On the phase of the de Sitter density of states

TL;DR

This paper investigates the complex phase of the one-loop gravitational path integral in Euclidean de Sitter space, proposing a method involving an observer to interpret the density of states more consistently.

Contribution

It analyzes the phase of the one-loop determinant in de Sitter space with an observer, using a two-dimensional dilaton gravity model to support the phase cancellation proposal.

Findings

The phase can be interpolated between probe and Nariai cases.

A positive density of states is obtained after revisiting the path integral to partition function transition.

Abstract

The one-loop gravitational path integral around Euclidean de Sitter space $S^D$ has a complex phase that casts doubt on a state counting interpretation. Recently, it was proposed to cancel this phase by including an observer. We explore this proposal in the case where the observer is a charged black hole in equilibrium with the de Sitter horizon. We compute the phase of the one-loop determinant within a two-dimensional dilaton gravity reduction, using both numerical and analytical methods. Our results interpolate between previous studies of a probe geodesic observer and the Nariai solution. We also revisit the prescription for going from the Euclidean path integral to the state-counting partition function, finding a positive sign in the final density of states.