Null Energy Condition Violations in Eternal Inflation

TL;DR

This paper explores how quantum fluctuations of the energy-momentum tensor in de Sitter space can lead to violations of the Null Energy Condition, which are essential for eternal inflation scenarios.

Contribution

It demonstrates that smeared energy-momentum tensor fluctuations can cause NEC violations, supporting models of eternal inflation.

Findings

Fluctuations are well-defined and can induce NEC violations.

Results align with standard inflationary density fluctuation calculations.

Quantum fluctuations in the diffusive regime are large enough for frequent NEC violations.

Abstract

The usual scenario of ``eternal inflation'' involves an approximately de Sitter spacetime undergoing upward fluctuations of the local expansion rate $H$. This spacetime requires frequent violations of the Null Energy Condition (NEC). We investigate the fluctuations of the energy-momentum tensor of the scalar field in de Sitter space as a possible source of such violations. We find that fluctuations of the energy-momentum tensor smeared in space and time are well-defined and may provide the NEC violations. Our results for slow-roll inflation are consistent with the standard calculations of inflationary density fluctuations. In the diffusive regime where quantum fluctuations dominate the slow-roll evolution, the magnitude of smeared energy-momentum tensor fluctuations is large enough to create frequent NEC violations.