Semi-analytical approach to magnetized temperature autocorrelations

TL;DR

This paper presents a semi-analytical method to compute the effects of primordial magnetic fields on CMB temperature autocorrelations, providing constraints and implications for the origin of cosmic magnetic fields.

Contribution

It introduces a semi-analytical approach to analyze magnetic field effects on CMB anisotropies, focusing on harmonic regions relevant for Doppler oscillations.

Findings

Magnetic fields with amplitudes >0.1 nG affect the second peak of the power spectrum.

Steeper magnetic spectra allow larger magnetic field amplitudes, up to 20 nG.

Detectable effects are prominent only for specific magnetic spectral slopes.

Abstract

The cosmic microwave background (CMB) temperature autocorrelations, induced by a magnetized adiabatic mode of curvature inhomogeneities, are computed with semi-analytical methods. As suggested by the latest CMB data, a nearly scale-invariant spectrum for the adiabatic mode is consistently assumed. In this situation, the effects of a fully inhomogeneous magnetic field are scrutinized and constrained with particular attention to harmonics which are relevant for the region of Doppler oscillations. Depending on the parameters of the stochastic magnetic field a hump may replace the second peak of the angular power spectrum. Detectable effects on the Doppler region are then expected only if the magnetic power spectra have quasi-flat slopes and typical amplitude (smoothed over a comoving scale of Mpc size and redshifted to the epoch of gravitational collapse of the protogalaxy) exceeding 0.1 nG. If the magnetic energy spectra are bluer (i.e. steeper in frequency) the allowed value of the smoothed amplitude becomes, comparatively, larger (in the range of 20 nG). The implications of this investigation for the origin of large-scale magnetic fields in the Universe are discussed. Connections with forthcoming experimental observations of CMB temperature fluctuations are also suggested and partially explored.