A simple argument indicates that covariant loop gravity (spin foam theory) predicts a maximal acceleration and hence forbids the development of curvature singularities. This supports the results obtained for cosmology and black holes using canonical methods.

We compute the transition amplitude between coherent quantum states of geometry peaked on homogeneous-isotropic metrics. We work in the context of pure gravity without matter, we use the holomorphic representations of loop quantum gravity and the Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at first order in the vertex expansion, second order in the graph (multipole) expansion, and first order in volume-1. We show that the resulting amplitude is in the kernel of a differential operator whose classical limit is the canonical Hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an indication that the dynamics of loop quantum gravity defined by the new vertex reproduces the gravity part of the Friedmann equation in the appropriate limit.

Loop quantum cosmology yields two kinds of quantum corrections to the effective equations of motion for cosmological perturbations. Here we focus on the holonomy kind and we study the problem of the closure of the resulting algebra of constraints when a scalar field is considered in the matter Hamiltonian. Up to now, tensor, vector and scalar perturbations were studied independently, leading to different algebras of constraints. The structures of the related algebras were imposed by the requirement of anomaly freedom. In this article we show that the algebra can be modified by a very simple quantum correction, holding for all types of perturbations. The Mukhanov-Sasaki equations of motion are similarly modified by a simple term.

Quantum gravity effects could make a black hole explode in a time shorter than the Hawking radiation time, via local tunneling through a white hole solution. Here we estimate the size of a primordial black hole exploding today via this process, using a simple generic model. Fast radio bursts, strong signals with millisecond duration, which are probably of extragalactic origin and have an unknown source, have wavelengths not far from the expected size of the exploding hole. We also discuss the high-energy component of the signal. These results suggest a new window for quantum gravity phenomenology.

We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for describing general fluctuations of quantum geometry near the initial singularity. We show that the dynamical structure of the model reduces to that of loop quantum cosmology in the Born-Oppenheimer approximation. This result corroborates the assumptions that ground loop cosmology, sheds light on the physical and mathematical relation between loop cosmology and full loop quantum gravity, and on the nature of the cosmological approximation. Finally, we show that the non-graph-changing Hamiltonian constraint considered in the context of algebraic quantum gravity provides a viable effective dynamics within this approximation.