Preprint number: CP3-Origins-2014-16 DNRF90 and DIAS-2014-16

Authors:

External link: arXiv.org

The damping of a non-uniform magnetic field between the redshifts of about 10^{4} and 10^{6} injects energy into the photon-baryon plasma and causes the CMB to deviate from a perfect blackbody spectrum, producing a so-called μ-distortion. We can calculate the correlation 〈μ*T*〉 of this distortion with the temperature anisotropy *T* of the CMB to search for a correlation 〈*B*^{2}ζ〉 between the magnetic field *B* and the curvature perturbation ζ. Since the perturbations which produce the μ-distortion will be much smaller scale than the relevant density perturbations, the observation of this correlation is sensitive to the squeezed limit of 〈*B*^{2}ζ〉, which is naturally parameterized by *b*_{\textNL} (a parameter defined analogously to *f*_{\textNL}). We find that a PIXIE-like CMB experiments has a signal to noise *S*/*N* ≈ 1.0 ×*b*_{\textNL} (~*B*_{μ}/10\text *nG*)^{2}, where ~*B*_{μ} is the magnetic field’s strength on μ-distortion scales normalized to today’s redshift; thus, a 10 nG field would be detectable with *b*_{\textNL}=*O*(1). However, if the field is of inflationary origin, we generically expect it to be accompanied by a curvature bispectrum 〈ζ^{3}〉; for field strengths *B*_{μ} >~1 nG, the signal of this bispectrum in 〈μ*T*〉 would dominate over the signal from *b*_{\textNL}.

We also discuss the potential post-magnetogenesis sources of a 〈*B*^{2}ζ〉 correlation and explain why there will be no contribution from the evolution of the magnetic field in response to the curvature perturbation.