Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correspondence of $F(R)$ Gravity Singularities in Jordan and Einstein
  Frames   We study the finite time singularity correspondence between the Jordan and
Einstein frames for various $F(R)$ gravity theories. Particularly we
investigate the ordinary pure $F(R)$ gravity case and the unimodular $F(R)$
gravity cases, in the absence of any matter fluids. In the ordinary $F(R)$
gravity cases, by using specific illustrative examples, we show that it is
possible to have various correspondences of finite time singularities, and in
some cases it is possible a singular cosmology in one frame might be
non-singular in the other frame. In the unimodular $F(R)$ gravity case, the
unimodular constraint is affected from the conformal transformation, so this
has an effect on the metric we choose. Moreover, we study the Einstein frame
counterpart theory of the unimodular $F(R)$ gravity case, and we investigate
the correspondences of the singularities in the two theories by considering
specific illustrative examples. Finally, a brief dynamical system analysis is
performed for the vacuum unimodular $F(R)$ gravity and we demonstrate how the
dynamical system behaves near the future Big Rip singularity.

19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex