CMB Constraints on a Stochastic Background of Primordial Magnetic Fields

TL;DR

This paper constrains the strength of primordial magnetic fields using cosmic microwave background data, providing new limits and forecasting future constraints with Planck.

Contribution

It introduces a parametrization of stochastic primordial magnetic fields and derives constraints from multiple CMB datasets, including forecasts for Planck.

Findings

Primordial magnetic field strength constrained to less than 5.0 nG at 1 Mpc scale.

Derived spectra for energy-momentum correlators for any spectral index.

Forecasted Planck's improved sensitivity to primordial magnetic fields.

Abstract

We constrain a stochastic background of primordial magnetic field (PMF) by its contribution to the angular power spectrum of cosmic microwave background anisotropies. We parametrize such stochastic background by a power-law spectrum with index $n_B$ and by its Gaussian smoothed amplitude $B_\lambda$ on a comoving length $\lambda$. We give an approximation for the spectra of the relevant correlators of the energy-momentum of the stochastic background of PMF for any $n_B$. By using the WMAP 7 year data in combination with ACBAR, BICEP and QUAD we obtain the constraint $B_{1 {\rm Mpc}} < 5.0$ nG at 95% confidence level for a stochastic background of non-helical PMF. We discuss the relative importance of the scalar and vector contribution to CMB anisotropies in obtaining these constraints. We then forecast {\sc Planck} capabilities in constraining $B_{1 {\rm Mpc}}$.