Quantum Tunneling and the Emergence of Classical Spacetime in Einstein-Æther Quantum Cosmology
Abstract
We investigate a quantum cosmological model within the framework of Einstein-Æther gravity. The model consists of a positively curved FLRW Universe whose matter content is described by pressureless dust, in the presence of a positive cosmological constant Λ. We first perform a classical Hamiltonian analysis utilizing Schutz's variational formalism, constructing the phase space and deriving the dynamics of the scale factor. Notably, we identify specific initial conditions that lead to an inflationary expansion, which are extracted directly from the underlying quantum dynamics. Subsequently, we quantize the model following Dirac's formalism, obtaining the Wheeler-DeWitt equation for the wave function of the Universe. We solve this equation numerically and investigate our results using the WKB approximation to compute quantum tunneling probabilities TPWKB alongside an integrated tunneling probability TPint, the expectation value of the scale factor coming from the many-worlds interpretation of quantum mechanics, and the corresponding Bohmian trajectories. Finally, we analyze how these tunneling probabilities are influenced by variations in the fundamental parameters of the theory ($Λ, σ, β$) and the energy of the dust fluid E. Our results indicate a higher probability for the quantum birth of the Universe in a parameter regime characterized by larger values of $Λ, σ$, and fluid energy E, together with a smaller value of β.
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BibTeX
@misc{monerat2026quantum,
title = {{Quantum Tunneling and the Emergence of Classical Spacetime in Einstein-Æther Quantum Cosmology}},
author = {Germano A. Monerat and Alessandro O. Castro Junior and Eduardo V. Corrêa Silva and Gil O. Neto},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21814},
eprint = {2609.21814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21814},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Tunneling and the Emergence of Classical Spacetime in Einstein-Æther Quantum Cosmology
AU - Germano A. Monerat
AU - Alessandro O. Castro Junior
AU - Eduardo V. Corrêa Silva
AU - Gil O. Neto
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21814
UR - https://arxiv.org/abs/2609.21814
AB - We investigate a quantum cosmological model within the framework of Einstein-Æther gravity. The model consists of a positively curved FLRW Universe whose matter content is described by pressureless dust, in the presence of a positive cosmological constant Λ. We first perform a classical Hamiltonian analysis utilizing Schutz's variational formalism, constructing the phase space and deriving the dynamics of the scale factor. Notably, we identify specific initial conditions that lead to an inflationary expansion, which are extracted directly from the underlying quantum dynamics. Subsequently, we quantize the model following Dirac's formalism, obtaining the Wheeler-DeWitt equation for the wave function of the Universe. We solve this equation numerically and investigate our results using the WKB approximation to compute quantum tunneling probabilities TP_WKB alongside an integrated tunneling probability TP_int, the expectation value of the scale factor coming from the many-worlds interpretation of quantum mechanics, and the corresponding Bohmian trajectories. Finally, we analyze how these tunneling probabilities are influenced by variations in the fundamental parameters of the theory ($Λ, σ, β$) and the energy of the dust fluid E. Our results indicate a higher probability for the quantum birth of the Universe in a parameter regime characterized by larger values of $Λ, σ$, and fluid energy E, together with a smaller value of β.
ER -