  We study cosmological tensor perturbations induced by second-order scalar
perturbations in the presence of anisotropic non-Gaussianity. This class of
induced tensor modes arises on superhorizon scales through the intrinsic
quadrupole coupling between long modes and short modes. Scalar perturbations on
all scales from the inflationary Hubble radius to the Silk damping scale at
recombination contribute to the induced tensor powerspectrum at the cosmic
microwave background (CMB) scale. In addition, the induced tensor spectrum
becomes almost scale-invariant. The former property suggests that measurements
of the CMB offer a test of tiny scale physics. However, the latter implies the
secondary effect may contaminate the primordial tensor spectrum, which tells us
the energy scale of inflation. We derive the induced tensor modes originated
from two concrete examples of anisotropic non-Gaussianity; statistically
anisotropic scalar non-Gaussianity and scalar-scalar-tensor non-Gaussianity,
and discuss observational consequences of extremely short scale physics. Also,
we comment on various possibilities of enhancing the induced spectrum with
nonstandard early Universe physics.
