Dynamical interpretation of the wavefunction of the universe

Abstract

In this paper, we study the physical meaning of the wavefunction of the universe. With the continuity equation derived from the Wheeler-DeWitt (WDW) equation in the minisuperspace model, we show that the quantity $\rho (a)=|\psi (a){|}^2$ for the universe is inversely proportional to the Hubble parameter of the universe. Thus, $\rho (a)$ represents the probability density of the universe staying in the state $a$ during its evolution, which we call the dynamical interpretation of the wavefunction of the universe. We demonstrate that the dynamical interpretation can predict the evolution laws of the universe in the classical limit as those given by the Friedmann equation. Furthermore, we show that the value of the operator ordering factor $p$ in the WDW equation can be determined to be $p=-2$.

References in corpus (2)

• Spontaneous creation of the universe from nothing
• The Wheeler-DeWitt Quantization Can Solve the Singularity Problem

Cited by in corpus (14)

• WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings
• Class of solutions of the Wheeler-DeWitt equation with ordering parameter
• Class of solutions of the Wheeler-DeWitt equation in the Friedmann-Robertson-Walker universe
• Quantum cosmology of a Hořava-Lifshitz model coupled to radiation
• Wavefunction of the universe: Reparametrization invariance and field redefinitions of the minisuperspace path integral
• Classical and quantum cosmology of minimal massive bigravity
• Probability distribution for the quantum universe
• Gravitational Collapse via Wheeler-DeWitt Equation
• Wheeler-DeWitt equation rejects quantum effects of grown-up universes as a candidate for dark energy
• Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario
• Some exact results on quantum Newtonian cosmology
• Exact path integrals on half-line in quantum cosmology with a fluid clock and aspects of operator ordering ambiguity
• Exact solutions of the Wheeler-DeWitt equation with ordering term in a dark energy scenario
• Quantum relativistic cosmology: dynamical interpretation and tunneling universe