Utilizing the causal spectrum of gravitational waves
The low frequency part of the gravitational wave spectrum generated by local physics, such as a phase transition, is largely fixed by causality, offering a clean window into the early Universe. Due to the difference between sub-horizon and super-horizon physics, a distinct spectral feature can allow for the direct measurement of the conformal Hubble rate at which the phase transition occurred. As an example, free-streaming particles present during the phase transition affect the production of super-horizon modes. This leads to a steeper decrease in the spectrum at low frequencies as compared to the well-known causal k³ scaling. If the universe was not radiation dominated when the waves were generated, a similar feature is also present. As a surprising consequence, one can see that a period of matter domination following the production of gravity waves actually increases their power spectrum at low frequencies.