Effects of helical magnetic fields on the cosmic microwave background

Abstract

A complete numerical calculation of the temperature anisotropies and polarization of the cosmic microwave background in the presence of a stochastic helical magnetic field is presented which includes the contributions due to scalar, vector and tensor modes. The correlation functions of the magnetic field contributions are calculated numerically including a Gaussian window function to effectively cut off the magnetic field spectrum due to damping. Apart from parity-even correlations the helical nature of the magnetic field induces parity-odd correlations between the $E$ and $B$ mode of polarization as well as between temperature ($T$) and the polarization $B$ mode.