Gravitational wave–Gauge field oscillations

Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservation and exchange among the oscillators, the wave amplitudes lie on a multidimensional sphere, reminiscent of neutrino flavor oscillations. This phenomenon has implications for cosmological scenarios based on flavor-space locked gauge fields.

Figure 1

The oscillations of the gravitational wave amplitude $\mathcal{h}$ (black) and gauge field $\mathcal{y}$ (dashed) are shown for $\mathcal{N}=1$, 2 and 3 (bottom two panels). In all cases, $|\psi {|}^2=1$ and the coefficients $A_i$ are scaled so that $\omega =1$. The bottom panel shows that the squared amplitudes sum to unity.

Figure 2

The oscillations of the gravitational wave amplitude $\mathcal{h}$ (black) and gauge field $\mathcal{y}$ (dashed) are shown for $\mathcal{N}=3$ and $A_1=A_2=2|A_3|$. The upper and lower panels show the right- and left-circular polarizations.

Figure 3

The oscillations of the gravitational wave amplitude $\mathcal{h}$ (black) and gauge field $\mathcal{y}$ (dashed) are shown for $\mathcal{N}=2$ with different field strengths and couplings for the two SU(2) subgroups. The gravitational wave responds to these different couplings, and varies between different extrema. The amplitudes are normalized $|\psi {|}^2=1$ and the coefficients $A_i$ are scaled so that the oscillations repeat with a period $2\pi$.

Figure 4

The gravitational wave gauge field oscillations in Fig. 2 (upper) are illustrated using oscillating pistons. The gravitational and gauge field waves are represented by the central and surrounding pistons. (See Supplemental Material [18] or Ref. [19] to play animation.)