Related papers: Setting free the cosmic time in Quantum Universe
We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
In quantum cosmology, one has to select a specific wave function solution of the quantum state equations under consideration in order to obtain concrete results. The simplest choices have been already explored, in different frameworks,…
For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…
Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly…
This is in fact an Erratum to the paper published in Physics Letters A221 (1996) 359. The reduced-phase-space discussion remains essentially valid in spite of the fact that many equations are changed. However, the analysis based on the…
We consider a renormalizable two-dimensional model of dilaton gravity coupled to a set of conformal fields as a toy model for quantum cosmology. We discuss the cosmological solutions of the model and study the effect of including the…
This paper explores models of the FLRW universe that incorporate a time-varying cosmological term $\Lambda(t)$. Specifically, we assume a power-law form for the cosmological term as a function of the scale factor: $\Lambda(t)=\Lambda_{0}…
The development of last years in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage the main task was to apply known quantization schemes to…
One approach to defining dynamics for quantum gravity in a naturally timeless setting is to select a suitable matter degree of freedom as a 'clock' before quantisation. This idea of deparametrisation was recently introduced in group field…
Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p = \alpha\rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered.…
We show that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. Consistency of these opposite arrows is facilitated by quantum effects…
We reexamine the relationship between the path integral and canonical formulation of quantum general relativity. In particular, we present a formal derivation of the Wheeler-DeWitt equation from the path integral for quantum general…
An one-parameter regularization freedom of the Hamiltonian constraint for loop quantum gravity is analyzed. The corresponding spatially flat, homogenous and isotropic model includes the two well-known models of loop quantum cosmology as…
We examine the third quantization of $f(R)$-type gravity, based on its effective Lagrangian in the case of a flat Friedmann-Lemaitre-Robertson-Walker metric. Starting from the effective Lagrangian, we execute a suitable change of variable…
The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we…
Following a minisuperspace approach to the dynamics of a spherically symmetric shell, a reduced Lagrangian for the radial degree of freedom is derived directly from the Einstein-Hilbert action. The key feature of this new Lagrangian is its…
An inhomogeneous (1+1)-dimensional model of the quantum gravity is considered. It is found, that this model corresponds to a string propagating against some curved background space. The quantization scheme including the Wheeler-DeWitt…
We review how reparametrization of space and time, namely the procedure where both are made to depend on yet another parameter, can be used to formulate quantum physics in a way that is naturally conducive to relativity. This leads us to a…