Primordial gravitational waves and perturbations during an inhomogeneous inflation

TL;DR

This paper explores how inhomogeneous inflation, driven by scalar fields with spacelike gradients, affects cosmological perturbations, revealing mode correlations and polarization asymmetries in gravitational waves.

Contribution

It introduces a model of inhomogeneous inflation with scalar fields, calculates linear corrections to perturbation spectra, and uncovers mode correlations and polarization differences.

Findings

Perturbation power spectra depend on wave number ratios and angles.

Inhomogeneities cause correlations between different wave modes.

Gravitational wave polarizations are affected differently by background inhomogeneities.

Abstract

We investigate the inhomogeneous inflation, in which the space exponentially expands with inhomogeneities, and its cosmological perturbations. The inhomogeneous inflation is realized by introducing scalar fields with spacelike gradients that break the spatial symmetry. We find that the space can expand uniformly in different direction with the same rate. By using the perturbative method, we calculate the corrections to the power spectra of gravitational waves and curvature perturbation up to the linear order in the background inhomogeneities. Since the background is inhomogeneous, perturbations modes with different wave numbers get correlated. We show that generally the power spectra of perturbations depend on the ratio and the angle of wave numbers of the two correlated modes. In particular, the two circular polarization modes of the gravitational waves gain different powers when the background inhomogeneity is of vector or tensor type.