The Perils of Analytic Continuation

Abstract

A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyonic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrison's de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2=0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrison's spin two sector is not "physically equivalent" to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.

40 pages, 2 figures (6 figure files), uses LaTeX2e, Version 2 expanded to 43 pages, principally in section 3 to show that even the closed coordinate mode sums break de Sitter invariance and that claims to the contrary are based upon the (admitted) use of negative normed states

References in corpus (12)

• On the Instability of Global de Sitter Space to Particle Creation
• Gravitons Enhance Fermions during Inflation
• Infrared Propagator Corrections for Constant Deceleration
• Quantum Vacuum Instability of 'Eternal' de Sitter Space
• Quantum Gravity Corrections to the One Loop Scalar Self-Mass during Inflation
• A Maximally Symmetric Vector Propagator
• Group Averaging for de Sitter free fields
• Scalar Field Equations from Quantum Gravity during Inflation
• A Simple Operator Check of the Effective Fermion Mode Function during Inflation
• One Loop Corrected Mode Functions for SQED during Inflation
• Scalar Contribution to the Graviton Self-Energy during Inflation
• A graviton propagator for inflation

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• Large Logarithms from Quantum Gravitational Corrections to a Massless, Minimally Coupled Scalar on de Sitter
• Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter
• The Weyl tensor correlator in cosmological spacetimes
• Infrared Behavior of Quantum Fields in Inflationary Cosmology -- Issues and Approaches: an overview
• Infrared-finite graviton two-point function in static de Sitter space
• Representing the Graviton Self-Energy on de Sitter Background
• Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background
• Covariant and infrared-free graviton two-point function in de Sitter spacetime II
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• Vacuum states for gravitons field in de Sitter space
• Graviton Self-Energy from Gravitons in Cosmology
• Explaining Large Electromagnetic Logarithms from Loops of Inflationary Gravitons
• Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime
• Gauge Independent Logarithms from Inflationary Gravitons
• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• Hartle-Hawking state in the real-time formalism
• Some Inconvenient Truths