Primordial Non-Gaussianity in Supersolid Inflation
  We study primordial non-gaussianity in supersolid inflation. The dynamics of
supersolid is formulated in terms of an effective field theory based on four
scalar fields with a shift symmetric action minimally coupled with gravity. In
the scalar sector, there are two phonon-like excitations with a kinetic mixing
stemming from the completely spontaneous breaking of diffeomorphism. In a
squeezed configuration, $f_{\text{NL}}$ of scalar perturbations is angle
dependent and not proportional to slow-roll parameters showing a blunt
violation of the Maldacena consistency relation. Contrary to solid inflation,
the violation persists even after an angular average and generically the amount
of non-gaussianity is significant. During inflation, non-gaussianity in the TSS
and TTS sector is enhanced in the same region of the parameters space where the
secondary production of gravitational waves is sizeable enough to enter in the
sensitivity region of LISA, while the scalar $f_{\text{NL}}$ is still within
the current experimental limits.
