Inflationary tensor fossils in large-scale structure
  Inflation models make specific predictions for a tensor-scalar-scalar
three-point correlation, or bispectrum, between one gravitational-wave (tensor)
mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar
correlation leads to a local power quadrupole, an apparent departure from
statistical isotropy in our Universe, as well as characteristic four-point
correlations in the current mass distribution in the Universe. So far, the
predictions for these observables have been worked out only for single-clock
models in which certain consistency conditions between the tensor-scalar-scalar
correlation and tensor and scalar power spectra are satisfied. Here we review
the requirements on inflation models for these consistency conditions to be
satisfied. We then consider several examples of inflation models, such as
non-attractor and solid inflation models, in which these conditions are put to
the test. In solid inflation the simplest consistency conditions are already
violated whilst in the non-attractor model we find that, contrary to the
standard scenario, the tensor-scalar-scalar correlator probes directly relevant
model-dependent information. We work out the predictions for observables in
these models. For non-attractor inflation we find an apparent local quadrupolar
departure from statistical isotropy in large-scale structure but that this
power quadrupole decreases very rapidly at smaller scales. The consistency of
the CMB quadrupole with statistical isotropy then constrains the distance scale
that corresponds to the transition from the non-attractor to attractor phase of
inflation to be larger than the currently observable horizon. Solid inflation
predicts clustering fossils signatures in the current galaxy distribution that
may be large enough to be detectable with forthcoming, and possibly even
current, galaxy surveys.
