Constraints on holographic multi-field inflation

In holographic inflation, the four-dimensional cosmological dynamics is postulated to be dual to the renormalization group flow of a three-dimensional Euclidean conformal field theory with marginally relevant operators. The scalar potential of the $4D$ theory -in which inflation is realised- is highly constrained, with use of the Hamilton-Jacobi equations. We show that in multi-field holographic realizations of inflation, the dynamical masses of all fields additional to the inflaton must respect an upper bound of the form $\mu \leq 3 H / 2$ up to slow roll corrections. Indeed this bound applies to any multi-field model of inflation which uses the Hamilton-Jacobi equations. This upper bound reduces to the analytic continuation of the well known Breitenlohner-Freedman bound found in AdS spacetimes in the case when the masses are approximately constant, and it is found to be independent of the number of fields, the field space geometry and/or the shape of the inflationary trajectory followed in multi-field space. We infer that such models do not allow fields sufficiently heavy to be integrated out, and may present a number of interesting phenomenological consequences that could be confirmed or constrained by future surveys. For instance, a detection of "cosmological collider" oscillatory patterns in the non-Gaussian bispectrum due to massive fields, would uncover the existence of fields with dynamical masses larger than $3 H/2$ during inflation, therefore ruling out holographic inflation or any inflationary models based on the Hamilton-Jacobi equations.