[Paper Review] Modified Chaplygin Gas Cosmology with Bulk Viscosity in D Dimensions

H. Benaoum|arXiv (Cornell University)|Jan 30, 2014

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes a viscous modified Chaplygin gas (MCG) model in D-dimensional spacetime, analyzing its cosmological dynamics using analytical and numerical methods. It introduces a novel statefinder {r, s} diagnostic in D dimensions, recovering standard 4D results when D=4, and demonstrates that viscosity significantly alters the evolution of statefinder parameters, offering a refined tool for distinguishing MCG models via geometric diagnostics.

ABSTRACT

We investigate the viscous modified Chaplygin gas cosmological model. Solutions for different values of the viscosity parameter are obtained using both analytical and numerical methods. We have calculated the deceleration and defined {\em newly} statefinder $\{r, s \}$ pair in D dimensions. It is shown that when $D=4$, the usual statefinder parameters are recovered. Furthermore, we apply the statefinder diagnostic to the MCG model with and without viscosity in $D$ dimensions and explore these parameters graphically.

Motivation & Objective

• To extend the modified Chaplygin gas model to D-dimensional spacetime with bulk viscosity.
• To derive analytical and numerical solutions for the cosmological evolution under varying viscosity parameters.
• To define and compute a new statefinder {r, s} diagnostic pair in D dimensions.
• To compare the viscous and non-viscous MCG models using graphical analysis of statefinder parameters.
• To recover the standard 4D statefinder parameters as a limiting case when D=4.

Proposed method

• Formulating the energy-momentum tensor of the viscous MCG in D-dimensional spacetime with a bulk viscosity coefficient.
• Deriving the modified Friedmann equations in D dimensions under the assumption of a spatially flat, homogeneous, and isotropic universe.
• Applying analytical techniques to solve the resulting differential equations for the scale factor under different viscosity regimes.
• Using numerical methods to solve the cosmological equations for various values of the viscosity parameter and D.
• Defining the statefinder pair {r, s} in D dimensions using higher-order derivatives of the scale factor.
• Graphically comparing the evolution of {r, s} for viscous and non-viscous MCG models across different D values.

Experimental results

Research questions

• RQ1 How does bulk viscosity affect the cosmological evolution of the modified Chaplygin gas in D-dimensional spacetime?
• RQ2 What is the form of the statefinder {r, s} diagnostic in D dimensions, and how does it generalize the standard 4D case?
• RQ3 How do the statefinder parameters differ between viscous and non-viscous MCG models in D dimensions?
• RQ4 Can the D-dimensional statefinder diagnostic distinguish between viscous and non-viscous MCG models more effectively than standard diagnostics?
• RQ5 Does the standard 4D statefinder result emerge as a special case when D=4 in the D-dimensional formulation?

Key findings

• The statefinder {r, s} pair is successfully generalized to D-dimensional spacetime, with a well-defined mathematical formulation.
• When D=4, the derived statefinder parameters reduce to the standard 4D statefinder diagnostics, confirming consistency with established results.
• Viscosity alters the trajectories of the {r, s} parameters in the statefinder plane, indicating a distinct dynamical behavior compared to the non-viscous case.
• Numerical solutions show that the viscosity parameter significantly influences the evolution of the scale factor and the deceleration parameter in D dimensions.
• Graphical analysis reveals that the viscous MCG model exhibits different statefinder trajectories, suggesting improved distinguishability from other dark energy models.
• The D-dimensional formulation provides a framework for testing cosmological models beyond four dimensions, with viscosity as a key dynamical modifier.