Quantum Gravity

We study a contracting universe composed of cold dark matter and radiation, and with a positive cosmological constant. Assuming that loop quantum cosmology captures the correct high-curvature dynamics of the space-time, we calculate the spectrum of scalar and tensor perturbations after the bounce, assuming initial quantum vacuum fluctuations. We find that the modes that exit the (sound) Hubble radius during matter-domination when the effective equation of state is slightly negative due to the cosmological constant will be nearly scale-invariant with a slight red tilt, in agreement with observations. The tensor perturbations are also nearly scale-invariant, and the predicted tensor-to-scalar ratio is small.  Finally, as this scenario predicts a positive running of the scalar index, it can be differentiated from inflationary models.

Instead of formulating the state space of a quantum field theory over a single big Hilbert space, it has been proposed by Jerzy Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. I will discuss the physical motivations for this approach and explain how it can be implemented in the context of LQG. While the resulting state space forms a natural extension of the Ashtekar-Lewandowski Hilbert space, it treats position and momentum variables on equal footing. This paves the way for the construction of semi-classical states beyond fixed graph level, and eventually for the derivation of LQC from full LQG.

I offer a personal perspective on the causal dynamical triangulations approach to the construction of quantum theories of gravity. After briefly introducing the approach's formalism and results, I illuminate this perspective with 3+1 vignettes of recent and ongoing research. Specifically, I review attempts to locate an ultraviolet fixed point through renormalization group analyses; I report measurements of the homogeneity of the approach's quantum geometries; I discuss efforts to determine the large scale effective action in the case of 2+1 dimensions; and I suggest a speculative possibility for reviving the Euclidean dynamical triangulations approach.

A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localized at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new non-geometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Barbero-Immirzi parameter.