Kavli Affiliate: Misao Sasaki
| Summary:
$δN$ formalism is a useful method to calculate the curvature perturbation. Contrary to what it is typically done in the literature, we re-formulate the $δN$ formalism by using the $e$-folding number $n$ counted forward in time. For a fixed initial time $barn_0$, the probability density function (PDF) of the field perturbation $δφ_0$ and its velocity $δπ_0$ are specified by the solutions of the perturbation equation on subhorizon scales. As $δπ_0$ is fully correlated with $δφ_0$ after horizon exit, we find a novel $δn$ formalism to calculate the curvature perturbation as well as its PDF. It can naturally incorporate those trajectories for which inflation never ends, which are lost when counting $N$ backward in time.
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