Inflation without a beginning: A null boundary proposal

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 semiclassical 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 semieternal but nonsingular cosmologies.