Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Structure formation and generalized second law of thermodynamics in some
  viable $f(R)$-gravity models   Here, we investigate the growth of matter density perturbations as well as
the generalized second law (GSL) of thermodynamics in the framework of
$f(R)$-gravity. We consider a spatially flat FRW universe filled with the
pressureless matter and radiation which is enclosed by the dynamical apparent
horizon with the Hawking temperature. For some viable $f(R)$ models containing
the Starobinsky, Hu-Sawicki, Exponential, Tsujikawa and AB models, we first
explore numerically the evolution of some cosmological parameters like the
Hubble parameter, the Ricci scalar, the deceleration parameter, the density
parameters and the equation of state parameters. Then, we examine the validity
of GSL and obtain the growth factor of structure formation. We find that for
the aforementioned models, the GSL is satisfied from the early times to the
present epoch. But in the farther future, the GSL for the all models is
violated. Our numerical results also show that for the all models, the growth
factor for larger structures like the $\Lambda$CDM model fit the data very
well.

18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio