Numerical evaluation of the three-point scalar-tensor cross-correlations and the tensor bi-spectrum

Abstract

Utilizing the Maldacena formalism and extending the earlier efforts to compute the scalar bi-spectrum, we construct a numerical procedure to evaluate the three-point scalar-tensor cross-correlations as well as the tensor bi-spectrum in single field inflationary models involving the canonical scalar field.We illustrate the accuracy of the adopted procedure by comparing thenumerical results with the analytical results that can be obtained in the simpler cases of power law and slow roll inflation.We also carry out such a comparison in the case of the Starobinsky model described by a linear potential with a sudden change in the slope, whichprovides a non-trivial and interesting (but, nevertheless, analytically tractable) scenario involving a brief period of deviation from slow roll. We then utilize the code we have developed to evaluate the three-point correlation functions of interest (and the corresponding non-Gaussianity parameters that we introduce) for an arbitrary triangular configuration of the wavenumbers in three different classes of inflationary models which lead to features in the scalar power spectrum, as have been recently considered by the Planck team.We also discuss the contributions to the three-point functions duringpreheating in inflationary models with a quadratic minimum.We conclude with a summary of the main results we have obtained.