Initial states and infrared physics in locally de Sitter spacetime

TL;DR

This paper investigates how initial quantum states affect long wavelength physics in de Sitter spacetime, proposing a cutoff-based approximation for maximum entropy states and analyzing their impact on observable correlations.

Contribution

It introduces a cutoff-based approach to model initial states in de Sitter space, highlighting how these states influence infrared physics and potential observational uncertainties.

Findings

Cutoff states induce secular logarithmic divergences at early times.

For massive fields, these divergences sum to finite late-time corrections.

Differences between cutoff and Hartle-Hawking correlators quantify initial state uncertainties.

Abstract

The long wavelength physics in a de Sitter region depends on the initial quantum state. While such long wavelength physics is under control for massive fields near the Hartle-Hawking vacuum state, such initial states make unnatural assumptions about initial data outside the region of causal contact of a local observer. We argue that a reasonable approximation to a maximum entropy state, one that makes minimal assumptions outside an observer's horizon volume, is one where a cutoff is placed on a surface bounded by timelike geodesics, just outside the horizon. For sufficiently early times, such a cutoff induces secular logarithmic divergences with the expansion of the region. For massive fields, these effects sum to finite corrections at sufficiently late times. The difference between the cutoff correlators and Hartle-Hawking correlators provides a measure of the theoretical uncertainty due to lack of knowledge of the initial state in causally disconnected regions. These differences are negligible for primordial inflation, but can become significant during epochs with very long-lived de Sitter regions, such as we may be entering now.