Mean field squared and energy-momentum tensor for the hyperbolic vacuum in dS spacetime
arXiv:2110.06662 · doi:10.1016/j.aop.2021.168728
Abstract
We evaluate the Hadamard function and the vacuum expectation values (VEVs) of the field squared and energy-momentum tensor for a massless conformally coupled scalar field in -dimensional de Sitter (dS) spacetime foliated by spatial sections of negative constant curvature. It is assumed that the field is prepared in the hyperbolic vacuum state. An integral representation for the difference of the Hadamard functions corresponding to the hyperbolic and Bunch-Davies vacua is provided that is well adapted for the evaluation of the expectation values in the coincidence limit. It is shown that the Bunch-Davies state is interpreted as thermal with respect to the hyperbolic vacuum. An expression for the corresponding density of states is provided. The relations obtained for the difference in the VEVs for the Bunch-Davies and hyperbolic vacua are compared with the corresponding relations for the Fulling-Rindler and Minkowski vacua in flat spacetime. The similarity between those relations is explained by the conformal connection of dS spacetime with hyperbolic foliation and Rindler spacetime. As a limiting case, the VEVs for the conformal vacuum in the Milne universe are discussed.
arXiv comment18 pages, no figures, discussion added
References in corpus (30)
- Conformal Vacua and Entropy in de Sitter Space
- An Open Universe from Inflation
- Entanglement entropy in de Sitter space
- Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes
- Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
- Large Angle CMB Anisotropy in an Open Universe in the One-Bubble Inflationary Scenario
- Euclidian Vacuum Mode Functions for a Scalar Field on Open De Sitter Spacetime
- LARGE SCALE PERTURBATIONS IN THE OPEN UNIVERSE
- Comments on the Stress-Energy Tensor Operator in Curved Spacetime
- Open inflation in the landscape
- Entanglement entropy of -vacua in de Sitter space
- Casimir energy-momentum tensor for a brane in de Sitter spacetime
- Quasi-open inflation
- Vacuum State of the Dirac Field in de Sitter Space and Entanglement Entropy
- Polarization of the Fulling-Rindler vacuum by uniformly accelerated mirror
- Quantum entanglement in de Sitter space with a wall, and the decoherence of bubble universes
- Multi-field open inflation model and multi-field dynamics in tunneling
- Entanglement Entropy of de Sitter Space α-Vacua
- Casimir densities for a spherical boundary in de Sitter spacetime
- Back(reaction) to the Future in the Unruh-de Sitter State
- On the response of a particle detector in Anti-de Sitter spacetime
- de Sitter Vacua of Strongly Interacting QFT
- QCD Axion Window and False Vacuum Higgs Inflation
- Casimir densities from coexisting vacua
- Instability of De Sitter Spacetime induced by Quantum Conformal Anomaly
- The conformal anomaly in N-dimensional space having a hyperbolic spatial section
- Vacua and correlators in hyperbolic de Sitter space
- Emergent -like fermionic vacuum structure and entanglement in the hyperbolic de Sitter spacetime
- The Casimir densities for a sphere in the Milne universe
- Casimir densities induced by a sphere in the hyperbolic vacuum of de Sitter spacetime