Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Note on bouncing backgrounds   The theory of inflation is one of the fundamental and revolutionary
developments of modern cosmology that became able to explain many issues of
early universe in the context of the standard cosmological model (SCM).
However, the initial singularity of the universe, where physics is indefinite,
is still obscure in the combined `SCM+inflation' scenario. An alternative to
`SCM+inflation' without the initial singularity is thus always welcome, and
bouncing cosmology is an attempt of that. The current work is thus motivated to
investigate the bouncing solutions in modified gravity theories when the
background universe is described by the spatially flat
Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. We show that the simplest
way to obtain the bouncing cosmologies in such spacetime is to consider some
kind of Lagrangians whose gravitational sector depends only on the square of
the Hubble parameter of the FLRW universe. For these modified Lagrangians, the
corresponding Friedmann equation, a constraint in the dynamics of the universe,
depicts a curve in the phase space $(H,rho)$, where $H$ is the Hubble parameter
and $rho$ being the energy density of the universe. As a consequence, a
bouncing cosmology is obtained when this curve is closed and crosses the axis
$H = 0$ at least twice, and whose simplest particular example is the ellipse
depicting the well-known holonomy corrected Friedmann equation in Loop Quantum
Cosmology (LQC). Sometimes, a crucial point in such theories is the appearance
of the Ostrogradski instability at the perturbative level, however, fortunately
enough, in the present work as long as the linear level of perturbations is
concerned, this instability does not appear but such instability may appear at
the higher-order of perturbations.

4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th