No-boundary extremal surfaces in slow-roll inflation and other cosmologies

TL;DR

This paper investigates no-boundary extremal surfaces in slow-roll inflation and other cosmologies, revealing complex area corrections that relate to the wavefunction and extend previous de Sitter space results.

Contribution

It extends the study of extremal surfaces to slow-roll inflation and other cosmologies, analyzing their complex areas and connections to the wavefunction.

Findings

Real and imaginary area corrections match semiclassical wavefunction expansions

In pure de Sitter space, the extremal surface area equals half the de Sitter entropy

The approach applies to 3D inflation and Schwarzschild de Sitter spaces with small mass

Abstract

Building on previous work on de Sitter extremal surfaces anchored at the future boundary, we study no-boundary extremal surfaces in slow-roll inflation models, with perturbations to no-boundary global $dS$ preserving the spatial isometry. While in pure de Sitter space the Euclidean hemisphere gives a real area equalling half de Sitter entropy, the no-boundary extremal surface areas here have nontrivial real and imaginary pieces overall. We evaluate the area integrals in the complex time-plane defining appropriate contours. For the 4-dim case, the real and imaginary finite corrections at leading order in the slow-roll parameter match those in the semiclassical expansion of the Wavefunction (or action), and corroborate the cosmic brane interpretation discussed previously. We also study no-boundary extremal surfaces in other cosmologies including 3-dimensional inflation and Schwarzschild de Sitter spaces with small mass.