Phase space analysis and singularity classification for linearly interacting dark energy models

Abstract

In this paper, applying the Hartman-Grobman theorem we carry out a qualitative late-time analysis of some unified dark energy-matter Friedmann cosmological models, where the two interact through linear energy exchanges, and the dark energy fluid obeys to the dynamical equation of state of Redlich-Kwong, Modified Berthelot, and Dieterici respectively. The identification of appropriate late-time attractors allows to restrict the range of validity of the free parameters of the models under investigation. We show that the strength of deviation from an ideal fluid for the dark energy does not influence the stability of the late-time attractors, as well as the values of all the cosmological parameters at equilibrium, but for the Hubble function (which represents the age of the universe). Our analysis also shows that a singularity in the effective equation of state parameter for the dark energy fluid is not possible within this class of models.

Phase Space Analysis and Thermodynamics of Interacting Umami Chaplygin Gas in FRW Universe

“…These choices of dnamical variables have also been adopted in studying various form of equation of states of dark energy in dynamical analysis (see Ref. [83]). Using the variables (9), the Friedmann equation (3) puts a constraint on the dimensionless density parameter as m ≡ ρ m 3H 2 = 1 − x.…”

Cosmological evolution with quadratic gravity and nonideal fluids

“…The former assumption will allow us to account for the early-time dynamics, while the latter for the present-day epoch. Both these two models have been investigated separately in a number of literature works [18][19][20][21][22][23][24][25][26][27]. Here, we will obtain a cosmological dynamics with a rich variety of different behaviors like a nonsingular bounce, two de Sitter-like epochs (thanks to the non-linear equation of state of the cosmic fluid in which w(ρ) is not a constant), possibly two radiation-dominated epochs, and possibly a phantom regime (the latter only in the Redlich-Kwong scenario).…”

“…We will tackle the technical difficulties arising in a fourthorder gravity theory like this one by adopting the set of dimensionless variables constructed in [33] which allows to cast the dynamical equations into a system of autonomous first-order equations suited for a dynamical system analysis. Such technique constitutes a powerful mathematical tool for describing the qualitative evolution of the the cosmological model under investigation not only in modified gravity [33][34][35][36][37][38][39][40][41][42][43], but also in multi-interacting fluid models [25,[44][45][46][47][48][49][50][51], and in exact or perturbed anisotropic and inhomogeneous cos-mological models [52][53][54][55][56][57][58], just to mention a few examples. However, we will also propose a novel cosmologically transparent interpretation for those variables which was still lacking in the literature by deriving the physical restrictions they should obey to for avoiding tachyonic and ghost instabilities and connecting them to the cosmographic parameters, such as the deceleration, jerk and snap parameters which can be astrophysically constrained.…”

Analysis of the H0 tension problem in the Universe with viscous dark fluid

“…On the other hand, available observational data do provide some hints, partially shedding light on this dark energy problem. Nowadays, from the observational data alone, in a model-independent way, it is possible to decide what are the directions to look for, and the possible candidates for dark energy to be seriously considered, in order to solve the accelerated expanding Universe problems (for dark energy models with fluids, see [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and references therein).…”

“…We refer the readers to[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and references therein for further detailed discussion about fluid dark energy with related problems and its possible resolution.…”