Examining the consistency relations describing the three-point functions
  involving tensors
  It is well known that the non-Gaussianity parameter $f_{_{\rm NL}}$
characterizing the scalar bi-spectrum can be expressed in terms of the scalar
spectral index in the squeezed limit, a property that is referred to as the
consistency relation. In this work, we consider the consistency relations
associated with the three-point cross-correlations involving scalars and
tensors as well as the tensor bi-spectrum in inflationary models driven by a
single, canonical, scalar field. Characterizing the cross-correlations in terms
of the dimensionless non-Gaussianity parameters $C_{_{\rm NL}}^{\mathcal R}$
and $C_{_{\rm NL}}^{\mathcal \gamma}$ that we had introduced earlier, we
express the consistency relations governing the cross-correlations as relations
between these non-Gaussianity parameters and the scalar or tensor spectral
indices, in a fashion similar to that of the purely scalar case. We also
discuss the corresponding relation for the non-Gaussianity parameter $h_{_{\rm
NL}}$ used to describe the tensor bi-spectrum. We analytically establish these
consistency relations explicitly in the following two situations: a simple
example involving a specific case of power law inflation and a non-trivial
scenario in the so-called Starobinsky model that is governed by a linear
potential with a sharp change in its slope. We also numerically verify the
consistency relations in three types of inflationary models that permit
deviations from slow roll and lead to scalar power spectra with features which
typically result in an improved fit to the data than the more conventional,
nearly scale invariant, spectra. We close with a summary of the results we have
obtained. (Abridged)
