Setting free the cosmic time in Quantum Universe
David Vasak
TL;DR
The paper addresses the problem of time freezing in quantum cosmology caused by the time-free Wheeler-DeWitt equation $H psi = 0$. It adopts the extended Hamiltonian formalism to absorb the lapse function into a dynamical time variable, introducing a constant energy $E$ conjugate to time and yielding a time-dependent Schrödinger equation $i ∂_t psi = H psi$. The key result is the modified constraint $H(a,p_a) - E = 0$, which preserves cosmic time as an evolution parameter in 3rd quantized cosmology. This approach clarifies the role of gauge degrees of freedom in time reparametrization and offers a concrete path to dynamic quantum cosmology within the mini-superspace framework.
Abstract
The standard Wheeler-DeWitt approach to Quantum Cosmology leads to the problematic freeze of time. The reason is the enforcement of time re-parametrization invariance via the lapse function that is treated at least partially as an independent dynamical field. We show that the correct treatment of time re-parametrization gauge along the lines of the extended Hamiltonian formalism lifts the notorious ban on the cosmic time as evolution parameter in 3rd quantized cosmology.