$δn$ formalism: A new formulation for the probability density of the curvature perturbation

Kavli Affiliate: Misao Sasaki

| First 5 Authors: Diego Cruces, Shi Pi, Misao Sasaki, ,

| Summary:

$delta N$ formalism is a useful method to calculate the curvature
perturbation. Contrary to what it is typically done in the literature, we
re-formulate the $delta N$ formalism by using the $e$-folding number $n$
counted forward in time. For a fixed initial time $bar{n}_0$, the probability
density function (PDF) of the initial conditions $deltaphi_0$ and
$deltapi_0$ are specified by the solutions of the perturbation equation on
subhorizon scales. As $deltapi_0$ is fully correlated with $deltaphi_0$
after horizon exit, we find a simple formula to calculate the curvature
perturbation as well as its PDF by using the $delta N$ method reformulated in
terms of $n$, the $delta n$ formalism.

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