The monster and the police: Dexter to Hobbes

On 25 February 2002, Rafael Perez, a former officer of the LAPD’s Community Resources Against Street Hoodlums unit (CRASH), appeared in court accused of various crimes: covering up a bank robbery, shooting and framing an innocent citizen, stealing and selling cocaine from evidence lockers, being a member of the Los Angeles gang called the Bloods, and murdering the rapper The Notorious B.I.G. In his statement to the court he pointed out that above the threshold of doors that lead to CRASH offices there are philosophical mottos such as ‘Some rise by sin and some by virtue fall’ and ‘We intimidate those who intimidate others’. Perez commented: ‘To those mottos, I offer this: “Whoever chases monsters should see to it that in the process he does not become a monster himself.”

Cosmological evolution of interacting phantom (quintessence) model in Loop Quantum Gravity

The dynamics of interacting dark energy model in loop quantum cosmology (LQC) is studied in this paper. The dark energy has a constant equation of state $w_x$ and interacts with dark matter through a form $3cH(\rho_x+\rho_m)$. We find for quintessence model ($w_x>-1$) the cosmological evolution in LQC is the same as that in classical Einstein cosmology; whereas for phantom dark energy ($w_x<-1$), although there are the same critical points in LQC and classical Einstein cosmology, loop quantum effect reduces significantly the parameter spacetime ($c, w_x$) required by stability. If parameters $c$ and $w_x$ satisfy the conditions that the critical points are existent and stable, the universe will enter an era dominated by dark energy and dark matter with a constant energy ratio between them, and accelerate forever; otherwise it will enter an oscillatory regime. Comparing our results with the observations we find at $1\sigma$ confidence level the universe will accelerate forever.Comment: 15 pages, 8 figures, to appear in JCA

Non-commutative flux representation for loop quantum gravity

The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by *-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.Comment: 12 pages, matches published versio

Classical Setting and Effective Dynamics for Spinfoam Cosmology

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with N links. We describe the canonical data using the recent formulation of the phase space in terms of spinors, and implement a symmetry-reduction to the homogeneous and isotropic sector. From the canonical point of view, we construct a consistent Hamiltonian for the model and discuss its relation with Friedmann-Robertson-Walker cosmologies. Then, we analyze the dynamics from the spinfoam approach. We compute exactly the transition amplitude between initial and final coherent spin networks states with support on the 2-vertex graph, for the choice of the simplest two-complex (with a single space-time vertex). The transition amplitude verifies an exact differential equation that agrees with the Hamiltonian constructed previously. Thus, in our simple setting we clarify the link between the canonical and the covariant formalisms.Comment: 38 pages, v2: Link with discretized loop quantum gravity made explicit and emphasize

Free vacuum for loop quantum gravity

We linearize extended ADM-gravity around the flat torus, and use the associated Fock vacuum to construct a state that could play the role of a free vacuum in loop quantum gravity. The state we obtain is an element of the gauge-invariant kinematic Hilbert space and restricted to a cutoff graph, as a natural consequence of the momentum cutoff of the original Fock state. It has the form of a Gaussian superposition of spin networks. We show that the peak of the Gaussian lies at weave-like states and derive a relation between the coloring of the weaves and the cutoff scale. Our analysis indicates that the peak weaves become independent of the cutoff length when the latter is much smaller than the Planck length. By the same method, we also construct multiple-graviton states. We discuss the possible use of these states for deriving a perturbation series in loop quantum gravity.Comment: 30 pages, 3 diagrams, treatment of phase factor adde

On knottings in the physical Hilbert space of LQG as given by the EPRL model

We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the amplitude under consistent deformations, which are deformations of the embedded two-complex where faces are allowed to pass through each other in a controlled way. Using this surprising invariance, we are able to show that in the physical Hilbert space as defined by the sum over all spin foams contains no knotting classes of graphs anymore.Comment: 22 pages, 14 figure

3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory

An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models.Comment: 17 pages, revtex4, 1 figur

Finiteness and Dual Variables for Lorentzian Spin Foam Models

We describe here some new results concerning the Lorentzian Barrett-Crane model, a well-known spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a concise proof of finiteness of the partition function associated to all non-degenerate triangulations of 4-manifolds and for a class of degenerate triangulations not previously shown. This is accomplished by a suitable re-factoring and re-ordering of integration, through which a large set of variables can be eliminated. The resulting formulation can be interpreted as a ``dual variables'' model that uses hyperboloid variables associated to spin foam edges in place of representation variables associated to faces. We outline how this method may also be useful for numerical computations, which have so far proven to be very challenging for Lorentzian spin foam models.Comment: 15 pages, 1 figur