Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: {\delta}N formalism   Precise understanding of nonlinear evolution of cosmological perturbations
during inflation is necessary for the correct interpretation of measurements of
non-Gaussian correlations in the cosmic microwave background and the
large-scale structure of the universe. The "{\delta}N formalism" is a popular
and powerful technique for computing non-linear evolution of cosmological
perturbations on large scales. In particular, it enables us to compute the
curvature perturbation, {\zeta}, on large scales without actually solving
perturbed field equations. However, people often wonder why this is the case.
In order for this approach to be valid, the perturbed Hamiltonian constraint
and matter-field equations on large scales must, with a suitable choice of
coordinates, take on the same forms as the corresponding unperturbed equations.
We find that this is possible when (1) the unperturbed metric is given by a
homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker metric; and (2)
on large scales and with a suitable choice of coordinates, one can ignore the
shift vector (g0i) as well as time-dependence of tensor perturbations to
gij/a2(t) of the perturbed metric. While the first condition has to be assumed
a priori, the second condition can be met when (3) the anisotropic stress
becomes negligible on large scales. However, in order to explicitly show that
the second condition follows from the third condition, one has to use
gravitational field equations, and thus this statement may depend on the
details of theory of gravitation. Finally, as the {\delta}N formalism uses only
the Hamiltonian constraint and matter-field equations, it does not a priori
respect the momentum constraint. We show that the violation of the momentum
constraint only yields a decaying mode solution for {\zeta}, and the violation
vanishes when the slow-roll conditions are satisfied.

32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin