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

We study the evolution of Abelian $U(1)$ electromagnetic as well as non-Abelian $SU(2)$ 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.

Figure 1

${\mathbf{E}}^2$ at $t=4{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 2

${\mathbf{B}}^2$ at $t=4{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 3

${\mathrm{E}}_{SU(2)}^2$ at $t=4{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 4

${\mathrm{B}}_{SU(2)}^2$ at $t=4{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 5

$\mathrm{\Delta }{\rho }_{E_{1-0}}$ for random fluctuations.

Figure 6

$\mathrm{\Delta }{\rho }_{E_{1-0}}$ for random fluctuations.

Figure 7

$\mathrm{\Delta }{\rho }_{E_{1-0}}$ for $L=8{\mathrm{\Lambda }}^{-1}$ and scaled $L=2{\mathrm{\Lambda }}^{-1}$ results.

Figure 8

$\mathrm{\Delta }{\rho }_{E_{1-0}}$ for $L=8{\mathrm{\Lambda }}^{-1}$ with random fluctuations.

Figure 9

${\rho }_E$ vs $t$ in continuum.

Figure 10

${\rho }_E$ vs $t$ for $k_x=\omega$.

Figure 11

${\sigma }_E(z)$ for different $xy$ planes.

Figure 12

${\rho }_E$ vs $t$ for $3+1$ dimensions.

Figure 13

$\mathrm{\Delta }{\rho }_E$ between $SU(2)$ and $U(1)$.

Figure 14

${\rho }_1$ at $t=3{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 15

${\rho }_1$ at $t=4{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 16

${\rho }_2$ at $t=3{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 17

${\rho }_2$ at $t=4{\mathrm{\Lambda }}^{-1}$ for initial configuration with random fluctuations.

Figure 18

${\rho }_1$ at $t=0.10{\mathrm{\Lambda }}^{-1}$.

Figure 19

${\rho }_1$ at $t=0.60{\mathrm{\Lambda }}^{-1}$.

Figure 20

${\rho }_2$ at $t=0.10{\mathrm{\Lambda }}^{-1}$.

Figure 21

${\rho }_2$ at $t=0.60{\mathrm{\Lambda }}^{-1}$.