Signature flipping of isotropic homogeneous space-time with holographic dark energy in $f\left(G\right)$gravity

Highlights

• The piece of the work is achieved towards power and exponential inflation cosmologies.

• The perceived cosmologies are singular and singularity observed at an initial epoch.

• The Gauss-Bonnet energy density is unity while Gauss-Bonnet matter-energy density is null i.e. not observed in the model.

• The equation of state parameter of both the models are affected by the value of constant $n$.

• Gauss-Bonnet term in linear and quadratic model is just like as cosmological constant which described $\Lambda \mathrm{CDM}$model.

Abstract

Present investigation devoted to the dynamical study of isotropic and homogeneous FRW space-time filled with a Holographic dark energy fluid with cosmic string in the framework of numerous form of $f\left(G\right)$gravity models say linear, quadratic and inverse model. We determine the aspects of the model by considering the hybrid expansion law for the average scale factor that yields power and exponential inflation cosmologies, in its special cases. As per the observation, the model is singular and singularity observed at an initial epoch. The contribution of Gauss-Bonnet term in linear and quadratic model is just like as cosmological constant hence for whole expansion it is $\Lambda \mathrm{CDM}$model which supports and resembles with the observational fact that the usual matter is about 4% and the dark energy occupies near about 73% of the energy also the results with several high precision observational experiments, especially the Wilkinson Microwave Anisotropic Probe (WMAP) satellite experiment.

Introduction

An observational evidences of recent observations like SNe-Ia Supernova, CMBR, LSS, and WMAP favors that the universe is spatially flat and at late-time it has an accelerating expansion which is not fit within the framework of Einstein’s General Theory of Relativity (GTR). The proposals that have been put forward to explain this observed phenomenon can be classified into one, an exotic component with negative pressure so called Dark Energy which introduce into GTR. A many candidates of dark energy are present among which Holographic dark energy has recently been studied due to the property that the event horizon as the cosmological scale and the model is consistent with the cosmological observations and the correspondence between the quintessence, tachyon, k-essence and dilation dark energy models etc (Li, 2004, Granda, Oliveros, 2009). Debnath (2012), Malekjani (2013), Sarkar (2014), Bhoyar et al. (2018) are the some researchers who have investigated several aspects of holographic dark energy with different cosmological models.

Another category to obtain an accelerating expansion of the Universe is the change in the gravity law through the modification of action in GTR. Various modification in the action of GTR is present, out of which one replaces the Ricci scalar R in the Einstein-Hilbert action by an arbitrary function of R belongs to the well-known $f\mathrm{(}R\mathrm{)}$modified gravity. Vacuum solution in cylindrically symmetric space-time in the same gravity studied by Azadi et al. (2008) along with many authors have discussed some features of same gravity in Sharif and Yousaf (2014), Bhoyar et al. (2016a), Chirde and Shekh (2016), Chirde and Shekh (2017). Second one is the gravitational action includes an arbitrary function of the Ricci scalar and trace of the stress-energy tensor known as$f\mathrm{(}R,T\mathrm{)}$gravity. An authors who have investigated the aspects of cosmological models in this gravity is Sahoo et al. (2014), Bhoyar, Chirde, Shekh, 2015, Bhoyar, Chirde, Shekh, 2016b. Another one way to look at the theory beyond GTR is the Teleparallel Gravity which uses the Weitzenbock connection in place of the Levi-Civita connection and so it has no curvature but has torsion which is responsible for the acceleration of the Universe. Some relevant works in this gravity are presented by Bohmer et al. (2011), Chirde, Shekh, 2015a, Chirde, Shekh, 2015b, Bhoyar et al. (2017).

Another theory that has gained popularity in the last few years is Gauss-Bonnet gravity (Nojiri, Odintsov, 2005, Cognola, Elizalde, Nojiri, Odintsov, Zerbini, 2007). It is also known as the$f\mathrm{(}G\mathrm{)}$theory of gravity, where$f\mathrm{(}G\mathrm{)}$is a generic function of the Gauss-Bonnet invariant G which is put forward that this theory may describe the late-time cosmic acceleration by passing the solar system tests for some specific choices of $f\left(G\right)$gravity models. Some interesting work has been done so far in this theory. Recently, Nojiri and Odintsov (2007) developed the reconstruction techniques for$f\mathrm{(}G\mathrm{)}$gravity and it was demonstrated that how cosmological sequence of matter dominance, deceleration-acceleration transition and acceleration era could emerge by using a modified theory. Fayaz et al. (2015) investigated power-law solutions with an anisotropic background in$f\mathrm{(}G\mathrm{)}$gravity and it was concluded that Bianchi type-I power-law solutions only existed for some special choices of $f\mathrm{(}G\mathrm{)}$gravity models. Abbas et al. (2015) gave the possibility for the existence of anisotropic compact stars in$f\left(G\right)$gravity. Sharif and Fatima (2016) argued the role of Gauss-Bonnet term in the late time accelerated phases of the universe.