Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second-order cosmological perturbations. II. Produced by scalar-tensor
  and tensor-tensor couplings   We study the second-order perturbations in the Einstein-de Sitter Universe in
synchronous coordinate. We solve the second-order perturbed Einstein equation
with scalar-tensor, and tensor-tensor couplings between 1st order
perturbations, and obtain, for each coupling, the solutions of scalar, vector,
tensor metric perturbations, including both the growing and decaying modes for
general initial conditions. We perform general synchronous-to-synchronous gauge
transformations up to 2nd order, which are generated by a 1st order vector
field and a 2nd order vector field, and obtain all the residual gauge modes of
the 2nd order metric perturbations in synchronous coordinates. We show that
only the 2nd order vector field is effective for the 2nd order transformations
that we consider because the 1st order vector field was already fixed in
obtaining the 1st order perturbations. In particular, the 2nd order tensor is
invariant under 2nd order gauge transformations using $\xi^{(2)\mu}$ only, just
like the 1st order tensor is invariant under 1st order transformations.

1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph