Causal gravitational waves as a probe of free streaming particles and the expansion of the Universe

The low frequency part of the gravitational wave spectrum generated by local physics, such as a phase transition or parametric resonance, is largely fixed by causality, offering a clean window into the early Universe. In this work, this low frequency end of the spectrum is analyzed with an emphasis on a physical understanding, such as the suppressed production of gravitational waves due to the excitation of an over-damped harmonic oscillator and their enhancement due to being frozen out while outside the horizon. Due to the difference between sub-horizon and super-horizon physics, it is inevitable that there will be a distinct spectral feature that could allow for the direct measurement of the conformal Hubble rate at which the phase transition occurred. As an example, free-streaming particles (such as the gravity waves themselves) 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 k(3) super-horizon scaling of stochastic gravity waves. If a sizable fraction of the energy density is in free-streaming particles, they even lead to the appearance of oscillatory features in the spectrum. If the universe was not radiation dominated when the waves were generated, a similar feature also occurs at the transition between sub-horizon to super-horizon causality. These features are used to show surprising consequences, such as the fact that a period of matter domination following the production of gravity waves actually increases their power spectrum at low frequencies.

Automated summary

This article focuses on analyzing the low frequency end of the gravitational wave spectrum, explaining the phenomena of suppressed production of gravitational waves due to the excitation of an over-damped harmonic oscillator and their enhancement when frozen outside the horizon from a physics perspective. The differences between sub-horizon and super-horizon physics lead to distinct spectral features that can directly measure the conformal Hubble rate at which a phase transition occurred. Additionally, the presence of free-streaming particles during a phase transition affects the behavior of super-horizon modes in the spectrum, resulting in oscillatory features and a steeper decrease in the spectrum at low frequencies.