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The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
We quantize the solution to the Belinski-Khalatnikov-Lifshitz (BKL) scenario using the integral quantization method. Quantization smears the gravitational singularity avoiding its localization in the configuration space. The latter is…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
In contrast to scalar and tensor modes, vector modes of linear perturbations around an expanding Friedmann--Robertson--Walker universe decay. This makes them largely irrelevant for late time cosmology, assuming that all modes started out at…
We investigate a large class of gravity theories that respect spatial covariance, and involve kinetic terms for both the spatial metric and the lapse function. Generally such kind of theories propagate four degrees of freedom, one of which…
Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…
The cosmological tensor perturbation equation with generalized holonomy corrections is derived in the framework of effective loop quantum gravity. This results in a generalized dispersion relation for gravitational waves, encompassing…
We discuss a model where a spontaneous quantum collapse is induced by the gravitational interaction, treated classically. Its dynamics couples the standard wave function of a system with the Bohmian positions of its particles, which are…
Collapse models are phenomenological models introduced to solve the measurement problem in quantum mechanics. They modify the Schr\"odinger equation by adding non-linear and stochastic terms, which induce the wavefunction collapse in space.…
Background independence is often emphasized as an important property of a quantum theory of gravity that takes seriously the geometrical nature of general relativity. In a background-independent formulation, quantum gravity should determine…
Classical generalization of general relativity is considered as gravitational alternative for unified description of the early-time inflation with late-time cosmic acceleration. The structure and cosmological properties of number of…
We study the gravitational collapse of a massless scalar field within the effective scenario of loop quantum gravity. Classical singularity is avoided and replaced by a quantum bounce in this model. It is shown that, quantum gravity effects…
Nonlinear modifications of quantum theory are considered potential candidates for the theory of quantum gravity, with the intuitive argument that since Einstein field equations are nonlinear, quantum gravity should be nonlinear as well.…
There are fundamental reasons as to why there should exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. It follows as a consequence that quantum mechanics as we know it is a limiting case of a…
In this work we derive general quantum phenomenological equations of gravitational dynamics and analyse its features. The derivation uses the formalism developed in thermodynamics of spacetime and introduces low energy quantum gravity…
We give a brief review of the problem of quantum gravity. After the discussion of the nonrenormalizability of general relativity, we briefly mention the main research directions which aim to resolve this problem. Our attention then focuses…
In the last 20 years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous,…
We construct a large class of spacetimes that are smoothly matched to homogeneous, spherically symmetric clouds of matter. The evolution of the clouds is left arbitrary to allow for the incorporation of modifications by quantum effects,…
Aspects of the full theory of loop quantum gravity can be studied in a simpler context by reducing to symmetric models like cosmological ones. This leads to several applications where loop effects play a significant role when one is…
In this paper we study the gravitational collapse in loop quantum gravity. We consider the space-time region inside the Schwarzschild black hole event horizon and we divide this region in two parts, the first one where the matter (dust…