Abstract

In this paper, we study two different models of dark energy based on Chaplygin gas equation of state. The first model is the variable modified Chaplygin gas while the second one is the extended Chaplygin gas. Both models are considered in the framework of higher order $f(R)$ modified gravity. We also consider the case of time varying gravitational constant $G$ and $\Lambda$ for both models. We investigate some cosmological parameters such as the Hubble, the deceleration and the equation of state parameters. Then we showed that the model that we considered, extended Chaplygin gas with time-dependent $G$ and $\Lambda$, is consistent with the observational data. Finally we conclude with the discussion of cosmological perturbations of our model.

Highlights

  • In this paper, we study two different models of dark energy based on the Chaplygin gas equation of state

  • Cosmological and astrophysical data obtained thanks to the Supernovae Ia (SNeIa), the Cosmic Microwave Background (CMB) radiation anisotropies, the Large Scale Structure (LSS) and X-ray experiments provide strong evidence supporting a phase of accelerated expansion of the present day universe [1,2,3,4,5,6,7,8,9,10,11,12,13]

  • The cosmological constant, which solves the equation of state (EoS) parameter ω = −1, represents the simplest candidate proposed to explain the accelerated expansion of the universe

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Summary

Introduction

Cosmological and astrophysical data obtained thanks to the Supernovae Ia (SNeIa), the Cosmic Microwave Background (CMB) radiation anisotropies, the Large Scale Structure (LSS) and X-ray experiments provide strong evidence supporting a phase of accelerated expansion of the present day universe [1,2,3,4,5,6,7,8,9,10,11,12,13]. Instead, according to the cosmic coincidence problem, the vacuum energy and Dark Matter (DM) models are nearly equal nowadays, they have evolved independently and from different mass scales (which is a particular fortuity if no interaction exists between them). A successful model to describe DE is based on the Chaplygin gas (CG) equation of state [26,27] and yields the Generalized Chaplygin Gas (GCG) model [28,29]. It initially emerged in cosmology from string theory point of view [30,31,32].

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The models
Numerical results with constant G and
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Numerical results with varying G and
Variable modified Chaplygin gas model
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Statefinder diagnostics
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