superluminal propagation, causality and emergent geometry
• Lecture Notes on General Relativity
• Extended tachyon field, Chaplygin gas and solvable k-essence cosmologies
• Early dark energy from massive neutrinos -- a natural resolution of the Hubble tension
• The Raychaudhuri equations: a brief review
• Bouncing cosmology with future singularity from modified gravity
• Quantum Raychaudhuri equation
• A question mark on the equivalence of Einstein and Jordan frames
• On the modification of Hamiltonians' spectrum in gravitational quantum mechanics
• A singularity-free space-time
• Early dark energy in $k$-essence
• Formation of caustics in k-essence and Horndeski theory
• Focusing of geodesic congruences in an accelerated expanding Universe
• The Hawking temperature in the context of dark energy
• Atypical k-essence cosmologies
• Anisotropic k-essence cosmologies
• Is the DBI scalar field as fragile as other $k$-essence fields?
• DBI models for the unification of dark matter and dark energy
• Comparison of Frames: Jordan vs Einstein Frame for a Non-minimal Dark Energy Model
• Gravitational Collapse for the K-essence Emergent Vaidya Spacetime
• The Hawking Temperature in the context of Dark Energy for Reissner-Nordstrom and Kerr background
• K-essence Emergent Spacetime as Generalized Vaidya Geometry
• The Hawking temperature in the context of dark energy for Kerr-Newman and Kerr-Newman-AdS backgrounds
• A 1-dimensional hydrodynamic model for accretion, cooling and heating of gas in dark matter halos from $z=6$ to $z=0$
• Raychaudhuri equation in scalar-tensor theory
• Covariant Generalisation of Codazzi-Raychaudhuri and Area Change Equations for Relativistic Branes
• A comparison between the Jordan and Einstein Frames in Brans-Dicke theories with torsion

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• NEC violation in $f(\bar{R},\bar{T})$ gravity in the context of a non-canonical theory via modified Raychaudhuri equation
• Null geodesic structure for the Barriola-Vilenkin spacetime via $k$-essence
• Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework
• Primordial Cosmology of an Emergent-like Universe from Modified Gravity: Reconstruction and Phenomenology Optimization with a Genetic Algorithm
• Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory
• From Geometry to Observation: Gravitational Waves and the Raychaudhuri Equation
• Geometric formulation of $k$-essence and late-time acceleration