Vacua and correlators in hyperbolic de Sitter space

Abstract

We study the power - and bi -spectrum of vacuum fluctuations in a hyperbolic section of de Sitter space, comparing two states of physical interest: the Bunch-Davies and hyperbolic vacuum. We introduce a one -parameter family of de Sitter hyperbolic sections and their natural vacua, and identify a limit in which it reduces to the planar section and the corresponding Bunch -Davies vacuum state. Selecting the Bunch -Davies vacuum for a massless scalar field implies a mixed reduced density matrix in a hyperbolic section of de Sitter space. We stress that in the Bunch -Davies state the hyperbolic de Sitter $n$-point correlation functions have to match the planar de Sitter $n$-point correlation functions. The expressions for the planar and hyperbolic Bunch -Davies correlation functions only appear different because of the transformation from planar to hyperbolic coordinates. Initial state induced deviations from the standard inflationary predictions are instead obtained by considering the pure hyperbolic vacuum, as we verify explicitly by computing the power - and bi -spectrum. For the bi -spectrum in the hyperbolic vacuum we find that the corrections as compared to the standard Bunch -Davies result are not enhanced in specific momentum configurations and strongly suppressed for momenta large compared to the hyperbolic curvature scale. We close with some final remarks, in particular regarding the implications of these results for more realistic inflationary bubble scenarios.

Added references, removed typos, added author, extensions in first section and conclusions. 34 pages, 4 figures

References in corpus (30)

• Non-Gaussian features of primordial fluctuations in single field inflationary models
• The Anthropic Landscape of String Theory
• An Open Universe from Inflation
• Observational Consequences of a Landscape
• Enhanced Non-Gaussianity from Excited Initial States
• Signatures of Initial State Modifications on Bispectrum Statistics
• Entanglement entropy in de Sitter space
• Non-gaussianities and the Stimulated creation of quanta in the inflationary universe
• Euclidian Vacuum Mode Functions for a Scalar Field on Open De Sitter Spacetime
• CMB in Open Inflation
• Effective field theory and non-Gaussianity from general inflationary states
• First Observational Tests of Eternal Inflation
• A Note on Calm Excited States of Inflation
• Quantum fluctuations and CMB anisotropies in one-bubble open inflation models
• De Sitter Holography with a Finite Number of States
• Inflation after False Vacuum Decay: Observational Prospects after Planck
• Gravitational Waves in Open de Sitter Space
• Open inflation in the landscape
• What can the observation of nonzero curvature tell us?
• Eternal Inflation
• Spectrum of Cosmological Perturbations in the One-Bubble Open Universe
• Cosmic Bubble Collisions
• Eternal Inflation, Bubble Collisions, and the Disintegration of the Persistence of Memory
• Impact of quantum entanglement on spectrum of cosmological fluctuations
• Universal Correction to the Inflationary Vacuum
• The Energy-Momentum Tensor in Fulling-Rindler Vacuum
• Analyzing Cosmic Bubble Collisions
• Bispectrum from open inflation
• Local thermal observables in spatially open FRW spaces
• Where do all the supercurvature modes go?

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• Optimal CMB estimators for bispectra from excited states
• Quantum steering for continuous variable in de Sitter space
• Quantum Entanglement in Multi-field Inflation
• Mean field squared and energy-momentum tensor for the hyperbolic vacuum in dS spacetime
• Fermionic condensate in de Sitter spacetime
• Casimir densities induced by a sphere in the hyperbolic vacuum of de Sitter spacetime
• Quantum field theory in a de Sitter universe transiting to the radiation stage