Can Two-Point Correlations Determine Gravitational Waves from Sound Waves?

Abstract

Sound waves are expected to be a dominant source of gravitational waves (GWs) from cosmological first-order phase transitions. Their spectrum is commonly predicted using the fluid velocity two-point correlation function under the Gaussian approximation. However, since the GW source is quadratic in velocity, connected four-point correlations may also contribute to the GW spectrum. Through two analytical toy examples, we demonstrate that velocity two-point correlations alone does not always uniquely determine the GW spectrum. Moving beyond these idealized examples, we investigate a realistic acoustic source based on stochastic bubble nucleation and growth, proving that the connected contribution becomes subleading during subsequent linear acoustic propagation, although cosmic expansion limits this suppression. These results clarify when two-point reconstruction is reliable and how higher-order velocity correlations and the duration of acoustic emission affect GW predictions.