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

Understand

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.