Dynamical analysis with thermodynamic aspects of anisotropic dark energy bounce cosmological model in f(R, G) gravity

doi:10.1016/j.newast.2020.101464

New Astronomy

Volume 83, February 2021, 101464

https://doi.org/10.1016/j.newast.2020.101464 Get rights and content

Highlights

•
The model is purely accelerating corresponds to $0 = q = - 1$ .
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The model is fully engaged with both matter which exist initially for short expansion and dark energy dominated era and rests existing in quintessence dominated era.
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For sufficiently large time derived model forecasts that the anisotropy of the model will damp out and the Universe will turn out to be isotropic one.
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Quintessence dominated era the temperature and entropy density of anticipated model are positive definite.

Abstract

Present analysis dedicated to the dynamical investigation of anisotropic dark energy LRS Bianchi type-I cosmological model in the context of modified gravity in which Langrangian be the arbitrary function of Ricci scalar and Gouss-Bonnet invariant say f(R, G) gravity in the way of anisotropic fluid. The classification of the field equations towards $f (R, G) = f_{0} R^{m} G^{1 - m}$ make available that the model is purely accelerating corresponds to $0 \leq q \leq - 1$ . We govern the features of the derived cosmological model in view of the hybrid law inflation in bounce form (which involve power and de-Sitter cosmology) for the average scale factor. Also discussed the singularity of the model with the help of curvature of the model. It is observed that the model is fully engaged with both matter which exist initially for short expansion and dark energy dominated era and rests existing in quintessence dominated era and for sufficiently large time derived model forecasts that the anisotropy of the model will damp out and the Universe will turn out to be isotropic one and also observed that for quintessence dominated era the temperature and entropy density of anticipated model are positive definite along with some physical and kinematical parameters of the bounce model is also discussed in details.

Introduction

Modern observational modifications, which take in account of the supernovae cosmology (SNe-Ia) (Riess, et al., 1998, Perlmutter, et al., 1999) have delivered the major suggestions for the cosmic speeding up of the model, along with some interpretations like those of the distant supernovae, large scale structure (LSS) (Tegmark, 2004) fluctuations of the cosmic microwave background radiation (CMBA), the wilkinson microwave anisotropy probe (WMAP) (Knop, 2003), the Sloan Digital Sky Survey (SDSS) (Seljak, 2005) and the Chandra X-ray observatory (Allen, 2004) suggest that our universe is flat in nature and undergo an accelerated expansion. Such a behavior of the model is due to two types: (i) As, the major part of the universe filled with dark energy and dark matter. There are more than a few dark energy models which can be renowned by their equation of state parameter ( $ω = p_{d e} / ρ_{d e}$ ). Astrophysical data indicate that, this equation of state parameter ω is very close to -1. The case $ω = - 1$ agree with the cosmological constant, which is to be sure the vacuum energy and be the simplest and most popular contestant for dark energy (Weinberg, 1989, Peebles, Ratra, 2003). The case $ω < - 1$ related to the phantom dark energy model (Caldwell, 2002) and for $- 1 < ω < - 1 / 3$ the dark energy is described by Quintessence (Ratra, Peebles, 1988, Wetterich, 1988) and (ii) By modifying the principal of General Relativity theory called as Modified Gravity. A various modified gravities are presented such that, one f(R) and f(R, T) gravity obtained by replacement of Ricci scalar with an arbitrary function of the Ricci scalar and function of both Ricci scalar and trace of energy tensor in the gravitational action (Capozziello, Martin-Moruno, Rubano, 2008, Azadi, Momeni, Nouri-Zonoz, 2008, Harko, Lobo, Nojiri, Odintsov, 2011, Sharif, Zubair, 2012, Chaubey, Shukla, 2013, Sahoo, Mishra, ChakradharReddy, 2014, Chirde, Shekh, 2015, Chirde, Shekh, 2016, Chirde, Shekh, 2016, Bhoyar, Chirde, Shekh, 2015, Moraes, Sahoo, Taori, Sahoo, 2019, Mishra, Tarai, Tripathy, 2018, Mishra, Ribeiro, Moraes, 2019).

The theory to look beyond the General Relativity is the Teleparallel Gravity which has no curvature. In this theory the acceleration of the model occurred due to torsion. More or less significant works in Teleparallel Gravity has been done by Sharif and Rani (2011), Bhmer et al. (2011), Chirde and Shekh (2014), Nashed (2015), Bhoyar et al. (2017). Very recently Shekh and Chirde (2019) have inspected the homogeneous and anisotropic cosmological model in various theories of gravitation say General Relativity, f(R) and f(T) gravity with the source involving hydrodynamics. It is detected that the hydrodynamics fluid in General Relativity is fully employed with quintessence dark energy whereas the model shows both matter and dark energy dominated era in f(R) gravity and remains present in matter dominated era while in f(T) gravity, the model initially shows standard ΛCDM model and with the expansion it is fully occupied with quintessence dark energy fluid. Recent development in the General Relativity theory is acquaint with Lovelock invariants such as function of Ricci scalar the Gauss-Bonnet scalar. The theory which combines the Ricci scalar and Gauss-Bonnet scalar called f(R, G) theory. La and Sez-Gmez (2012) accomplished the deep analysis on the stability of some important cosmological solutions which is not only influence to constrain the form of the gravitational action, but also further help in better accepting of the perturbations comportment in f(R, G) theory which will lead to a more particular exploration of the full spectrum of cosmological perturbations. Makarenko et al. (2013) established the phantom type cosmological model by reconstructing f(R, G) gravity which do not lead to a future singularity. DeLaurentis et al. (2015) discussed cosmological inflation in the framework of f(R, G) theory and analyzed the fact that this f(R, G) theory can dissipate all the curvature budget interconnected to curvature invariants without allowing for derivatives of R, R_μν, $R_{σ μ ν}^{λ}$ etc. in the action. Shamir and Komal (2017) investigated the energy bounds in general four types of f(R, G) gravity with anisotropic locally rotationally symmetric Bianchi type-I background by obtaining energy conditions and investigated the viability of the above mentioned models using the Hubble, deceleration, jerk and snap parameters and observed that for first two f(R, G) gravity models, null energy condition (NEC), weak energy condition (WEC) and strong energy condition (SEC) are satisfied under suitable values of anisotropy and model parameters involved moreover, SEC is violated for the third and fourth models which predicts the cosmic expansion whereas Shamir and Zia (2017) highlighted the materialization of anisotropic compact stars namely Her X1, SAX J 1808–3658, and 4U 1820-30 in the context of f(R, G) theory of gravity and have shown that all three stars behave as usual as for positive values of the f(G) model parameter n. Recently, Odintsov et al. (2019) proposed a unified model, in the context of which the early and late-time dynamics are controlled by the f(R, G) gravity by producing inflation and the dark energy era, while the intermediate era is approximately identical. Also, analyzed the power spectrum of the primordial curvature perturbations corresponding to the unified f(R, G) gravity which is nearly scale invariant and compatible with the latest observational data constraints.

Section snippets

Basics of f(R, G) gravity with anisotropic dark energy

The most general action for f(R, G) gravity is given as (Shamir, Zia, 2017, Odintsov, Oikonomou, Banerjee, 2019) $S = \frac{1}{2 k} \int d^{4} x \sqrt{- g} (R + f (G)) + S_{M} (g^{i j}, φ),$ where S_M(g^ij, φ) is the matter action, R is Ricci scalar and G is Gauss-Bonnet invariant defined by $G = R^{2} - 4 R_{α β} R^{α β} + R_{α β σ ν} R^{α β σ ν},$ where, the notations R_αβ and R_αβσν are occupied for the Ricci and Riemann tensors respectively.

Variation of the standard action (1) with respect to the metric gives us the following gravitational field equation: $R_{μ ν} - \frac{1}{2} g_{μ ν} R = k T_{μ ν}^{m a t} + Σ_{μ ν},$

Metric with kinamatics and field quations

Let us first establish the equations of motion of a set of diagonals using the Cartesian coordinate metric, to describe the model of LRS Bianchi type-I, as $d s^{2} = d t^{2} - a_{1}^{2} d x^{2} - b_{1}^{2} (d y^{2} + d z^{2}),$ where a₁ and b₁ are the metric potentials, which are the functions of cosmic time t measure in Gyr.

So many authors who have considerd the above said model due to its physical importance that it is homogeneous and anisotropic, from which the process of isotropization of the universe is studied through the passage of

Solutions of field equations

As the field equations (15) to (17) are the three equations with six unknown parameters. In order to obtain exact solution of the field equations many authors assume various physical or mathematical conditions. From (12) and (13), if we consider the ratio of expansion scalar with shear scalar ( $\frac{θ^{2}}{σ^{2}}$ ) it comes out to be constant. Hence we say that θ²∝σ² which leads to ${(\frac{\dot{a_{1}}}{a_{1}} + 2 \frac{\dot{b_{1}}}{b_{1}})}^{2} \propto \frac{1}{3} {(\frac{{\dot{a}}_{1}}{a_{1}} - \frac{{\dot{b}}_{1}}{b_{1}})}^{2} .$ Solving above Eq. (18) for the relation between a₁ and b₁ one we get, $a_{1} = b_{1}^{n}$ Above Eq. (19), provide

Conclusion

In the dynamical investigation of spatially homogeneous and anisotropic locally rotationally symmetric Bianchi type-I cosmological model with anisotropic dark energy source within the framework of f(R, G) theory of gravity at $t = 0,$ the model is constant and metric potentials never approaches to vanishing value, hence the model represent regular bounce (where at which the scale factor never vanish) model also it is not possible that the model shows isotropy except for $n = 1$ .

Kinematical analysis:

The

Author Statement

All the points mentioned by the referee are covered and revision completed along with I, Dr. S. H. Shekh the author of the manuscript is very much grateful to the honorary referee and the editor for the illuminating suggestions that have significantly improved our work in terms of research quality and presentation.

Declaration of Competing Interest

From the author no conflict of interest to declare.

Acknowledgments

We are very much grateful to the honorary referee and the editor for the illuminating suggestions that have significantly improved our work in terms of research quality and presentation.

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Dynamical analysis with thermodynamic aspects of anisotropic dark energy bounce cosmological model in f(R, G) gravity

Highlights

Abstract

Introduction

Section snippets

Basics of f(R, G) gravity with anisotropic dark energy

Metric with kinamatics and field quations

Solutions of field equations

Conclusion

Author Statement

Declaration of Competing Interest

Acknowledgments

Phys. Lett. Sect. B

Phys. Lett. Sect. B

Phys. Lett. Sect. B

Phys. Lett. Sect. B.

Astrophys. J.

Generalized second law of thermodynamics in scalar-tensor gravity

Phys. Rev. D

Cosmology with hybrid expansion law: scalar field reconstruction of cosmic history and observational constraints

J. Cosmol. Astropart. Phys.

Constraints on dark energy from Chandra observations of the largest relaxed galaxy clusters

Mon. Not. R. Astron. Soc.

Interacting holographic polytropic gas model of dark energy with hybrid expansion law in Bianchi type-VI0 space-time

Astrophys. Space Sci.

Equation of state for dark energy in f(t) gravity

J. Cosmol. Astropart. Phys.

Existence of relativistic stars in f(t) gravity

Class. Quantum Gravity

Non-static plane symmetric cosmological model with magnetized anisotropic dark energy by hybrid expansion law in f(r, t) gravity

Int. J. Adv. Res.

Stability of accelerating universe with linear equation of state in f(t) gravity using hybrid expansion law

Astrophysics.

Generalized Bekenstein-Hawking system: logarithmic correction

Eur. Phys. J. C

On anisotropic dark energy

Mod. Phys. Lett. A

A new class of Bianchi cosmological models in f(r, t) gravity

Astrophys. Space Sci.

Barotropic bulk viscous FRW cosmological model in teleparallel gravity

Bulg. J. Phys.

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Isotropic background for interacting two fluid scenario coupled with zero mass scalar field in modified gravity

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J. Astrophys. Astron.

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Astrophys J.

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Commun Math Phys.

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Eur. Phys. J. C

Generalized second law of thermodynamics in f(t) gravity

J. Cosmol. Astropart. Phys.

New constraints on ωM, ωΛ, and ω from an independent set of 11 high-redshift supernovae observed with the hubble space telescope

Astrophys. J.

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Phys. Rev. D

New constraints on ω_M, ω_Λ, and ω from an independent set of 11 high-redshift supernovae observed with the hubble space telescope