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We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum…
We study scalar field theories invariant under transverse diffeomorphisms in cosmological contexts. We show that in the geometric optics approximation, the corresponding particles move along geodesics and contribute with the same active…
Several approaches to the dynamics of loop quantum gravity involve discretizing the equations of motion. The resulting discrete theories are known to be problematic since the first class algebra of constraints of the continuum theory…
Systems consisting of spheres rolling on elastic membranes have been used to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, such schemes cannot accurately represent…
We present a new, falsifiable, quantum theory of gravity, which we name Non-commutative Matter-Gravity. The commutative limit of the theory is classical general relativity. In the first two papers of this series, we have introduced the…
Scalar-tensor theories of gravity are known to allow significant deviations from general relativity through various astrophysical phenomena. In this paper, we formulate a scalar-connection gravity by setting up scalars and connection…
We investigate a non-minimally coupled scalar field theory within the framework of scalar-tensor gravity formulated in non-metricity geometry, focusing on spatially curved FLRW spacetimes. Employing the dynamical systems approach with…
We study several examples of kinetically constrained lattice models using dynamically accessible volume as an order parameter. Thereby we identify two distinct regimes exhibiting dynamical slowing, with a sharp threshold between them. These…
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying…
Several approaches to the quantum-gravity problem predict that spacetime should be "fuzzy", but have been so far unable to provide a crisp physical characterization of this notion. An intuitive picture of spacetime fuzziness has been…
It is generally believed that any quantum theory of gravity should have a generic feature --- a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such…
Quantum Gravity by Causal Dynamical Triangulation has over the last few years emerged as a serious contender for a nonperturbative description of the theory. It is a nonperturbative implementation of the sum-over-histories, which relies on…
Scale invariance is considered in the context of gravitational theories where the action, in the first order formalism, is of the form $S = \int L_{1} \Phi d^4x$ + $\int L_{2}\sqrt{-g}d^4x$ where the volume element $\Phi d^4x$ is…
A spinfoam model of 3D gravity non-minimally coupled with a scalar field is studied. By discretization of the scalar field, the model is worked out precisely in a purely combinational way. It is shown that the quantum physics of the scalar…
In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…
It is suggested that not only the curvature, but also the signature of spacetime is subject to quantum fluctuations. A generalized D-dimensional spacetime metric of the form $g_{\mu \nu}=e^a_\mu \eta_{ab} e^b_\nu$ is introduced, where…
Starting from an heuristic approach to the semiclassical limit in loop quantum gravity, the construction of effective Hamiltonians describing Planck length corrections to the propagation of photons and spin 1/2 fermions, leading to modified…
We investigate the presence of instabilities in the Cascading DGP model. We start by discussing the problem of the cosmological late time acceleration, and we introduce the modified gravity approach. We then focus on brane induced gravity…
We consider a proposed alternative to quantum gravity, in which the spacetime metric is treated as classical, even while matter fields remain quantum. Consistency of the theory necessarily requires that the metric evolve stochastically.…
We consider a non-standard generalized model of gravity coupled to a neutral scalar "inflaton" as well as to the fields of the electroweak bosonic sector. The essential new ingredient is employing two alternative non-Riemannian space-time…