Logarithmic Duality of the Curvature Perturbation by Shi Pi et al. on Monday 28 November

We study the comoving curvature perturbation $\mathcal{R}$ in general

single-field inflation models whose potential can be approximated by a

piecewise quadratic potential $V(\varphi)$ by using the $\delta N$ formalism.

We find a general formula for $\mathcal{R}(\delta\varphi)$, which consists of a

sum of logarithmic functions of the field perturbation $\delta\varphi$ at the

point of interest, as well as of its field velocity perturbations $\delta\pi_*$

at the boundaries of each quadratic piece, which are functions of

$\delta\varphi$ through the equations of motion. In some simple cases,

$\mathcal{R}(\delta\varphi)$ reduces to a single logarithm, which yields either

the renowned ``exponential tail'' of the probability distribution function of

$\mathcal{R}$ or the Gumbel distribution.

arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.13932v1