General formula for the running of local fNL

Abstract

We compute the scale dependence of f NL for models of multi-field inflation, allowing for an arbitrary field space metric. We show that, in addition to multi-field effects and self interactions, the curved field space metric provides another source of scale dependence, which arises from the field-space Riemann curvature tensor and its derivatives. The scale dependence may be detectable within the near future if the amplitude of f NL is not too far from the current observational bounds.

Inflation in a scale-invariant universe

“…For α T , considering the limiting expression as α 1 → 0 gives even more accurate results (due to the extra α 1 suppression factor -see equation (37)) and we there obtain (37) α T ∼ −1.4 · 10 −5 · (α 2 − 1)…”

“…While an exploration of the full bi-and trispectrum is beyond our scope, the local non-Gaussian parameter f NL provides an observable of particular interest, since it is strongly suppressed in single field models [34,35] and can therefore provide a smoking-gun for multi-field dynamics, if sizeable enough to be measured. Focusing on this local limit, one can then obtain the following expression [36,37] f local NL ≈ 5 6…”

Multi-field inflation and cosmological perturbations

“…These moments are common to all modes of observational interest, and hence the momentum dependence which is of crucial observational importance is not explicit. This however becomes manifest by taking into account the moment of horizon crossing for each mode as follows [59]. For a certain mode with k, the horizon crossing happens at t 0 < t 1 , i.e.…”

Running of scalar spectral index in multi-field inflation

“…k = (aH) 0 . Then, until t i at which we evaluate Q a for the δN formalism, each mode gains k-dependent e-folds as [16], from the definition,…”