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In the framework of a flat Friedmann-Lema{\^\i}tre-Robertson-Walker (FLRW) geometry, we present a nonsingular model (no big bang singularity at finite time) of our universe describing its evolution starting from its early inflationary era…
One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why 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,…
We propose a theory of quantum gravity which formulates the quantum theory as a nonperturbative path integral, where each spacetime history appears with a weight given by the exponentiated Einstein-Hilbert action of the corresponding causal…
The quantum nature of the Big Bang is reexamined in the framework of Loop Quantum Cosmology. The strict application of a regularization procedure to the Hamiltonian, originally developed for the Hamiltonian in loop quantum gravity, leads to…
The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wavefunction solutions is such that a…
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…
We study the natural norm on the space of solutions to the Wheeler-DeWitt equation in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and…
We present a rigorous formulation of the Quantum Big Bounce for the closed isotropic Universe, filled with a self-interacting scalar field, that emerges from the interaction with an ekpyrotic potential. Working in a covariant approach to…
The ADM approach to canonical general relativity combined with Dirac's method of quantizing constrained systems leads to the Wheeler-DeWitt equation. A number of mathematical as well as physical difficulties that arise in connection with…
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and…
We derive exact series solutions for the Wheeler-DeWitt equation corresponding to a spatially closed Friedmann-Robertson-Walker universe with cosmological constant for arbitrary operator ordering of the scale factor of the universe. The…
We calculate the probability distribution for the volume of the Universe after slow-roll inflation both in the eternal and in the non-eternal regime. Far from the eternal regime the probability distribution for the number of e-foldings,…
In this paper, we systematically study the evolution of the Universe in the framework of a modified loop quantum cosmological model (mLQC-I) with various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky,…
In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt quantizations, and some aspects of general…
Making cosmological predictions in a multiverse is a fundamental theoretical challenge. Assuming that (quasi-)de Sitter vacua are quantum mechanically described by a finite-dimensional Hilbert space, we develop a detailed framework for…
We present a detailed analysis of a quantum model for Loop Quantum Cosmology based on strict application of the Thiemann regularization algorithm for the Hamiltonian in Loop Quantum Gravity, extending the results presented previously in our…
Using the Ashtekar-Sen variables of loop quantum gravity, a new class of exact solutions to the equations of quantum cosmology is found for gravity coupled to a scalar field, that corresponds to inflating universes. The scalar field, which…
We consider a Bohmian approach to the Wheeler-DeWitt quantization of the Friedmann-Lemaitre-Robertson-Walker model and investigate the question whether or not there are singularities, in the sense that the universe reaches zero volume. We…