Primordial magnetic field from noninflationary cosmic expansion in Hořava-Lifshitz gravity

Abstract

The origin of large-scale magnetic field in the Universe is one of the greatest mysteries in modern cosmology. We present a new mechanism for generation of large-scale magnetic field, based on the power-counting renormalizable theory of gravitation recently proposed by Ho\ifmmode \check{r}\else \v{r}\fi{}ava. Contrary to the usual case in general relativity, the $U(1)$ gauge symmetry of a Maxwell action in this theory permits terms breaking conformal invariance in the ultraviolet. Moreover, for high frequency modes, the anisotropic scaling intrinsic to the theory inevitably makes the sound horizon far outside the Hubble horizon. Consequently, noninflationary cosmic expansion in the early Universe naturally generates superhorizon quantum fluctuations of the magnetic field. Specializing our consideration to the case with the dynamical critical exponent $z=3$, we show an explicit set of parameters for which (i) the amplitude of generated magnetic field is large enough as a seed for the dynamo mechanism; (ii) backreaction to the cosmic expansion is small enough; and (iii) the high-energy dispersion relation is consistent with the most recent observational limits from MAGIC and Fermi collaborations.