Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes

TL;DR

This paper derives quantum inequalities constraining negative energy in static Robertson-Walker spacetimes, accounting for curvature effects and recovering flat spacetime results in the appropriate limit.

Contribution

It provides a general inequality for negative energy in static spacetimes and explicitly evaluates it for scalar fields in Robertson-Walker universes, including curvature effects.

Findings

Inequalities constrain negative energy magnitude and duration.

Flat spacetime inequalities are recovered in the zero-curvature limit.

Curvature introduces subdominant corrections at short sampling times.

Abstract

Quantum inequality restrictions on the stress-energy tensor for negative energy are developed for three and four-dimensional static spacetimes. We derive a general inequality in terms of a sum of mode functions which constrains the magnitude and duration of negative energy seen by an observer at rest in a static spacetime. This inequality is evaluated explicitly for a minimally coupled scalar field in three and four-dimensional static Robertson-Walker universes. In the limit of vanishing curvature, the flat spacetime inequalities are recovered. More generally, these inequalities contain the effects of spacetime curvature. In the limit of short sampling times, they take the flat space form plus subdominant curvature-dependent corrections.