Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Propagation of Gravitational Waves in Chern-Simons Axion $F(R)$ Gravity   In this paper we shall study the evolution of cosmological gravitational
waves in the context of Chern-Simons axion $F(R)$ gravity. In the case of
Chern-Simons axion $F(R)$ gravity there exist spin-0, spin-2 and spin-1 modes.
As we demonstrate, from all the gravitational waves modes of the Chern-Simons
axion $F(R)$ gravity, only the two tensor modes are affected, while the spin-0
and spin-1 modes are not affected at all. With regard to the two tensor modes,
we show that these modes propagate in a non-equivalent way, so the resulting
tensor modes are chiral. Notably, with regard to the propagation of the spin-2
graviton modes, the structure of the dispersion relations becomes more
complicated in comparison with the Einstein gravity with the Chern-Simons
axion, but the resulting qualitative features of the propagating modes are not
changed. With regard to the spin-0 and spin-1 modes, the Chern-Simons axion
$F(R)$ gravity contains two spin-0 modes and no vector spin-1 mode at all. We
also find that for the very high energy mode, both the group velocity and the
phase velocity are proportional to the inverse of the square root of the wave
number, and therefore the velocities become smaller for larger wave numbers or
even vanish in the limit that the wave number goes to infinity.

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The categories of this paper are: solv-int
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas