No Rescue for the No Boundary Proposal

Abstract

In recent work, we introduced Picard-Lefschetz theory as a tool for defining the Lorentzian path integral for quantum gravity in a systematic semiclassical expansion. This formulation avoids several pitfalls occurring in the Euclidean approach. Our method provides, in particular, a more precise formulation of the Hartle-Hawking no boundary proposal, as a sum over real Lorentzian four-geometries interpolating between an initial three-geometry of zero size, {\it i.e}, a point, and a final three-geometry. With this definition, we calculated the no boundary amplitude for a closed universe with a cosmological constant, assuming cosmological symmetry for the background and including linear perturbations. We found the opposite semiclassical exponent to that obtained by Hartle and Hawking for the creation of a de Sitter spacetime "from nothing". Furthermore, we found the linearized perturbations to be governed by an {\it inverse} Gaussian distribution, meaning they are unsuppressed and out of control. Recently, Diaz Dorronsoro {\it et al.} followed our methods but attempted to rescue the no boundary proposal by integrating the lapse over a different, intrinsically complex contour. Here, we show that, in addition to the desired Hartle-Hawking saddle point contribution, their contour yields extra, non-perturbative corrections which again render the perturbations unsuppressed. We prove there is {\it no} choice of complex contour for the lapse which avoids this problem. We extend our discussion to include backreaction in the leading semiclassical approximation, fully nonlinearly for the lowest tensor harmonic and to second order for all higher modes. Implications for quantum de Sitter spacetime and for cosmic inflation are briefly discussed.

60 pages, 13 figures. Version to appear in Phys. Rev. D, including minor amendments and two new figures showing the effects of nonlinear backreaction to be modest

References in corpus (4)

• De Sitter Space and Eternity
• The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology
• Functional Determinants in Quantum Field Theory
• Infrared instability of the de Sitter space

Cited by in corpus (12)

• The No-Boundary Proposal as a Path Integral with Robin Boundary Conditions
• A Safe Beginning for the Universe?
• The no-boundary proposal in biaxial Bianchi IX minisuperspace
• Non-Singular Bounces Catalysed by Dark Energy
• Spinor driven cosmic bounces and their cosmological perturbations
• Effective Field Theory of Loop Quantum Cosmology
• Surprises in Lorentzian path-integral of Gauss-Bonnet gravity
• Gravitational Decoupling and Picard-Lefschetz
• Revisiting the no-boundary proposal with a scalar field
• Lorentzian quantum cosmology in novel Gauss-Bonnet gravity from Picard-Lefschetz methods
• Aspects of quantum gravity
• Lorentzian quantum cosmology with $R^2$ correction