Primordial Anisotropies in the Gravitational Wave Background from Cosmological Phase Transitions

Phase transitions in the early Universe can readily create an observable stochastic gravitational wave background. We show that such a background necessarily contains anisotropies analogous to those of the cosmic microwave background (CMB) of photons, and that these too may be within reach of proposed gravitational wave detectors. Correlations within the gravitational wave anisotropies and their cross-correlations with the CMB can provide new insights into the mechanism underlying primordial fluctuations, such as multifield inflation, as well as reveal the existence of nonstandard “hidden sectors” of particle physics in earlier eras.

Figure 1

A sketch of the anisotropies in GW produced by a cosmic PT. GW reaching the detector from different directions now, were emitted from distant regions of the Universe long ago when the temperature there was $T_{\mathrm{PT}}$, and bubbles of the low-$T$ phase were produced and collided in numerous Hubble patches. This emitting surface (dotted purple) is not a perfect sphere (solid grey) because of temperature inhomogeneties. GW from more distant parts of the emitting surface will redshift longer than GW from closers parts, giving rise to anisotropies in frequency and power.

Figure 2

Cosmological history of GW and CMB production and fluctuations in the presence of a hidden sector. The inflaton (solid black) reheats the HS (red) while an ALP field (dashed black) reheats the VS (blue) in which the PT occurs. The HS particles later also decay into the VS. The dashed lines can have large contrast, $\delta \rho /\rho >(\delta \rho /\rho {)}_{\mathrm{CMB}}\sim {10}^{-5}$, while the solid lines have $\delta \rho /\rho \le {10}^{-5}$, saturated by the final VS (solid blue), which contains the CMB itself. Depending on the respective sizes of fluctuations in the inflaton and the ALP, the GW signal (gray) can have different possible values of $\delta \rho /\rho$ and can be highly correlated with the CMB fluctuations or relatively uncorrelated.