Stability in a class of quartessence models

Abstract

Quartessence cosmological models with exponential and logarithmic equation of state are investigated using dynamical systems methods. We focus our analysis on the stability of these models.Keywords: Cosmology; Quartessence; Dynamical systems; Stability Progress in observational cosmology in the past few years suggests that the universe is dominated by two unknown components, namely, dark matter and dark energy. These two components have properties that are quite different from all the ordinary matter we know do exist in the physical world. Dark matter is a pressureless component, very important for structure formation, while dark energy, a negative pressure component, is responsible for the cosmic acceleration. From the point of view of simplicity, it would be interesting to describe both components with a single equation of state (EOS). This idea is the main motivation for quartessence models that try to unify dark matter and dark energy in a single component [1]. The most studied quartessence model is the Chaplygin gas model [2], [3]. Nevertheless other EOS for quartessence exist as, for instance, those suggested in the work by Reis et al. [4].In this work, we employ the methods of qualitative theory of dynamical system [5], [6] to study quartessence models with exponential and logarithmic EOS. Recently, M. Szydlowski and W. Czaja [7] investigated the structural stability of FRW cosmology with generalized Chaplygin gas. Here, we extend their analysis to other quartessence cosmologies.This paper is organized as follows. In Section II, we briefly describe the dynamical systems techniques we use to analyze quartessence cosmological models. In Section III we analyze the critical points of the considered quartessence models. In Section IV we investigate the stability of the system using the Lyapunov's method. Finally, in Section V we discuss the results. I. STUDY OF QUARTESSENCE MODELS WITH DYNAMICAL SYSTEMSThe main goal of quartessence cosmological models is to describe with a single equation of state, dark matter and dark energy. The prototype quartessence model is the generalized Chaplygin Gas (GCG) [3]. It is easy to show that for very high redshift these models behave like pressureless dark matter, while in the opposite limit the models asymptotically tend to a cosmological constant. Different aspects of the GCG models have been analyzed in the literature [2], [8], [9]. Recently, Reis et al. [4] suggested two other equations of state with the same asymptotic limits, namely Exponential and Logarithmic Quartessence [10]. It is clear that, in principle, many other equations of state can be used, but for the sake of simplicity, and because they capture the main properties of this class of models, here we limit our analysis to these two cases. The considered models have the following EOS:Exponential Quartessence:Logarithmic Quartessence:where ρ is the density energy, P the pressure, M has dimension of mass and α is a dimensionless parameter. We denote by H the Hubble parameter and the quantities (H, ρ) are chosen ...

On the viability of Planck scale cosmology with quartessence

“…Also within extended framework at hand the Big-Bang singularity can be absent due to bouncing mechanism induced by quantum correction terms in Friedmann dynamic equations [57]. The aforementioned positive feature concerning the resolving of initial condition problem from one side and valuable phenomenology functionality of the QCMs at large scales along with this fact that they are stable into standard cosmology [58,59], from other side, motivates us to explore the response of this question: "Whether the quartessence Chaplygin cosmologies (QCCs) are still stable in a free initial singularity cosmological framework suggested by Snyder NC space approach to QG?". The result would be desirable in case of "yes".…”