Abstract
The no-boundary proposal is a theory of the initial conditions of the universe formulated in semi-classical gravity, and relying on the existence of regular (complex) solutions of the equations of motion. We show by explicit computation that regular no-boundary solutions are modified, but not destroyed, upon inclusion of expected quantum gravity corrections that involve higher powers of the Riemann tensor as well as covariant derivatives thereof. We illustrate our results with examples drawn from string theory. Our findings provide a crucial self-consistency test of the no-boundary framework.
Highlights
The Hartle-Hawking no-boundary proposal [1,2] provides a theory of the quantum state of the universe
The proposal is formulated in semiclassical gravity and relies on the existence of solutions of the Einstein equations that replace the big bang singularity with a smooth geometry
The insight of Hartle and Hawking was that in the Euclidean signature regular solutions can exist, the prototype being a four-sphere of constant positive curvature
Summary
The Hartle-Hawking no-boundary proposal [1,2] provides a theory of the quantum state of the universe. Recent work has shown that fixing a zero initial size leads to trouble [5], while one can obtain a consistent path integral definition of the no-boundary proposal when one specifies the initial expansion rate to be Euclidean [6,7] This construction is supported by the analogous calculation in anti–de Sitter space, where one may use well-known results in black hole thermodynamics as guidance [8]. Even when covariant derivatives are included in the correction terms, no-boundary solutions are robust to these corrections in the sense that the solutions will be modified somewhat, but their smoothness property is not endangered This result represents an important self-consistency check of the noboundary proposal, as it implies that the results obtained using only the setting of semiclassical gravity will continue to hold without drastic modification in more complete theories of quantum gravity. We employ the convention that the Riemann tensor is defined as Rλμαν 1⁄4 ∂αΓλμν −∂νΓλμα þ ΓβμνΓλβα − ΓβμαΓλβν and the Ricci tensor as Rμν 1⁄4 Rλμλν
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
