Cosmological Perturbations of a Quartet of Scalar Fields with a Spatially Constant Gradient

TL;DR

This paper studies linear perturbations in a cosmological inflation model involving one scalar field and three additional scalar fields with a constant spatial gradient, revealing small corrections to cosmological spectra due to this gradient.

Contribution

It introduces a novel inflation model with a triad of scalar fields having a constant spatial gradient and analyzes its perturbations and cosmological implications.

Findings

Existence of a lower bound on comoving wavenumber for initial quantum states.

Small corrections to power spectra and spectral indices due to the spatial gradient.

Similar behavior observed in tensor perturbations with the same lower bound.

Abstract

We consider the linear perturbations for the single scalar field inflation model interacting with an additional triad of scalar fields. The background solutions of the three additional scalar fields depend on spatial coordinates with a constant gradient $\alpha$ and the ensuing evolution preserves the homogeneity of the cosmological principle. After we discuss the properties of background evolution including an exact solution for the exponential-type potential, we investigate the linear perturbations of the scalar and tensor modes in the background of the slow-roll inflation. In our model with small $\alpha$, the comoving wavenumber has {\it a lower bound} $\sim \alpha M_{\rm P}$ to have well-defined initial quantum states. We find that cosmological quantities, for instance, the power spectrums and spectral indices of the comoving curvature and isocurvature perturbations, and the running of the spectral indices have small corrections depending on {\it the lower bound}. Similar behaviors happen for the tensor perturbation with the same lower bound.