Abstract
In this paper, we delve into the gravitational path integral of Gauss-Bonnet gravity in four spacetime dimensions, in the mini-superspace approximation. Our primary focus lies in investigating the transition amplitude between distinct boundary configurations. Of particular interest is the case of Robin boundary conditions, known to lead to a stable Universe in Einstein-Hilbert gravity, alongside Neumann boundary conditions. To ensure a consistent variational problem, we supplement the bulk action with suitable surface terms. This study leads us to compute the necessary surface terms required for Gauss-Bonnet gravity with the Robin boundary condition, which wasn’t known earlier. Thereafter, we perform an exact computation of the transition amplitude. Through ħ → 0 analysis, we discover that the Gauss-Bonnet gravity inherently favors the initial configuration, aligning with the Hartle-Hawking no-boundary proposal. Remarkably, as the Universe expands, it undergoes a transition from the Euclidean (imaginary time) to the Lorentzian signature (real time). To further reinforce our findings, we employ a saddle point analysis utilizing the Picard-Lefschetz methods. The saddle point analysis allows us to find the initial configurations which lead to Hartle-Hawking no-boundary Universe that agrees with the exact computations. Our study concludes that for positive Gauss-Bonnet coupling, initial configurations corresponding to the Hartle-Hawking no-boundary Universe gives dominant contribution in the gravitational path-integral.
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Acknowledgments
We are thankful to Romesh Kaul for various illuminating discussions during the course of this work. We would also like to thank Chethan Krishnan for useful discussions at various stages of the work. We also thank the anonymous referee for the helpful suggestions.
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Ailiga, M., Mallik, S. & Narain, G. Lorentzian Robin Universe. J. High Energ. Phys. 2024, 124 (2024). https://doi.org/10.1007/JHEP01(2024)124
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DOI: https://doi.org/10.1007/JHEP01(2024)124