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arXiv · 2409.16272

Exactly solvable stochastic spectator

Masazumi Honda·Ryusuke Jinno·Koki Tokeshi
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Abstract

The stochastic formalism of inflation allows us to describe the scalar-field dynamics in a non-perturbative way. The correspondence between the diffusion and Schr\"{o}dinger equations makes it possible to exhaustively construct analytical solutions in stochastic inflation. Those exact statistical quantities such as distribution and correlation functions have one-to-one correspondence to the exactly solvable solutions in non-relativistic quantum mechanics in terms of classical orthogonal polynomials. A class of such solutions is presented by means of isospectral Hamiltonians with an underlying symmetry called shape invariance.

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Masazumi Honda, Ryusuke Jinno, Koki Tokeshi. 2024-09-24. Exactly solvable stochastic spectator. https://arxiv.org/abs/2409.16272

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