Fixed points and FLRW cosmologies: Flat case

Abstract

We use phase space method to study possible consequences of fixed points in flat FLRW models. One of these consequences is that a fluid with a finite sound speed, or a differentiable pressure, reaches a fixed point in an infinite time and has no finite-time singularities of types I, II and III described in hep-th/0501025. It is impossible for such a fluid to cross the phantom divide in a finite time. We show that a divergent $dp/dH$, or a speed of sound is necessary but not sufficient condition for phantom crossing. We use pressure properties, such as asymptotic behavior and fixed points, to qualitatively describe the entire behavior of a solution in flat FLRW models. We discuss FLRW models with bulk viscosity $\eta \sim {\rho }^r$, in particular, solutions for $r=1$ and $r=1/4$ cases, which can be expressed in terms of Lambert-W function. The last solution behaves either as a nonsingular phantom fluid or a unified dark fluid. Using causality and stability constraints, we show that the universe must end as a de Sitter space. Relaxing the stability constraint leads to a de Sitter universe, an empty universe, or a turnaround solution that reaches a maximum size, then recollapses.

20 pages, 8 figures. Several references added as well as comments on the r=1/4 case

References in corpus (8)

• Dark Energy and the Accelerating Universe
• Bouncing Universe with Quintom Matter
• Does Bulk Viscosity Create a Viable Unified Dark Matter Model?
• Worse than a big rip?
• Mapping the Cosmological Expansion
• Crossing the Phantom Divide
• Constraints on the Sound Speed of Dynamical Dark Energy
• Affine equation of state from quintessence and k-essence fields

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• On the Stability of Einstein Static Universe in Doubly General Relativity Scenario
• Inflationary universe in the presence of a minimal measurable length
• $f(T)$ cosmology: From Pseudo-Bang to Pseudo-Rip
• Classical and quantum dynamics of a perfect fluid scalar-energy dependent metric cosmology
• Generic Phase Portrait Analysis of the Finite-time Singularities and Generalized Teleparallel Gravity
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• Dissipative Unified Dark Fluid Model
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• Planck-Scale Corrections to Friedmann Equation
• Degenerate Bogdanov-Takens bifurcations in a bulk viscous cosmology
• Gauss-Bonnet Gravity and Spacetime Singularities