Aspects of some Rastall cosmologies
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Aspects of some Rastall cosmologies Ashutosh Singha
, Krishna C. Mishra
Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur, India Received: 12 June 2020 / Accepted: 16 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Rastall gravity paradigm producing mechanism for realizing singular and nonsingular cosmologies has been investigated. A solution in Rastall gravity with flat spatial sections which exhibits constant deceleration parameter has been obtained. The study of bouncing scenario in Rastall gravity infers that this scenario may satisfy an affine equation of state during the bounce. Moreover, the physical, kinematic and thermodynamic aspects of the model are discussed in detail. Furthermore, the Raychaudhuri-like equation and other field equations for homogeneous and anisotropic metrics are also derived. Pacs Nos 98.80.-k; 98.80.Jk; 95.30.Sf; 04.50.Kd
1 Introduction The late-time accelerated expansion of universe [1,2] may be explained by inclusion of exotic form of energy (called as dark energy), having very high negative pressure which may be a small, positive cosmological constant with equation of state parameter (γ ) equal to −1. The observational data constrain γ ∼ −1, but, in principle, different forms of dark fluids (quintessence, k-essence, phantom, quintom,...) satisfying a suitable equation of state are allowed [3,4]. However, the existence and nature of dark energy still remain open question. In another approach to explain the cosmic accelerated expansion of universe, alternative theories of gravity are available in the literature [5]. General relativity (GR) suffers a bunch of cosmological issues such as horizon problem, flatness problem, entropy problem, singularity problem, to name a few. Inflationary scenario [6,7] solves various cosmological problems, but the initial singularity problem still remains unsolved [8]. In other words, the problem suffered by primordial inflation is that inflationary space-time is past incomplete due to the presence of a space-like singularity. One possible alternative of inflationary model is the bouncing model of universe which solves the initial singularity problem. In view of historical perspective, Tolman [9] was the first who suggested the possibility of re-expansion of a collapsing closed universe. In the bouncing models, the big-bang singularity is replaced with a smooth transition from contraction to expansion (big-bounce) scenario. In standard model, the bounce in Friedmann–Robertson– Walker (FRW) space-time is not possible if active gravitational mass is positive, that is, ρ + 3 p > 0. Violation of the condition ρ + 3 p > 0 is not an exclusive scenario in bouncing GR models only. Quantum fields as well as classical fields can also violate the condition
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ρ + 3 p > 0. Old or new inflation (but not the eternal or chaotic inflatio
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