No-boundary prescriptions in Lorentzian quantum cosmology

Abstract

We analyse the impact of various boundary conditions on the (minisuperspace) Lorentzian gravitational path integral. In particular we assess the implications for the Hartle-Hawking no-boundary wavefunction. It was shown recently that when this proposal is defined as a sum over compact metrics, problems arise with the stability of fluctuations. These difficulties can be overcome by an especially simple implementation of the no-boundary idea: namely to take the Einstein-Hilbert action at face value while adding no boundary term. This prescription simultaneously imposes an initial Neumann boundary condition for the scale factor of the universe and, for a Bianchi IX spacetime, Dirichlet conditions for the anisotropies. Another way to implement the no-boundary wavefunction is to use Robin boundary conditions. A sub-class of Robin conditions allows one to specify the Hubble rate on the boundary hypersurface, and we highlight the surprising aspect that specifying the final Hubble rate (rather than the final size of the universe) significantly alters the off-shell structure of the path integral. The conclusion of our investigations is that all current working examples of the no-boundary wavefunction force one to abandon the notion of a sum over compact and regular geometries, and point to the importance of an initial Euclidean momentum.

Lessons for quantum cosmology from anti–de Sitter black holes

“…Our AdS calculation in this case can be brought into one-to-one correspondence with the recent definition of the no-boundary proposal in Ref. [9] and shows that using momentum conditions at the big bang rather than summing over compact metrics is, in fact, quite natural from the holographic point of view.…”

“…In this work, we will reproduce features of the Hawking-Page phase transition by calculating explicitly the gravitational path integral in the minisuperspace approach [8]. Our studies for black holes in AdS space are motivated by recent developments in cosmology, as there is a very close analogy between the calculations performed in the present work and novel studies of the no-boundary proposal in cosmology utilising the minisuperspace Ansatz [9]. The idea is to make use of the firm results for the thermodynamics of black holes to learn lessons for path integrals in quantum cosmology.…”

“…For such saddle points, the weighting is larger when the fluctuations are larger, and this results in unphysical predictions. 1 By contrast, path integrals with an initial Neumann condition allow for a consistent and stable formulation of the Hartle-Hawking wave function [9]. 2 In the present work, we study gravitational path integrals in AdS with the aim of using holographic intuitions to shed light on the aforementioned studies in cosmology.…”

“…Here, as in Ref. [9], we will be careful to consider the boundary conditions as arising from the full Einstein-Hilbert action, thus guaranteeing that our treatment is covariant. One may also consider more general conditions that form a linear combination of Dirichlet and Neumann conditions [21].…”

Swampland constraints on no-boundary quantum cosmology

“…Note that the wave function predicted by Feldbrugge et al is Green's function rather than a solution to the Wheeler-DeWitt equation. See also related discussions [23][24][25][26][27][28].…”