Cosmological Models and Renormalization Group Flow

TL;DR

This paper explores diverse cosmological solutions in Einstein gravity with a positive cosmological constant, interpreting them as renormalization group flows and analyzing their causal structures and entropy bounds.

Contribution

It introduces a geometric interpretation of the c-function as the apparent horizon area and discusses quantum effects on early causal structures.

Findings

Re-collapsing and bounce models are tall, revealing entire spatial slices before conformal time ends.

De Sitter-like models can be short or tall, affecting observer visibility.

Quantum effects modify the early causal structure of some big-bang solutions.

Abstract

We study cosmological solutions of Einstein gravity with a positive cosmological constant in diverse dimensions. These include big-bang models that re-collapse, big-bang models that approach de Sitter acceleration at late times, and bounce models that are both past and future asymptotically de Sitter. The re-collapsing and the bounce geometries are all tall in the sense that entire spatial slices become visible to a comoving observer before the end of conformal time, while the accelerating big-bang geometries can be either short or tall. We consider the interpretation of these cosmological solutions as renormalization group flows in a dual field theory and give a geometric interpretation of the associated c-function as the area of the apparent cosmological horizon in Planck units. The covariant entropy bound requires quantum effects to modify the early causal structure of some of our big-bang solutions.