Abstract
Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena’s single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space.
Highlights
The inflationary background is characterized by a spatially flat Friedmann-LemaıtreRobertson-Walker (FLRW) metric with scale factor a(t) and Hubble parameter H(t) = a /a, and by homogeneous scalar fields φI (t)
Full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations
In some two-field models of the type we consider, one may be able to integrate out a heavy field at the level of the full action, resulting at lowest order in derivatives in an effective effective field theory (EFT) for a single scalar field which is of P (X, φ) type [8]
Summary
We consider general two-field non-linear sigma models of inflation, described by the action. With GIJ the metric of the internal field space manifold. Our convention for the Riemann tensor is RIJKL = ΓIJL,K + ΓIKM ΓM JL − (K ↔ L) ,. Where we denote by ΓIJK the corresponding Levi-Civita connection. The fact that the field space is two-dimensional allows us to write. In terms of the field space Ricci scalar Rfs. Before considering cubic interactions in the two sections, here we set-up our notations, describe the gauge choice and covariant parameterization of the fluctuations that we employ, and briefly review the dynamics of the background and of linear fluctuations, that will be extensively used in the rest of the paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
