  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).
