Bianchi Type-I Dark Energy Cosmology with Power-Law Relation in Brans-Dicke Theory of Gravitation

S D Katore,D V Kapse

doi:10.1155/2018/2854567

Abstract

We have studied the interacting and non-interacting dark energy and dark matter in the spatially homogenous and anisotropic Bianchi type-I model in the Brans-Dicke theory of gravitation. The field equations have been solved (i) by using power-law relation and (ii) by assuming scale factor in terms of redshift. Here we have considered two cases of an interacting and non-interacting dark energy scenario and obtained general results. It has been found that for suitable choice of interaction between dark energy and dark matter we can avoid the coincidence problem which appears in the ΛCDM model. Some physical aspects and stability of the models are discussed in detail. The statefinder diagnostic pair, i.e., {r,s}, is adopted to differentiate our dark energy models.

Highlights

The recent cosmological observational data of Type Ia Supernovae (SNeIa) (Riess et al [1]; Perlmutter et al [2]), Cosmic Microwave Background (CMB) (Bennett et al [3]; Spergel et al [4]), Large Scale Structure (LSS) (Tegmark et al [5, 6]), the Sloan Digital Sky Survey (SDSS) (Seljak et al [7], AdelemanMcCarthy et al [8]), Wilkinson Microwave Anisotropy Probe (WMAP) (Knop et al [9]), and Chandra X-ray observatory (Allen et al [10]) strongly suggests that our universe is dominated by a component with large negative pressure called dark energy (DE)
To find the solution of coincidence problem, we have considered an energy transfer from dark energy to dark matter by assuming Q > 0, which ensures that the second law of thermodynamics is fulfilled (Pavon and Wang [55])
In order to get an accurate analysis to discriminate among the dark energy models Sahni et al [58] proposed a new geometrical diagnostic named as statefinder pair {r, s} which is constructed from scale factor (a) and its derivative up to third order

Summary

Introduction

The recent cosmological observational data of Type Ia Supernovae (SNeIa) (Riess et al [1]; Perlmutter et al [2]), Cosmic Microwave Background (CMB) (Bennett et al [3]; Spergel et al [4]), Large Scale Structure (LSS) (Tegmark et al [5, 6]), the Sloan Digital Sky Survey (SDSS) (Seljak et al [7], AdelemanMcCarthy et al [8]), Wilkinson Microwave Anisotropy Probe (WMAP) (Knop et al [9]), and Chandra X-ray observatory (Allen et al [10]) strongly suggests that our universe is dominated by a component with large negative pressure called dark energy (DE). Rao et al [38], Sarkar [39, 40], Katore et al [41], Singh and Dewri [42], and Reddy et al [43, 44] have studied the cosmological models in Brans-Dicke theory of gravitation. Motivated by the above investigations, in this paper, we have extended the work of Amirhashchi et al [33] in Brans-Dicke theory of gravitation This is relevant because of the fact that scalar field plays an important role in the discussion of DE models. We have studied the interacting and non-interacting dark energy and dark matter in the spatially homogenous and anisotropic Bianchi type-I model in the Brans-Dicke theory of gravitation. The statefinder diagnostic pair, i.e., {r, s}, is adopted to characterize different phases of the universe in Section 6 and Section 7 contains some concluding remarks

The Metric and BD Field Equations

Solutions of Field Equations

Physical Acceptability and Stability Analysis

Statefinder Parameters

Conclusion