Yukawa coupling, and inflationary correlation functions for a spectator scalar via stochastic spectral expansion

TL;DR

This paper studies a spectator scalar field during inflation coupled to fermions via Yukawa interaction, analyzing its correlation functions and non-Gaussianity using stochastic spectral expansion, revealing how Yukawa coupling influences the power spectrum and non-Gaussian features.

Contribution

It introduces a novel numerical analysis of the spectator scalar's correlation functions in de Sitter space considering Yukawa coupling effects using stochastic spectral expansion.

Findings

Power spectrum exhibits a blue tilt with increasing Yukawa coupling.

Yukawa coupling flattens the shape function peak in the squeezed limit.

Local non-Gaussianity parameter increases with Yukawa coupling.

Abstract

We consider a stochastic spectator scalar field coupled to fermion via the Yukawa interaction, in the inflationary de Sitter background. We consider the fermion to be massless, and take the one loop effective potential found earlier by using the exact fermion propagator in de Sitter spacetime. We take the potential for the spectator scalar to be quintessence-like, $V(\phi)=\alpha |\phi|^p$ ($\alpha \ensuremath{>} 0,\ p\ensuremath{>} 4$), so that the total effective potential is generically bounded from below for all values of the parameters and couplings, and a late time equilibrium state is allowed. Using next the stochastic spectral expansion method, we numerically investigate the two point correlation function, as well as the density fluctuations corresponding to the spectator field, with respect to the three parameters of the total effective potential, $\alpha,\ p$ and the Yukawa coupling, $g$. In particular, we find that the power spectrum and the spectral index corresponds to blue tilt with increasing $g$. The three point correlation function and non-Gaussianity corresponding to the density fluctuation has also been investigated. The increasing Yukawa coupling is shown to flatten the peak of the shape function in the squeezed limit. Also in this limit, the increase in the same is shown to increase the local non-Gaussianity parameter.