Natural Magnetogenesis from Inflation

TL;DR

This paper proposes a natural, model-independent mechanism for primordial magnetogenesis where conformal invariance is broken during inflation by the Standard Model Z-boson mass generated through EW-Higgs dynamics. Gravitational production during inflation creates a nearly scale-invariant Z spectrum on superhorizon scales, which is converted into a hypermagnetic field at EW restoration and subsequently into a regular magnetic field at the EW transition. The resulting field spectrum scales as $B_{ m rms}(\ell) \propto 1/\ell$, and, when evolved to galaxy formation, yields seed fields $\sim 10^{-30}$ G at 10 kpc scales, sufficient to trigger galactic dynamos in a flat, dark-energy-dominated universe with GUT-scale inflation. The paper also investigates preheating as a potential amplifier and finds the hypercharge-field amplification via resonances to be subdominant under the considered scenarios, though it notes the need for numerical studies to fully resolve the conductivity and nonlinear backreaction during preheating.

Abstract

We consider the gravitational generation of the massive Z-boson field of the standard model, due to the natural breaking of its conformal invariance during inflation. The electroweak symmetry restoration at the end of inflation turns the almost scale-invariant superhorizon Z-spectrum into a hypermagnetic field, which transforms into a regular magnetic field at the electroweak phase transition. The mechanism is generic and is shown to generate a superhorizon spectrum of the form B~1/L on a length-scale L regardless of the choice of inflationary model. Scaled to the epoch of galaxy formation such a field suffices to trigger the galactic dynamo and explain the observed galactic magnetic fields in the case of a spatially flat, dark energy dominated Universe with GUT-scale inflation. The possibility of further amplification of the generated field by preheating is also investigated. To this end we study a model of Supersymmetric Hybrid Inflation with a Flipped SU(5) grand unified symmetry group.

Figures (2)

• Figure 1: Comoving magnetic field spectra and relevant seed field bounds, plotted against the comoving scale $\ell _c$. The steepest line (dash-dot-dot-dot) depicts the (unsubtracted) vacuum spectrum $B_{\rm vac}(\ell)\propto\ell^{-2}$. At the comoving scale $\ell_c=10$ kpc one has $B_{\rm vac}^{\rm com}(10$ kpc$)\sim 10^{-54}$Gauss. The line of intermediate steepness (dash-dot) corresponds to the thermal spectrum $B_{\rm th}(\ell)\propto\ell^{-3/2}$, which meets the vacuum spectrum at the comoving scale $\ell_H$ corresponding to the Horizon at the end of inflation. The solid line is the primordial magnetic field, resulting from inflation through our mechanism, $B_{\rm rms}(\ell)\propto\ell^{\nu-3/2}\approx\ell^{-1}$, as calculated by (\ref{['Bo']}). On the scale $\ell_c=10$ kpc we find $B_{\rm rms}^{\rm com}(10$ kpc$)\sim 10^{-34}$Gauss, i.e. about twenty orders of magnitude stronger than the value corresponding to the vacuum spectrum. This is to be compared with the dynamo bounds rescaled by a factor $10^{-4}$, corresponding to the collapse-amplification enhancement factor and the factor due to the scaling between galaxy formation and the present (see main text). These bounds read $B_{\rm seed}\geq 10^{-27}$Gauss for a Universe with critical matter density and $B_{\rm seed}\geq 10^{-34}$Gauss for a Universe dominated by dark energy (flat, low-density Universe). We also show (dotted line) the spectrum enhanced by helical turbulence (at $\ell_c=10$ kpc an enhancement of about 20 is obtained). Finally, we note that we expect our primordial magnetic field spectrum to depart from the $\ell^{-1}$ scaling law near the scale $\ell_H$ and approach approximately the thermal spectrum since $\nu\rightarrow 0$ towards the end of inflation. In that way the spectrum of our magnetic field joins the vacuum spectrum at $\ell_H$.
• Figure 2: The formation of a magnetic field from the generation of the $Z$-boson field has to pass through the intermediate hypercharge stage similarly to light when crossing a set of orthogonal polarizers, which needs an intermediate third polarizer at some angle $\theta$ in order to go through.