Inflation and de Sitter Holography

TL;DR

This work formulates inflationary IR physics with a Hamilton-Jacobi approach in de Sitter space, treating the spacetime action as a Hamilton-Jacobi functional and renormalizing infrared divergences with boundary counterterms. By applying this to both spectator scalars and the full gravity-scalar system, the authors derive explicit local counterterms and compute the slow-roll power spectra, reproducing the standard results for the curvature perturbation and its spectral index, while framing inflation as a broken-scale-invariance phenomenon. A holographic renormalization group viewpoint is developed, linking the IR structure of inflation to a three-dimensional boundary theory via RG and Callan-Symanzik equations, and offering a scaling-centered perspective on fine-tuning in inflation. The framework clarifies how logarithmic corrections modify scale invariance, separates local divergent structure from nonlocal physics, and provides a principled way to relate infrared gravitational effects to ultraviolet data in a dual description.

Abstract

We develop the relation between de Sitter holography and inflation in detail, with particular attention to cosmic density perturbations. We set up the Hamilton-Jacobi formalism to present a systematic treatment of the logarithmic corrections to a scale invariant spectrum. Our computations can be interpreted without reference to holography, as strong infra-red effects in gravity. This point of view may be relevant for the fine-tuning problems inherent to inflation.