Trispectrum estimation in various models of equilateral type non-Gaussianity

We calculate the shape correlations between trispectra in various equilateral non-Gaussian models, including Dirac-Born-Infeld inflation, ghost inflation and Lifshitz scalars, using the full trispectrum as well as the reduced trispectrum. We find that most theoretical models are distinguishable from the shapes of primordial trispectra except for several exceptions where it is difficult to discriminate between the models, such as single field Dirac-Born-Infeld inflation and a Lifshitz scalar model. We introduce an estimator for the amplitude of the trispectrum, gNLequil and relate it to model parameters in various models. Using constraints on gNLequil from WMAP5, we give constraints on the model parameters.