Hamiltonian analysis of SO(4,1) constrained BF theory

In this paper we discuss canonical analysis of SO(4,1) constrained BF theory. The action of this theory contains topological terms appended by a term that breaks the gauge symmetry down to the Lorentz subgroup SO(3,1). The equations of motion of this theory turn out to be the vacuum Einstein equations. By solving the B field equations one finds that the action of this theory contains not only the standard Einstein-Cartan term, but also the Holst term proportional to the inverse of the Immirzi parameter, as well as a combination of topological invariants. We show that the structure of the constraints of a SO(4,1) constrained BF theory is exactly that of gravity in Holst formulation. We also briefly discuss quantization of the theory.Comment: 9 page

Three-body equations of motion in successive post-Newtonian approximations

There are periodic solutions to the equal-mass three-body (and N-body) problem in Newtonian gravity. The figure-eight solution is one of them. In this paper, we discuss its solution in the first and second post-Newtonian approximations to General Relativity. To do so we derive the canonical equations of motion in the ADM gauge from the three-body Hamiltonian. We then integrate those equations numerically, showing that quantities such as the energy, linear and angular momenta are conserved down to numerical error. We also study the scaling of the initial parameters with the physical size of the triple system. In this way we can assess when general relativistic results are important and we determine that this occur for distances of the order of 100M, with M the total mass of the system. For distances much closer than those, presumably the system would completely collapse due to gravitational radiation. This sets up a natural cut-off to Newtonian N-body simulations. The method can also be used to dynamically provide initial parameters for subsequent full nonlinear numerical simulations.Comment: 8 pages, 9 figure

Snyder's Quantized Space-time and De Sitter Special Relativity

There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the \dS-invariant special relativity. This indicates that physics at the Planck length $\ell_P$ and the scale $R=3/\Lambda$ should be dual to each other and there is in-between gravity of local \dS-invariance characterized by a dimensionless coupling constant $g=\ell_P/R\sim 10^{-61}$.Comment: 8 page

Constraints on the quantum gravity scale from kappa - Minkowski spacetime

We compare two versions of deformed dispersion relations (energy vs momenta and momenta vs energy) and the corresponding time delay up to the second order accuracy in the quantum gravity scale (deformation parameter). A general framework describing modified dispersion relations and time delay with respect to different noncommutative kappa -Minkowski spacetime realizations is firstly proposed here and it covers all the cases introduced in the literature. It is shown that some of the realizations provide certain bounds on quadratic corrections, i.e. on quantum gravity scale, but it is not excluded in our framework that quantum gravity scale is the Planck scale. We also show how the coefficients in the dispersion relations can be obtained through a multiparameter fit of the gamma ray burst (GRB) data.Comment: 9 pages, final published version, revised abstract, introduction and conclusion, to make it clear to general reade

The linearization of the Kodama state

We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte

Signals from the Noise: Image Stacking for Quasars in the FIRST Survey

We present a technique to explore the radio sky into the nanoJansky regime by employing image stacking using the FIRST radio sky survey. We begin with a discussion of the non-intuitive relationship between the mean and median values of a non-Gaussian distribution in which measurements of the members of the distribution are dominated by noise. Following a detailed examination of the systematic effects present in the 20 cm VLA snapshot images that comprise FIRST, we demonstrate that image stacking allows us to recover the average properties of source populations with flux densities a factor of 30 or more below the rms noise level. With the calibration described herein, mean estimates of radio flux density, luminosity, radio loudness, etc. are derivable for any undetected source class having arcsecond positional accuracy. We demonstrate the utility of this technique by exploring the radio properties of quasars found in the Sloan Digital Sky Survey. We compute the mean luminosities and radio-loudness parameters for 41,295 quasars in the SDSS DR3 catalog. There is a tight correlation between optical and radio luminosity, with the radio luminosity increasing as the 0.72 power of optical luminosity. This implies declining radio-loudness with optical luminosity, with the most luminous objects (M{sub UV} = -30) having on average ten times lower radio-to-optical ratios than the least luminous objects (M{sub UV} = -21). There is also a striking correlation between optical color and radio loudness: quasars that are either redder or bluer than the norm are brighter radio sources. Quasars having g-r {approx} 0.8 magnitudes redder than the SDSS composite spectrum are found to have radio-loudness ratios that are higher by a factor of 8. We examine the radio properties of the subsample of quasars with broad absorption lines, finding, surprisingly, that BAL quasars have higher mean radio flux densities at all redshifts, with the greatest disparity arising in the rare low-ionization BAL subclass. We conclude with examples of other problems for which the stacking analysis developed here is likely to be of use

Trans-Planckian Physics and the Spectrum of Fluctuations in a Bouncing Universe

In this paper, we calculate the spectrum of scalar field fluctuations in a bouncing, asymptotically flat Universe, and investigate the dependence of the result on changes in the physics on length scales shorter than the Planck length which are introduced via modifications of the dispersion relation. In this model, there are no ambiguities concerning the choice of the initial vacuum state. We study an example in which the final spectrum of fluctuations depends sensitively on the modifications of the dispersion relation without needing to invoke complex frequencies. Changes in the amplitude and in the spectral index are possible, in addition to modulations of the spectrum. This strengthens the conclusions of previous work in which the spectrum of cosmological perturbations in expanding inflationary cosmologies was studied, and it was found that, for dispersion relations for which the evolution is not adiabatic, the spectrum changes from the standard prediction of scale-invariance.Comment: 10 pages, 6 figures, RevTeX4. Analytical determination of the spectrum, corrected some typos, conclusions unchange

Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory

We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagatorsComment: 46 pages, the wrong file was first submitte