Trispectrum estimator in equilateral type non-Gaussian models
  We investigate an estimator to measure the primordial trispectrum in
equilateral type non-Gaussian models such as k-inflation, single field DBI
inflation and multi-field DBI inflation models from Cosmic Microwave Background
(CMB) anisotropies. The shape of the trispectrum whose amplitude is not
constrained by the bispectrum in the context of effective theory of inflation
and k-inflation is known to admit a separable form of the estimator for CMB
anisotropies. We show that this shape is $87 \%$ correlated with the full
quantum trispectrum in single field DBI inflation, while it is $33 \%$
correlated with the one in multi-field DBI inflation when curvature
perturbation is originated from purely entropic contribution. This suggests
that $g_{\rm NL} ^{equil}$, the amplitude of this particular shape, provides a
reasonable measure of the non-Gaussianity from the trispectrum in equilateral
non-Gaussian models. We relate model parameters such as the sound speed, $c_s$
and the transfer coefficient from entropy perturbations to the curvature
perturbation, $T_{\mathcal{R} S}$ with $g_{\rm NL} ^{equil}$, which enables us
to constrain model parameters in these models once $g_{\rm NL}^{equil}$ is
measured in WMAP and Planck.
