Chaplygin gas dominated anisotropic brane world cosmological models

M. K. Mak and T. Harko

Phys. Rev. D 71, 104022 – Published 20 May 2005

Abstract

We present exact solutions of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi type I geometry, with a generalized Chaplygin gas as matter source. The generalized Chaplygin gas, which interpolates between a high density relativistic era and a nonrelativistic matter phase, is a popular dark energy candidate. For a Bianchi type I space-time brane filled with a cosmological fluid obeying the generalized Chaplygin equation of state the general solution of the gravitational field equations can be expressed in an exact parametric form, with the comoving volume taken as parameter. In the limiting cases of a stiff cosmological fluid, with pressure equal to the energy density, and for a pressureless fluid, the solution of the field equations can be expressed in an exact analytical form. The evolution of the scalar field associated to the Chaplygin fluid is also considered and the corresponding potential is obtained. The behavior of the observationally important parameters like shear, anisotropy, and deceleration parameter is considered in detail.

Received 23 February 2005

DOI:https://doi.org/10.1103/PhysRevD.71.104022

Authors & Affiliations

M. K. Mak^* and T. Harko^†

Department of Physics, The University of Hong Kong, Pok Fu Lam Road, Hong Kong

^*Electronic address: mkmak@vtc.edu.hk
^†Electronic address: harko@hkucc.hku.hk

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Vol. 71, Iss. 10 — 15 May 2005

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Images

Figure 1
Expansion scalar $θ$ of the Chaplygin gas filled Bianchi type I brane universe as a function of the dimensionless time parameter $τ$ for $γ = 1 / 3$ , $α = 0.5$ and $b = 0.01$ (solid curve), $b = 0.02$ (dotted curve), $b = 0.03$ (dashed curve) and $b = 0.04$ (long dashed curve). We have assumed a vanishing effective cosmological constant on the brane, $λ_{0} = 0$ . The relation between $τ$ and the cosmic time $t$ is $t \approx 10^{17} h^{- 1} \times τ s^{- 1}$ , $0.5 \leq h \leq 1$ .Reuse & Permissions
Figure 2
Anisotropy parameter $A$ of the Chaplygin gas filled Bianchi type I brane universe as a function of the dimensionless time parameter $τ$ for $γ = 1 / 3$ , $α = 0.5$ , and $b = 0.01$ (solid curve), $b = 0.011$ (dotted curve), $b = 0.012$ (dashed curve), and $b = 0.013$ (long dashed curve). We have assumed a vanishing effective cosmological constant on the brane, $λ_{0} = 0$ . The relation between $τ$ and the cosmic time $t$ is $t \approx 10^{17} h^{- 1} \times τ s^{- 1}$ , $0.5 \leq h \leq 1$ .Reuse & Permissions
Figure 3
Shear scalar $σ^{2}$ of the Chaplygin gas filled Bianchi type I brane universe as a function of the dimensionless time parameter $τ$ for $γ = 1 / 3$ , $α = 0.5$ , and $b = 0.01$ (solid curve), $b = 0.02$ (dotted curve), $b = 0.03$ (dashed curve), and $b = 0.04$ (long dashed curve). We have assumed a vanishing effective cosmological constant on the brane, $λ_{0} = 0$ . The relation between $τ$ and the cosmic time $t$ is $t \approx 10^{17} h^{- 1} \times τ s^{- 1}$ , $0.5 \leq h \leq 1$ .Reuse & Permissions
Figure 4
Deceleration parameter $q$ of the Chaplygin gas filled Bianchi type I brane universe as a function of the dimensionless time parameter $τ$ for $γ = 1 / 3$ , $α = 0.5$ , and $b = 0.01$ (solid curve), $b = 0.015$ (dotted curve), $b = 0.02$ (dashed curve), and $b = 0.025$ (long dashed curve). We have assumed a vanishing effective cosmological constant on the brane, $λ_{0} = 0$ . The relation between $τ$ and the cosmic time $t$ is $t \approx 10^{17} h^{- 1} \times τ s^{- 1}$ , $0.5 \leq h \leq 1$ .Reuse & Permissions
Figure 5
Chaplygin gas associated scalar field $ϕ$ evolution on the Bianchi type I brane universe as a function of the dimensionless time parameter $τ$ for $γ = 1 / 3$ , $α = 0.5$ , and $b = 0.005$ (solid curve), $b = 0.01$ (dotted curve), $b = 0.015$ (dashed curve), and $b = 0.02$ (long dashed curve). We have assumed a vanishing effective cosmological constant on the brane, $λ_{0} = 0$ . The relation between $τ$ and the cosmic time $t$ is $t \approx 10^{17} h^{- 1} \times τ s^{- 1}$ , $0.5 \leq h \leq 1$ .Reuse & Permissions
Figure 6
The potential $U (ϕ)$ of the Chaplygin gas associated scalar field as a function of the scalar field $ϕ$ for $γ = 1 / 3$ , $α = 0.5$ , and $b = 0.005$ (solid curve), $b = 0.01$ (dotted curve), $b = 0.015$ (dashed curve), and $b = 0.02$ (long dashed curve). We have assumed a vanishing effective cosmological constant on the brane, $λ_{0} = 0$ .Reuse & Permissions

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