Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fixed points and FLRW cosmologies: Flat case   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.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
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The categories of this paper are: cs
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn