On the phase of the de Sitter density of states

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Abstract
A bstract: 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.
Funding Information
  • U.S. Department of Energy (DE-SC0021085)
  • U.S. Department of Energy (DE-SC0026143)
  • Simons Foundation (926198)
  • National Natural Science Foundation of China (12447108)
  • National Natural Science Foundation of China (12342501)
  • National Natural Science Foundation of China (12475071)
  • National Science Foundation (PHY-2210452)

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