CMB and matter power spectra from cross correlations of primordial curvature and magnetic fields

TL;DR

This paper presents a detailed numerical analysis of how cross correlations between primordial magnetic fields and curvature perturbations influence CMB anisotropies and matter power spectra, highlighting their dominance at large scales.

Contribution

It introduces a comprehensive numerical framework to evaluate the effects of magnetic-curvature cross correlations on CMB and matter spectra, considering inflationary magnetic field generation.

Findings

Cross correlation dominates at low multipoles in CMB anisotropies.

Large-scale matter power spectrum is similarly affected by the cross correlation.

For a 1 nG magnetic field, significant contributions are observed at large scales.

Abstract

A complete numerical calculation of the temperature anisotropies and the polarization of the cosmic microwave background (CMB) is presented for a non zero cross correlation of a stochastic magnetic field with the primordial curvature perturbation. Such a cross correlation results, for example, if the magnetic field is generated during inflation by coupling electrodynamics to a scalar field which is identified with the curvaton. For a nearly scale invariant magnetic field of 1 nG it is found that at low multipoles the contribution due to the cross correlation dominates over that of the pure magnetic mode. A similar behaviour on large scales is found for the linear matter power spectrum.