No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics

Abstract

In minisuperspace quantum cosmology, the Lorentzian path integral formulations of the no-boundary and tunneling proposals have recently been analyzed. But it has been pointed out that the wave function of linearized perturbations around a homogeneous and isotropic background is of an inverse Gaussian form and thus that their correlation functions are divergent. In this paper, we revisit this issue and consider the problem of perturbations in Lorentzian quantum cosmology by modifying the dispersion relation based on trans-Planckian physics. We consider two modified dispersion relations, the generalized Corley-Jacobson dispersion relation with higher momentum terms and the Unruh dispersion relation with a trans-Planckian mode cut-off, as examples. We show that the inverse Gaussian problem of perturbations in Lorentzian quantum cosmology is hard to overcome with the trans-Planckian physics modifying the dispersion relation at short distances.

25 pages, 11 figures, v2: final published version

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Cited by in corpus (8)

• Review of the No-Boundary Wave Function
• Resurgence in Lorentzian quantum cosmology: No-boundary saddles and resummation of quantum gravity corrections around tunneling saddle points
• Hartle-Hawking No-boundary Proposal and Hořava-Lifshitz Gravity
• No smooth spacetime: Exploring primordial perturbations in Lorentzian quantum cosmology
• Jackiw-Teitelboim Gravity and Lorentzian Quantum Cosmology
• Boundary choices and one-loop complex gravitational path integral
• Dissipative Emergence of Inflation from Quasi-Cyclic Universe
• Summing over Non-singular Paths in Quantum Cosmology