The size of local bispectrum and trispectrum in a non-minimal inflation

Abstract

Focusing on the local type primordial non-Gaussianities, we study the bispectrum and trispectrum during a non-minimal slow-roll inflation. We use the so-called δN formalism to investigate the super-horizon evolution of the primordial perturbations in this setup. Firstly we obtain the main equations of the model and introduce the framework of the δN formalism for this case. Then we give analytical expressions for the nonlinear parameters describing the non-Gaussianity in the slowroll approximation. We analyze the bispectrum by its non-linear parameter, fNL. Furthermore, we calculate τNL and gNL which are non-linear parameters characterizing the amplitude of trispectrum. Finally, by adopting a quadratic form for both the potential and non-minimal coupling (NMC) function, we test our setup in the light of Planck2015 data and constrain the model parameters space. Although the non-Gaussianity parameters are so small in this setup, this model is consistent with recent observation. We extend our analysis to see the situation in the Einstein frame and compare the results in these two frames.PACS numbers: 98.80.Cq , 98.80.Es

Exact Bianchi type-I inflationary model with non-minimally coupled scalar field

“…The Planck satellite is unable to measure such a small value of non-Gaussianity. Contrarily, the non-minimal coupled case [13,14] supports Planck-2015 [15] and Planck-2018 [16] released data that suggest a nearly scale-invariant power spectrum with a large non-Gaussian power spectrum ( f NL ? 1).…”

“…W and , is covariant D'Lambertian for f. The equation (13) for the metric (4) leads to following equation…”