Session B12: Quantum Aspects of Gravitation

Lorentz invariance in loop quantum gravity

We reconsider the argument of Collins, Perez, Sudarsky, Urrutia and Vucetich concerning violations of Lorentz invariance in the context of loop quantum gravity. We show that even if one introduces a lattice that violates Lorentz invariance at the Planck scale, this does not translate itself into large violations that would conflict with experiment.   

Role of intrinsic curvature in generic resolution of singularity

In recent years loop quantum gravity has proved to be useful for singularity resolution in many situations of cosmology. Singularity resolution is achieved due to the underlying quantum geometric effects which results in a bound on space-time curvature. We investigate in detail the effective dynamics of anisotropic spacetimes in the presence of spatial curvature by evaluating geometric quantities like expansion parameter, the shear scalar and curvature invariants and also point out certain subtleties in these models regarding the generic resolution of singularity. We also discuss the impact of the presence of intrinsic curvature on the method of quantization. As an example we analyze the effective dynamics of Bianchi II and Bianchi IX models.   

Quantum Geometry Phenomenology: Angle

Using the loop quantum gravity approach to quantizing general relativity the phenomenology of an atom of space will be discussed. The combinatorics of the model of spatial geometry give deviations from flat space that are in principle detectable. The angle operator effects neither involve the Planck scale directly nor introduce violations of local Lorentz invariance in the usual sense. The effects will be discussed in the context of scattering experiments.   

Extremal and Nonextremal Kerr/CFT Correspondences

The extremal Kerr/CFT correspondence describes black hole thermodynamics in terms of a dual conformal field theory at the horizon. I describe two variations applicable to nonextremal black holes, one in which the entropy is split between the inner and outer horizons and one in which the relevant degrees of freedom live on a stretched Killing horizon.   

Protected operators in de Sitter quantum gravity and dS/CFT

We investigate the infrared behavior of graviton and stress-energy tensor correlation functions in a de Sitter background. In particular, we examine the two- and three-point functions of these fields with respect to the de Sitter-invariant vacuum state of the interacting theory. We show that the Ward identities associated to stress-energy conservation, along with the de Sitter invariance of the vacuum, greatly constrain the infrared behavior of these correlation functions. We find that, in an appropriate gauge, the leading infrared behavior of the correlation functions is given by the Born approximation; that is, loop corrections do not effect the leading infrared behavior. We verify this statement in a number of examples. Our results indicate that de Sitter space is stable with respect to quantum gravitational perturbations. Our results also support the general notion of a dS/CFT correspondence: the bulk graviton is a protected operator whose asymptotic behavior near the conformal boundaries is not significantly altered by perturbative interactions in the bulk.   

Volume Spectrum from Bohr-Sommerfeld Quantization

As first observed by Roger Penrose, angular momentum vectors can be used to describe geometrical objects, such as convex polyhedra. A remarkable outgrowth of this idea is that spaces of geometrical shapes can be endowed with a phase space structure. This allows all the tools of dynamical systems and semiclassical mechanics to be explored in the context of geometrical shapes. From the perspective of discrete approaches to gravity, such as the Regge Calculus where space is chopped into tetrahedral pieces, this opens fascinating new prospects. Here we present a discrete spectrum for the volume of a tetrahedron as obtained from Bohr-Sommerfeld quantization. We discuss connections with Loop Quantum Gravity and the implications for approximate treatments of more complex geometries.   

Setting the Scale of Dimensional Reduction in Causal Dynamical Triangulations

Within the causal dynamical triangulations approach to quantization of gravity, striking evidence has emerged that the effective dimensionality of spacetime dynamically reduces at small scales. Specifically, in the case of topological sphericity, the expectation value of the spectral dimension decreases with the scale being probed from the topological value of four to an apparent value of two. Thus far the physical scale at which this dynamical dimensional reduction occurs has not been ascertained. In this talk I present the first determinations of this scale. By fitting the expectation value of the spacetime geometry to a classical minisuperspace model, I extract the triangulation lattice spacing in units of the Planck length and the effective cosmological constant in units of the inverse Planck length squared. The former value allows me to establish directly the scales probed by the random walk that defines the spectral dimension. The latter value allows me to establish indirectly these scales via the heat trace for the minisuperspace geometry. This work also yields preliminary indications of the flow of the cosmological constant within this model of quantum geometry.