Inflation without a beginning: a null boundary proposal

TL;DR

This paper proposes a model of eternal inflation with no initial singularity, using null boundary conditions on an elliptic de Sitter spacetime, leading to a consistent arrow of time and novel quantum properties.

Contribution

It introduces a null boundary condition framework for past-eternal inflation, avoiding the big bang singularity and exploring the implications for cosmological symmetry and quantum features.

Findings

Inflation can be modeled as past-eternal with a steady-state distribution.

The model admits a well-defined arrow of time for observers.

It suggests a classical and quantum structure of elliptic de Sitter spacetime.

Abstract

We develop our recent suggestion that inflation may be made past eternal, so that there is no initial cosmological singularity or "beginning of time". Inflation with multiple vacua generically approaches a steady-state statistical distribution of regions at these vacua, and our model follows directly from making this distribution hold at all times. We find that this corresponds (at the semi-classical level) to particularly simple cosmological boundary conditions on an infinite null surface near which the spacetime looks de Sitter. The model admits an interesting arrow of time that is well-defined and consistent for all physical observers that can communicate, even while the statistical description of the entire universe admits a symmetry that includes time-reversal. Our model suggests, but does not require, the identification of antipodal points on the manifold. The resulting "elliptic" de Sitter spacetime has interesting classical and quantum properties. The proposal may be generalized to other inflationary potentials, or to boundary conditions that give semi-eternal but non-singular cosmologies.