Scalar correlation functions for a double-well potential in de Sitter space. (arXiv:2001.04494v1 [gr-qc])

<a href="http://arxiv.org/find/gr-qc/1/au:+Markkanen_T/0/1/0/all/0/1">Tommi Markkanen</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Rajantie_A/0/1/0/all/0/1">Arttu Rajantie</a>

We use the spectral representation of the stochastic Starobinsky-Yokoyama

approach to compute correlation functions in de Sitter space for a scalar field

with a symmetric or asymmetric double-well potential. The terms in the spectral

expansion are determined by the eigenvalues and eigenfunctions of the

time-independent Fokker-Planck differential operator, and we solve them

numerically. The long-distance asymptotic behaviour is given by the lowest

state in the spectrum, but we demonstrate that the magnitude of the coeffients

of different terms can be very different, and the correlator can be dominated

by different terms at different distances. This can give rise to potentially

observable cosmological signatures. In many cases the dominant states in the

expansion do not correspond to small fluctuations around a minimum of the

potential and are therefore not visible in perturbation theory. We discuss the

physical interpretation these states, which can be present even when the

potential has only one minimum.

We use the spectral representation of the stochastic Starobinsky-Yokoyama

approach to compute correlation functions in de Sitter space for a scalar field

with a symmetric or asymmetric double-well potential. The terms in the spectral

expansion are determined by the eigenvalues and eigenfunctions of the

time-independent Fokker-Planck differential operator, and we solve them

numerically. The long-distance asymptotic behaviour is given by the lowest

state in the spectrum, but we demonstrate that the magnitude of the coeffients

of different terms can be very different, and the correlator can be dominated

by different terms at different distances. This can give rise to potentially

observable cosmological signatures. In many cases the dominant states in the

expansion do not correspond to small fluctuations around a minimum of the

potential and are therefore not visible in perturbation theory. We discuss the

physical interpretation these states, which can be present even when the

potential has only one minimum.

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