Constraints on holographic multi-field inflation and models based on the Hamilton-Jacobi formalism

TL;DR

This paper explores constraints on multi-field holographic inflation models using the Hamilton-Jacobi formalism, revealing that additional fields cannot oscillate independently and establishing bounds on their masses, which impacts the interpretation of cosmological collider signals.

Contribution

It proves that extra fields in multi-field holographic inflation cannot exhibit underdamped oscillations, and derives an upper mass bound related to the Breitenlohner--Freedman bound, independent of model specifics.

Findings

Extra fields lack oscillatory phases, regardless of model details.

An upper mass bound of m ≤ 3H/2 for additional fields is established.

Detection of oscillations in non-Gaussianity would rule out multiple inflation models.

Abstract

In holographic inflation, the $4D$ cosmological dynamics is postulated to be dual to the renormalization group flow of a $3D$ Euclidean conformal field theory with marginally relevant operators. The scalar potential of the $4D$ theory ---in which inflation is realized--- is highly constrained, with use of the Hamilton--Jacobi equations. In multi-field holographic realizations of inflation, fields additional to the inflaton cannot display underdamped oscillations (that is, their wavefunctions contain no oscillatory phases independent of the momenta). We show that this result is exact, independent of the number of fields, the field space geometry and the shape of the inflationary trajectory followed in multi-field space. In the specific case where the multi-field trajectory is a straight line or confined to a plane, it can be understood as the existence of an upper bound on the dynamical masses $m$ of extra fields of the form $m \leq 3 H / 2$ up to slow roll corrections. This bound corresponds to the analytic continuation of the well known Breitenlohner--Freedman bound found in AdS spacetimes in the case when the masses are approximately constant. The absence of underdamped oscillations implies that a detection of "cosmological collider" oscillatory patterns in the non-Gaussian bispectrum would not only rule out single field inflation, but also holographic inflation or any inflationary model based on the Hamilton--Jacobi equations. Hence, future observations have the potential to exclude, at once, an entire class of inflationary theories, regardless of the details involved in their model building.