Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ghost-free $F(R)$ bigravity and accelerating cosmology   We propose a bigravity analogue of the $F(R)$ gravity. Our construction is
based on recent ghost-free massive bigravity where additional scalar fields are
added and the corresponding conformal transformation is implemented. It turns
out that $F(R)$ bigravity is easier to formulate in terms of the auxiliary
scalars as the explicit presentation in terms of $F(R)$ is quite cumbersome.
The consistent cosmological reconstruction scheme of $F(R)$ bigravity is
developed in detail, showing the possibility to realize nearly arbitrary
physical universe evolution with consistent solution for second metric. The
examples of accelerating universe which includes phantom, quintessence and
$\Lambda$CDM acceleration are worked out in detail and their physical
properties are briefly discussed.

3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
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The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph