Dynamics of classes of barotropic fluids in spatially curved FRW spacetimes

Abstract

In this article we perform dynamical analysis of a broad class of barotropic fluids in the spatially curved Friedmann-Robertson-Walker (FRW) spacetime background without considering the cosmological constant. The first part of our study concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS) having as the only assumption the non-negativity of the fluid's energy density. After defining a new set of dimensionless variables and a new evolution parameter, we introduce the function Γ that encodes the EoS. In this general setup several features of the system are identified: critical points, invariant subsets and the characteristics of the function Γ, along with their cosmological interpretations. The second part of our work provides two examples with specific Γ functions. In the first example we provide a Γ function and then we exhibit how it can be trimmed down to a specific class of EoS through physical arguments, while in the second example we discuss the quadratic EoS studied in Phys. Rev. D 74, 023523 (2006) by comparing our approach with their analysis.

$f(T,B)$ gravity in a Friedmann-Lema\^ıtre-Robertson-Walker universe with nonzero spatial curvature

“…In order to study the dynamics of the field equations ( 24)-( 26) we define the new variables [53] x = φ…”

Dynamical Analysis and Cosmological Evolution in Weyl Integrable Gravity

“…where the new variable Y is defined as Y = Ae − 1 2 (1+α)φ θ −(2+α) . The stationary points C = (x(C), Y(C) )of the dynamical system ( 27), (28), with Ω m > 0 are…”

“…Furthermore, from the analysis of the asymptotic dynamics, that is, of the determination of the stationary points, the complete cosmological history can be constructed [21][22][23]. Indeed, constraints for the free parameters of a given model can be constructed through the analysis of the stationary points and the specific requirements for the stability of the stationary points [24][25][26][27][28].…”

Cosmological evolution in $f(T,B)$ gravity

“…Such an analysis is important in order to understand the general evolution of the cosmological evolution and to infer about the viability of the theory. This method has been applied in various cosmological theories with many interesting results, see for instance [45][46][47][48][49][50][51][52] and references therein. For n = 1, or Λ 0 = 0, the complete analysis of the dynamics was performed in [34].…”