Microwave background signatures of a primordial stochastic magnetic field

A stochastic magnetic field in the early universe will produce anisotropies in the temperature and polarization of the cosmic microwave background. We derive analytic expressions for the microwave background temperature and polarization power spectra induced by vector and tensor perturbations from a power-law magnetic field. For a scale-invariant stochastic magnetic field smoothed over a comoving scale of 1 Mpc, the Microwave Anisotropy Probe satellite has the potential to constrain the comoving mean-field amplitude to be no greater than approximately 210^-9 G. Limits improve as the power-law slope increases: for causally generated power-law magnetic fields, the comoving mean-field amplitude has an upper bound of approximately 410^-13 G. Such constraints will surpass all current limits on galactic-scale primordial stochastic magnetic fields at decoupling.