Dynamics of Electroweak Gauge Fields during and after Higgs Inflation
  We study the dynamics of $SU(2)_L$ times $U(1)_Y$ electroweak gauge fields during and after Higgs inflation. In particular, we investigate configurations of the gauge fields during inflation and find the gauge fields remain topologically non-trivial. We also find that the gauge fields grow due to parametric resonances caused by oscillations of a Higgs field after inflation. We show that the Chern-Simons number also grows significantly. Interestingly, the parametric amplification gives rise to sizable magnetic fields after the inflation whose final amplitudes depend on the anisotropy survived during inflation. 
Ippei Obata, Takashi Miura and Jiro Soda
hep-th astro-ph.CO hep-ph