Primordial Gravitational Wave Probes of Non-Standard Thermal Histories

Primordial gravitational waves propagate almost unimpeded from the moment they are generated to the present epoch. Nevertheless, they are subject to convolution with a non-trivial transfer function. Within the standard thermal history, shifts in the temperature-redshift relation combine with damping effects by free streaming neutrinos to non-trivially process different wavelengths during radiation domination, with subsequently negligible effects at later times. Presuming a nearly scale invariant primordial spectrum, one obtains a characteristic late time spectrum, deviations from which would indicate departures from the standard thermal history. Given the paucity of probes of the early universe physics before nucleosynthesis, it is useful to classify how deviations from the standard thermal history of the early universe can be constrained from observations of the late time stochastic background. The late time spectral density has a plateau at high frequencies that can in principle be significantly enhanced or suppressed relative to the standard thermal history depending on the equation of state of the epoch intervening reheating and the terminal phase of radiation domination, imprinting additional features from bursts of entropy production, and additional damping at intermediate scales via anisotropic stress production. In this paper, we survey phenomenologically motivated scenarios of early matter domination, kination, and late time decaying particles as representative non-standard thermal histories, elaborate on their late time stochastic background, and discuss constraints on different model scenarios.