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Review of the No-Boundary Wave Function
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When the universe is treated as a quantum system, it is described by a wave function. This wave function is a function not only of the matter fields, but also of spacetime. The no-boundary proposal is the idea that the wave function should be calculated by summing over geometries that have no boundary to the past, and over regular matter configurations on these geometries. Accordingly, the universe is finite, self-contained and the big bang singularity is avoided. Moreover, given a dynamical theory, the no-boundary proposal provides probabilities for various solutions of the theory. In this sense it provides a quantum theory of initial conditions. This review starts with a general overview of the framework of quantum cosmology, describing both the canonical and path integral approaches, and their interpretations. After recalling several heuristic motivations for the no-boundary proposal, its consequences are illustrated with simple examples, mainly in the context of cosmic inflation. We review how to include perturbations, assess the classicality of spacetime and how probabilities may be derived. A special emphasis is given to explicit implementations in minisuperspace, to observational consequences, and to the relationship of the no-boundary wave function with string theory. At each stage, the required analytic and numerical techniques are explained in detail, including the Picard-Lefschetz approach to oscillating integrals.
Forward citations
Cited by 7 Pith papers
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Relational path integral, effective actions and quantum frame covariance in gravity
The gravitational path integral is reformulated with dynamical reference frames, producing gauge-invariant correlators, frame-dependent vacua, and effective actions, with sharpness of events becoming frame-relative.
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Birth of Inflationary Universes via Wineglass Wormholes and their No-Boundary Relatives
Wineglass wormholes with a local maximum in the scale factor mediate the birth of inflationary spacetimes and split into background plus no-boundary geometries at small axionic or magnetic charge.
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A Menagerie of Wormholes and Cosmologies in the Gravitational Path Integral
The paper identifies a variety of Euclidean saddle solutions including wormholes and oscillatory configurations in Einstein-Scalar-Maxwell models, demonstrates how oscillations are controlled by lifting flat potential...
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Stochastic inflation as an open quantum system
Stochastic inflation emerges from an open-quantum-system derivation, with a Lindblad master equation that reduces to and corrects Starobinsky's Fokker-Planck equation.
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Junctions, strings, clocks and gravitational memory in three dimensional dS space
Transient closed-string fluctuations in dS3 are shown order by order to be encoded in gravitational junction shifts at I±, with the monotonic time shift forming an emergent clock.
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Particles, Forces and the Early Universe
The paper asserts a unified scenario of preon supersymmetry, no-boundary cosmology, and Chern-Simons gravity without providing new derivations or quantitative predictions.
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