Consistency relations and conservation of $\zeta$ in holographic inflation

TL;DR

This paper demonstrates that in holographic inflation, the constancy of the curvature perturbation $$ is linked to the RG flow properties and consistency relations in the boundary theory, paralleling bulk conservation laws.

Contribution

It establishes a holographic perspective on the conservation of $$, connecting bulk superhorizon behavior to boundary RG flow and consistency relations.

Findings

Correlators of $$ are time-independent due to boundary cut-off independence.

The constancy of $$ correlators follows from boundary RG flow properties.

Consistency relations with a soft leg underpin the conservation of $$ in holographic inflation.

Abstract

It is well known that, in single clock inflation, the curvature perturbation $\zeta$ is constant in time on superhorizon scales. In the standard bulk description this follows quite simply from the local conservation of the energy momentum tensor in the bulk. On the other hand, in a holographic description, the constancy of the curvature perturbation must be related to the properties of the RG flow in the boundary theory. Here, we show that, in single clock holographic inflation, the time independence of correlators of $\zeta$ follows from the cut-off independence of correlators of the energy momentum tensor in the boundary theory, and from the so-called consistency relations for vertex functions with a soft leg.