  We develop a scenario of inflation with spontaneously broken time and space
diffeomorphisms, with distinctive features for the primordial tensor modes.
Inflationary tensor fluctuations are non adiabatic, and can acquire a mass
during the inflationary epoch. They can evade the Higuchi bound around de
Sitter space, thanks to interactions with the fields driving expansion.
Correspondingly, the primordial stochastic gravitational wave background (SGWB)
is characterised by a tuneable scale dependence, and can be detectable at
interferometer scales. In this set-up, tensor non-Gaussianity can be
parametrically enhanced in the squeezed limit. This induces a coupling between
long and short tensor modes, leading to a specific quadrupolar anisotropy in
the primordial SGWB spectrum, which can be used to build estimators for tensor
non-Gaussianity. We analyse how our inflationary system can be tested with
interferometers, also discussing how an interferometer can be sensitive to a
primordial anisotropic SGWB.
