Constraint on the primordial vector mode and its magnetic field generation from seven-year Wilkinson Microwave Anisotropy Probe Observations

TL;DR

This paper constrains the primordial vector mode using seven-year WMAP data and calculates the resulting magnetic field spectrum, revealing a maximum magnetic field strength of about 10^{-22} G and a spectral cutoff due to cancellation effects.

Contribution

It provides the first observational constraint on the primordial vector mode from WMAP data and computes the associated magnetic field spectrum with a characteristic cutoff.

Findings

Primordial vector mode constrained as rv ≲ 0.012 from WMAP data.

Maximum magnetic field generated is approximately 10^{-22} G.

Magnetic field spectrum exhibits a cutoff around k ≈ 1.0 Mpc^{-1}.

Abstract

A primordial vector mode and its associated magnetic field generation are investigated. Firstly, we put an observational constraint on the amount of the primordial vector mode from the seven-year WMAP data. The constraint is found as $r_v \lesssim -\frac{r}{40}+0.012$, where $r_v$ and $r$ are the amounts of vector and tensor perturbation amplitudes with respect to the scalar one, respectively. Secondly, we calculate the spectrum of magnetic fields inevitably created from the primordial vector mode, given the constraint on $r_v$. It is found that the maximum amount of magnetic fields generated from the vector mode is given by $B\lesssim 10^{-22}{\rm G} (\frac{r_v}{0.012})^{1/2} (\frac{k}{0.002})^{(n_v+1)/2}$ with $n_v$ being a spectral index of the vector mode. We find a non-trivial cancellation of the magnetic field generation in the radiation dominated era, which creates a characteristic cut off in the magnetic field spectrum around $k\approx 1.0$ Mpc$^{-1}$.