Quantum fluctuations in planar domain-wall space-times: A possible origin of primordial preferred direction

TL;DR

This paper investigates how a planar domain wall during inflation can induce a preferred direction in the primordial power spectrum by breaking rotational invariance through gravitational effects on quantum fluctuations.

Contribution

It provides an exact solution for a scalar field in de Sitter space with a domain wall, revealing how such walls cause scale-invariant rotational violations in the primordial spectrum.

Findings

Rotational invariance is broken without affecting translational invariance.

The violation strength depends on a parameter related to wall tension and cosmological constant.

In the small parameter limit, the effect is scale-invariant.

Abstract

We study the gravitational effects of a planar domain wall on quantum fluctuations of a massless scalar field during inflation. By obtaining an exact solution of the scalar field equation in de Sitter space, we show that the gravitational effects of the domain wall break the rotational invariance of the primordial power spectrum without affecting the translational invariance. The strength of rotational violation is determined by one dimensionless parameter $\beta$, which is a function of two physical parameters, the domain wall surface tension $\sigma$ and cosmological constant $\Lambda$. In the limit of small $\beta$, the leading effect of rotational violation of the primordial power spectrum is scale-invariant.