Unitary Evolution and Cosmological Fine-Tuning

TL;DR

This paper examines the implications of unitary evolution on cosmological fine-tuning, finding that flatness is natural but homogeneity and inflation are highly fine-tuned, with inflation occurring in an extremely small fraction of histories.

Contribution

It applies the invariant measure on Einstein solutions to analyze fine-tuning issues, challenging the necessity of inflation for explaining flatness and highlighting its role as a target for initial condition theories.

Findings

Most Robertson-Walker cosmologies are spatially flat.

Homogeneity requires significant fine-tuning.

Inflation occurs in less than 1 in 10^{6.6×10^7} histories.

Abstract

Inflationary cosmology attempts to provide a natural explanation for the flatness and homogeneity of the observable universe. In the context of reversible (unitary) evolution, this goal is difficult to satisfy, as Liouville's theorem implies that no dynamical process can evolve a large number of initial states into a small number of final states. We use the invariant measure on solutions to Einstein's equation to quantify the problems of cosmological fine-tuning. The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat. The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real. When perturbations are taken into account, inflation only occurs in a negligibly small fraction of cosmological histories, less than $10^{-6.6\times 10^7}$. We argue that while inflation does not affect the number of initial conditions that evolve into a late universe like our own, it nevertheless provides an appealing target for true theories of initial conditions, by allowing for small patches of space with sub-Planckian curvature to grow into reasonable universes.