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We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis…
The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that…
Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since…
Current theories of particle physics, including the standard model, are dominated by the paradigm that nature is basically translation invariant. Deviations from translation invariance are described by the action of forces. General…
We review recent progress in 2D gravity coupled to $d<1$ conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related…
In the context of $f(R)$ theories of gravity, we study the evolution of scalar cosmological perturbations in the metric formalism. Using a completely general procedure, we find the exact fourth-order differential equation for the matter…
We expand the study of generalized brane cosmologies by allowing for an $f(\tilde{\cal R})$ gravity term on the brane, with $\tilde{\cal R}$ the curvature scalar derived from the induced metric. We also include arbitrary matter components…
We consider the four dimensional abelian topological BF theory with a planar boundary introduced following the Symanzik's method. We find the most general boundary conditions compatible with the fields equations broken by the boundary. The…
We discuss in detail the uniform discretization approach to the quantization of totally constrained theories. This approach allows to construct the continuum theory of interest as a well defined, controlled, limit of well behaved discrete…
We describe the application of methods from the study of discrete dynanmical systems to the problem of the continuum limit of evolving spin networks. These have been found to describe the small scale structure of quantum general relativity…
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local…
We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in $d \geq 4$ dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond…
Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework: the GFT partition function defines the sum of spinfoam transition…
Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric…
We propose a spin foam model of four-dimensional quantum gravity which is based on the integration of the tetrads in the path integral for the Palatini action of General Relativity. In the Euclidian gravity case we show that the model can…
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these…
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we…
We derive the condition on f(R) gravities that admit Killing spinor equations and construct explicit such examples. The Killing spinor equations can be used to reduce the fourth-order differential equations of motion to the first order for…
We analyze the common four types of the finite-time singularities using a generic framework of the phase portrait geometric approach. This technique requires that the Friedmann system to be written as a one dimensional autonomous system. We…
We study generalizations of 3- and 4-dimensional BF-theory in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of…