Gravitational entropy and the flatness, homogeneity and isotropy puzzles

TL;DR

This paper proposes a new gravitational entropy-based explanation for the universe's observed flatness, homogeneity, and isotropy, using boundary conditions and instantons in Einstein's gravity with matter.

Contribution

It introduces boundary conditions enforcing CPT symmetry and analyticity, leading to new gravitational instantons that explain large-scale universe properties.

Findings

Gravitational entropy of cosmologies relates to de Sitter entropy and radiation entropy.

Most probable universe is flat when gravitational entropy exceeds de Sitter entropy.

Perturbation analysis supports large-scale homogeneity and isotropy.

Abstract

We suggest a new explanation for the observed large scale flatness, homogeneity and isotropy of the universe. The basic ingredients are elementary and well-known, namely Einstein's theory of gravity and Hawking's method of computing gravitational entropy. The new twist is provided by the boundary conditions we recently proposed for "big bang" type singularities dominated by conformal matter, enforcing $CPT$ symmetry and analyticity. Here, we show that, besides allowing us to describe the big bang, these boundary conditions allow new gravitational instantons, enabling us to calculate the gravitational entropy of cosmologies which include radiation, dark energy and space curvature of either sign. We find the gravitational entropy of these universes, $S_g \sim S_\Lambda^{1/ 4} S_r$, where $S_\Lambda$ is the famous de Sitter entropy and $S_r$ is the total entropy in radiation. To the extent that $S_g$ exceeds $S_\Lambda$, the most probable universe is flat. By analysing the perturbations about our new instantons, we argue it is also homogeneous and isotropic on large scales.