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arXiv · 2505.21429

Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators

Yuta Nasuda·Koki Tokeshi·Yuki Watanabe
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Abstract

The stochastic dynamics of a scalar field in de Sitter spacetime can be regarded as a non-perturbative diffusion process, to which exact distribution and correlation functions are constructed by utilising the correspondence between diffusion and Schr\"{o}dinger equations. The Krein--Adler transformation of the quantum harmonic oscillator deletes several pairs of the energy levels to define anharmonic oscillators that we dub quantum deficient oscillators, based on which this article constructs a new class of exact solutions in stochastic inflation. In addition to the simplest single-well model, an exactly solvable double-well model is also presented. The results are further extended to exactly solvable models with multiple wells, allowing analytical studies on various cosmological phenomenologies.

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Yuta Nasuda, Koki Tokeshi, Yuki Watanabe. 2025-05-27. Scalar field stochastic dynamics in de Sitter spacetime from exact solutions of quantum deficient oscillators. https://doi.org/10.1093/ptep%2Fptaf143

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