Eur. Phys. J. Plus (2012) 127: 30
https://doi.org/10.1140/epjp/i2012-12030-2

Regular Article

Dynamical system analysis of interacting variable modified Chaplygin gas model in FRW universe

Department of Mathematics, Bengal Engineering and Science University, 711 103, Shibpur, Howrah, India

^* e-mail: bhadra.jhumpa@gmail.com

Received: 30 December 2011
Revised: 4 February 2012
Accepted: 7 February 2012
Published online: 14 March 2012

Abstract

In this work, we have considered the interacting dynamical model taking the variable modified Chaplygin gas (VMCG) which plays as dark energy coupled to cold dark matter in the flat FRW universe. For the VMCG equation of state, we have chosen B(a) = B ₀ a ⁻ⁿ . Since the nature of dark energy and dark matter is still unknown, it is possible to have an interaction between them and phenomenologically we choose the interaction term Q = 3cH ρ, where c is the coupling parameter. We have converted all the equations in the dynamical system of equations by considering the dimensionless parameters and seen the evolution of the corresponding autonomous system. The feasible critical point has been found and for the stability of the dynamical system about the critical point, we linearize the governing equation around the critical point. We found that there exists a stable scaling (attractor) solution at late times of the Universe and found some physical range of n and the interaction parameter c. We have shown that for our calculated physical range of the parameters, the Universe explores upto quintessence stage. The deceleration parameter, statefinder parameters, Hubble parameter and the scale factor have been calculated around the critical point. Finally, some consequences around the critical point, i.e., the distance measurement of the Universe like lookback time, luminosity distance, proper distance, angular diameter distance, comoving volume, distance modulus and probability of intersecting objects have been analyzed before and after the present age of the Universe.