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A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum…
A key test of any quantum theory of gravity is its ability to reproduce the known thermodynamic properties of black holes. A statistical mechanical description of the Bekenstein-Hawking entropy once seemed remote, but today we suffer an…
The vacuum of quantum fields contains correlated fluctuations. When restricted to one side of a surface these have a huge entropy of entanglement that scales with the surface area. If UV physics renders this entropy finite, then a…
In this talk we entertain the possibility that the synthesis of general covariance and quantum mechanics requires an extension of the basic kinematical setup of quantum mechanics. According to the holographic principle, regions of spacetime…
In recent years, Loop Quantum Gravity has emerged as a solid candidate for a nonperturbative quantum theory of General Relativity. It is a background independent theory based on a description of the gravitational field in terms of…
The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered,…
We provide a formulation and proof of the gravitational entropy bound. We use a recently given framework which expresses the measurable quantities of a quantum theory as a weighted sum over paths in the theory's phase space. If this…
Covariant models of loop quantum gravity generically imply dynamical signature change at high density. This article presents detailed derivations that show the fruitful interplay of this new kind of signature change with wave-function…
The linear cosmological perturbation theory of almost homogeneous and isotropic perfect fluid and scalar field universes is reconsidered and formally simplified. Using the existence of a covariant conserved quantity on large perturbation…
Inspired by the entropy-area relation of black hole thermodynamics, we study the thermodynamics of cosmological apparent horizon in a spatially flat Friedmann-Robertson-Walker (FRW) universe in the framework of an Extended Uncertainty…
The entropic gravity scenario recently proposed by Erik Verlinde reproduced the Newton's law of purely classical gravity yet the key assumptions of this approach all have quantum mechanical origins. This is atypical for emergent phenomena…
The canonical ``loop'' formulation of quantum gravity is a mathematically well defined, background independent, non perturbative standard quantization of Einstein's theory of General Relativity. Some among the most meaningful results of the…
The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a…
We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing…
Loop quantum cosmology is an application of recent developments for a non-perturbative and background independent quantization of gravity to a cosmological setting. Characteristic properties of the quantization such as discreteness of…
We review our recent proposal of a method to extend the quantization of spherically symmetric isolated horizons, a seminal result of loop quantum gravity, to a phase space containing horizons of arbitrary geometry. Although the details of…
The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on…
After discussing some old (and not-so-old) entropy bounds both for isolated systems and in cosmology, I will argue in favour of a "Hubble entropy bound" holding in the latter context. I will then apply this bound to recent developments in…
To ask a question about a black hole in quantum gravity, one must restrict initial or boundary data to ensure that a black hole is actually present. For two-dimensional dilaton gravity, and probably a much wider class of theories, I show…
The general properties of a perfect relativistic fluid resulting from the quantum gravitational anomaly are investigated. It is found that, in the limit of a weak gravitational field, this fluid possesses a polytropic equation of state…