The rise of the primordial tensor spectrum from an early scalar-tensor epoch

Primordial gravitational waves (PGW) produced during inflation span a large range of frequencies, carrying information on the dynamics of the primordial universe. During an early scalar-tensor dominated epoch, the amplitude of the PGW spectrum can be enhanced over a wide range of frequencies. To study this phenomenon, we focus on a class of scalar-tensor theories, well motivated by high energy theories of dark energy and dark matter, where the scalar is conformally and disformally coupled to matter during the early cosmological evolution. For a conformally dominated epoch, the PGW spectrum has a flat step-like shape. More interestingly, a disformally dominated epoch is characterised by a peaked spectrum with a broken power-law profile, with slopes depending on the scalar-tensor theory considered. We introduce a graphical tool, called broken power-law sensitivity curve, as a convenient visual indicator for understanding whether a given broken power-law profile can be detected by GW experiments. We then analyse the GW spectra for a variety of representative conformal and disformal models, discussing their detectability prospects with the Einstein Telescope (ET), Laser Interferometer Space Antenna (LISA), DECi-hertz Interferometer Gravitational wave Observatory (DECIGO), and Big Bang Observer (BBO).