Related papers: Loop Quantum Cosmology IV: Discrete Time Evolution
The paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since General Relativity does not have a privileged time variable…
In [1] we initiated an approach towards quantizing the Hamiltonian constraint in Loop Quantum Gravity (LQG) by requiring that it generates an anomaly-free representation of constraint algebra off-shell. We investigated this issue in the…
We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an…
We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
We construct a formalism for evolving spherically symmetric black hole initial data sets within a canonical approach to quantum gravity. This problem can be formulated precisely in quantum reduced loop gravity, a framework which has been…
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 compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an…
A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
It is well known that Einstein's equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that {\em time} evolution of the…
Combinatorial quantum gravity is governed by a discrete Einstein-Hilbert action formulated on an ensemble of random graphs. There is strong evidence for a second-order quantum phase transition separating a random phase at strong coupling…
The Wheeler-DeWitt (WdW) equation does not describe any explicit time evolution of the wave function, and somehow related to this issue, there is no natural way of defining an invariant inner product that provides a viable probability…
The discrete phase space continuous time representation of relativistic quantum mechanics involving a characteristic length $l$ is investigated. Fundamental physical constants such as $\hbar$, $c$, and $l$ are retained for most sections of…
We use the vacuum Bianchi I model as an example to investigate the concept of physical evolution in Loop Quantum Cosmology (LQC) in the absence of the massless scalar field which has been used so far in the literature as an internal time.…
Unlike noncommutative space, when space and time are noncommutative, it seems necessary to modify the usual scheme of quantum mechanics. We propose in this paper a simple generalization of the time evolution equation in quantum mechanics to…
Shape dynamics is a reformulation of general relativity, locally equivalent to Einstein's theory, in which the refoliation invariance of the older theory is traded for local scale invariance. Shape dynamics is here derived in a formulation…
The hypothesis of a discrete fabric of the universe--the "Planck scale"--is always on stage, since it solves mathematical and conceptual problems in the infinitely small. However, it clashes with special relativity, which is designed for…
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…