De Sitter Holography and the Cosmic Microwave Background

TL;DR

This paper proposes a holographic view of cosmology based on the dS/CFT correspondence, conceiving the universe's evolution as an RG flow between IR and UV fixed points of a dual Euclidean field theory. Inflation is recast as an irrelevant deformation near the IR fixed point, with the CMB spectrum determined by scaling violations encoded in the β-function and anomalous dimensions, yielding concrete relations such as $ε=β^2/2$, $n_S-1=-4ε+2η$, and $r=4ε$, which in leading order become $n_S≈1-2λ$, $n_T≈-β^2$, $r≈2β^2$ with $β≪λ≪1$. A toy 3D QFT with a φ^6 interaction is used to illustrate how β and λ can be computed perturbatively and how CMB-like predictions emerge, while acknowledging limitations of the simple model. The framework offers a fresh perspective on inflationary fine-tuning, the cosmological constant problem, and initial conditions, suggesting that holography ties these issues to fixed-point structure and RG-flow properties, though a fully realistic dual description remains an open challenge.

Abstract

We interpret cosmological evolution holographically as a renormalisation group flow in a dual Euclidean field theory, as suggested by the conjectured dS/CFT correspondence. Inflation is described by perturbing around the infra-red fixed point of the dual field theory. The spectrum of the cosmic microwave background radiation is determined in terms of scaling violations in the field theory. The dark energy allows similar, albeit less predictive, considerations. We discuss the cosmological fine-tuning problems from the holographic perspective.