Time-covariant Schrödinger equation and invariant decay probability: The $\Lambda$-Kantowski-Sachs universe

Abstract

The system under study is the $\Lambda$-Kantowski-Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $t=f(\tilde{t})$) decay probability is defined and thus ``observers'' which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $a=0$ (where $a$ the radial scale factor) is calculated to be of the order $\sim 10^{-42}-10^{-41}\mathrm{s}$. The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler-DeWitt equation.

Latex2e source file, 21 pages, no figures, minor changes to match published version

References in corpus (19)

• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• A Short Review of Loop Quantum Gravity
• Loop Quantum Gravity: An Inside View
• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• An effective approach to the problem of time
• Quantum Cosmology of $f(R,T)$ gravity
• Revisiting observables in generally covariant theories in the light of gauge fixing methods
• Singularity resolution depends on the clock
• Noether Symmetries and Quantum Cosmology in Extended Teleparallel Gravity
• An Inflationary Non-singular Quantum Cosmological Model
• Quantum Black Hole Wave Packet: Average Area Entropy and Temperature Dependent Width
• Eisenhart--Duval lift for minisuperspace quantum cosmology
• f(R) Quantum Cosmology
• Quantization of inhomogeneous spacetimes with cosmological constant term
• Minisuperspace Quantization of $f\left(T,B\right)$ Cosmology
• Quantum cosmology of Bianchi VIII, IX LRS geometries
• Correlations across horizons in quantum cosmology
• String Theory: Progress and Problems
• Restoring Time Dependence into Quantum Cosmology