Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inclusion of the first-order vector- and tensor-modes in the
  second-order gauge-invariant cosmological perturbation theory   Gauge-invariant treatments of the second-order cosmological perturbation in a
four dimensional homogeneous isotropic universe are formulated without any
gauge fixing. We have derived the Einstein equations in the case of the single
perfect fluid without ignoring any modes. These equations imply that any types
of mode-coupling arise due to the second-order effects of the Einstein
equations.

22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics