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Universe with quadratic equation of state: A dynamical systems perspective

Rakesh Raushan

Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India

E-mail Address: rakesh.raushan4@bhu.ac.in

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Ashutosh Singh

Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur, India

E-mail Address: theprabhu.09@gmail.com

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R. Chaubey

http://orcid.org/0000-0003-1912-6677

Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India

E-mail Address: rchaubey@bhu.ac.in

Corresponding author.

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, and

T. Singh

Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India

E-mail Address: drtrilokisingh@yahoo.co.in

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https://doi.org/10.1142/S0219887820500644Cited by:20 (Source: Crossref)

Abstract

This paper deals with the dynamical systems analysis of Friedmann–Robertson–Walker (FRW) model of the Universe in the framework of general relativity with quadratic equation of state and bulk viscosity. The evolution equations are transformed into an autonomous system of differential equations using suitable variables transformation. Stability analysis of cosmological models with quadratic equation of state parameter are discussed in detail in two different scenarios viz, first Universe filled with barotropic fluid and second filled with bulk viscous fluid. The nature of critical points is analyzed for both cases accordance with respective eigenvalues. We have also analyzed the stable attractor for both cases and examined their properties from the point of cosmological view.

Keywords:

AMSC: 83F05, 83C05, 37N20

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