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No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics
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No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics
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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.
Forward citations
Cited by 1 Pith paper
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A Small-Throat Boundary Condition for the Tunneling Wave Function of the Universe
Tunneling wave function of a closed universe is recovered as the ε o0 limit of a Neumann-plus-small-domain path integral with radiation-induced throat, excluding the unsuppressed outer saddle.
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