Parametric resonance in Abelian and non-Abelian gauge fields via spacetime oscillations

We study the evolution of Abelian $U\left(1\right)$ electromagnetic as well as non-Abelian $SU\left(2\right)$ gauge fields, in the presence of spacetime oscillations. Analysis of the time evolution of Abelian gauge fields shows the presence of parametric resonance in spatial modes. A similar analysis in the case of non-Abelian gauge fields, in the linear approximation, shows the presence of the same resonant spatial modes. The resonant modes induce large fluctuations in physical observables including those that break the $CP$ symmetry. We also carry out time evolution of small random fluctuations of the gauge fields, using numerical simulations in $2+1$ and $3+1$ dimensions. These simulations help to study nonlinear effects in the case of non-Abelian gauge theories. Our results show that there is an increase in energy density with the coupling, at late times. These results suggest that gravitational waves may excite non-Abelian gauge fields more efficiently than electromagnetic fields. Also, gravitational waves in the early Universe and from the merger of neutron stars, black holes, etc., may enhance $CP$ violation and generate an imbalance in chiral charge distributions, magnetic fields, etc.