Automorphism covariant representations of the holonomy-flux *-algebra

We continue an analysis of representations of cylindrical functions and fluxes which are commonly used as elementary variables of Loop Quantum Gravity. We consider an arbitrary principal bundle of a compact connected structure group and following Sahlmann's ideas define a holonomy-flux *-algebra whose elements correspond to the elementary variables. There exists a natural action of automorphisms of the bundle on the algebra; the action generalizes the action of analytic diffeomorphisms and gauge transformations on the algebra considered in earlier works. We define the automorphism covariance of a *-representation of the algebra on a Hilbert space and prove that the only Hilbert space admitting such a representation is a direct sum of spaces L^2 given by a unique measure on the space of generalized connections. This result is a generalization of our previous work (Class. Quantum. Grav. 20 (2003) 3543-3567, gr-qc/0302059) where we assumed that the principal bundle is trivial, and its base manifold is R^d.Comment: 34 pages, 1 figure, LaTeX2e, minor clarifying remark

Chemical abundances of stars with brown-dwarf companions

It is well-known that stars with giant planets are on average more metal-rich than stars without giant planets, whereas stars with detected low-mass planets do not need to be metal-rich. With the aim of studying the weak boundary that separates giant planets and brown dwarfs (BDs) and their formation mechanism, we analyze the spectra of a sample of stars with already confirmed BD companions both by radial velocity and astrometry. We employ standard and automatic tools to perform an EW-based analysis and to derive chemical abundances from CORALIE spectra of stars with BD companions. We compare these abundances with those of stars without detected planets and with low-mass and giant-mass planets. We find that stars with BDs do not have metallicities and chemical abundances similar to those of giant-planet hosts but they resemble the composition of stars with low-mass planets. The distribution of mean abundances of $\alpha$-elements and iron peak elements of stars with BDs exhibit a peak at about solar abundance whereas for stars with low-mass and high-mass planets the [X$_\alpha$/H] and [X$_{\rm Fe}$/H] peak abundances remain at $\sim -0.1$~dex and $\sim +0.15$~dex, respectively. We display these element abundances for stars with low-mass and high-mass planets, and BDs versus the minimum mass, $m_C \sin i$, of the most-massive substellar companion in each system, and we find a maximum in $\alpha$-element as well as Fe-peak abundances at $m_C \sin i \sim 1.35\pm 0.20$ jupiter masses. We discuss the implication of these results in the context of the formation scenario of BDs in comparison with that of giant planets.Comment: Accepted for publication in Astronomy & Astrophysic

Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme

In this article and a companion paper we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) from full fledged Quantum General Relativity (QGR), starting from first principles. We stress that we do not claim to have a satisfactory answer to this question, rather our intention is to ignite a discussion by displaying the problems that have to be solved when carrying out such a program. In the present paper we propose a scheme that one might follow in order to arrive at such a limit. We discuss the technical and conceptual problems that arise in doing so and how they can be solved in principle. As to be expected, completely new issues arise due to the fact that QGR is a background independent theory. For instance, fundamentally the notion of a photon involves not only the Maxwell quantum field but also the metric operator - in a sense, there is no photon vacuum state but a "photon vacuum operator"! While in this first paper we focus on conceptual and abstract aspects, for instance the definition of (fundamental) n-particle states (e.g. photons), in the second paper we perform detailed calculations including, among other things, coherent state expectation values and propagation on random lattices. These calculations serve as an illustration of how far one can get with present mathematical techniques. Although they result in detailed predictions for the size of first quantum corrections such as the gamma-ray burst effect, these predictions should not be taken too seriously because a) the calculations are carried out at the kinematical level only and b) while we can classify the amount of freedom in our constructions, the analysis of the physical significance of possible choices has just begun.Comment: LaTeX, 47 p., 3 figure

Lorentz Invariance and the semiclassical approximation of loop quantum gravity

It is shown that the field equations derived from an effective interaction hamiltonian for Maxwell and gravitational fields in the semiclassical approximation of loop quantum gravity using rotational invariant states (such as weave states) are Lorentz invariant. To derive this result, which is in agreement with the observational evidence, we use the geometrical properties of the electromagnetic field.Comment: 6 page

On low energy quantum gravity induced effects on the propagation of light

Present models describing the interaction of quantum Maxwell and gravitational fields predict a breakdown of Lorentz invariance and a non standard dispersion relation in the semiclassical approximation. Comparison with observational data however, does not support their predictions. In this work we introduce a different set of ab initio assumptions in the canonical approach, namely that the homogeneous Maxwell equations are valid in the semiclassical approximation, and find that the resulting field equations are Lorentz invariant in the semiclassical limit. We also include a phenomenological analysis of possible effects on the propagation of light, and their dependence on energy, in a cosmological context.Comment: 12 page

Astrometric search for a planet around VB 10

We observed VB 10 in August and September 2009 using the FORS2 camera of the VLT with the aim of measuring its astrometric motion and of probing the presence of the announced planet VB 10b. We used the published STEPS astrometric positions of VB 10 over a time-span of 9 years, which allowed us to compare the expected motion of VB 10 due to parallax and proper motion with the observed motion and to compute precise deviations. The achieved single-epoch precisions of our observations are about 0.1 mas and the data showed no significant residual trend, while the presence of the planet should have induced an apparent proper motion larger than 10 mas/yr. Subtraction of the predicted orbital motion from the observed data produces a large trend in position residuals of VB 10. We estimated the probability that this trend is caused by random noise. Taking all the uncertainties into account and using Monte-Carlo resampling of the data, we are able to reject the existence of VB 10b with the announced mass of 6.4 M_J with the false alarm probability of only 0.0005. A 3.2 M_J planet is also rejected with a false alarm probability of 0.023.Comment: 6 pages, 6 figures, 2 tables, accepted for publication in A&

Entropy calculation for a toy black hole

In this note we carry out the counting of states for a black hole in loop quantum gravity, however assuming an equidistant area spectrum. We find that this toy-model is exactly solvable, and we show that its behavior is very similar to that of the correct model. Thus this toy-model can be used as a nice and simplifying `laboratory' for questions about the full theory.Comment: 18 pages, 4 figures. v2: Corrected mistake in bibliography, added appendix with further result

The SOPHIE search for northern extrasolar planets: VI. Three new hot Jupiters in multi-planet extrasolar systems

We present high-precision radial-velocity measurements of three solar-type stars: HD 13908, HD 159243, and HIP 91258. The observations were made with the SOPHIE spectrograph at the 1.93-m telescope of Observatoire de Haute-Provence (France). They show that these three bright stars host exoplanetary systems composed of at least two companions. HD 13908 b is a planet with a minimum mass of 0.865+-0.035 Mjup, on a circular orbit with a period of 19.382+-0.006 days. There is an outer massive companion in the system with a period of 931+-17 days, e = 0.12+-0.02, and a minimum mass of 5.13+-0.25 Mjup. The star HD 159243, also has two detected companions with respective masses, periods, and eccentricities of Mp = 1.13+-0.05 and 1.9+-0.13 Mjup, $P$ = 12.620+-0.004 and 248.4+-4.9 days, and e = 0.02+-0.02 and 0.075+-0.05. Finally, the star HIP 91258 has a planetary companion with a minimum mass of 1.068+-0.038 Mjup, an orbital period of 5.0505+-0.0015 days, and a quadratic trend indicating an outer planetary or stellar companion that is as yet uncharacterized. The planet-hosting stars HD 13908, HD 159243, and HIP 91258 are main-sequence stars of spectral types F8V, G0V, and G5V, respectively, with moderate activity levels. HIP 91258 is slightly over-metallic, while the two other stars have solar-like metallicity. The three systems are discussed in the frame of formation and dynamical evolution models of systems composed of several giant planets.Comment: accepted in A&

New insights in quantum geometry

Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a brief description of the main structures and results of quantum geometry, I review a new description of the quantized geometry in terms of polyhedra, new results on the volume operator, and a way to incorporate a classical background metric into the quantum description. Finally I describe a new type of exponentiated flux operator, and its application to Chern-Simons theory and black holes.Comment: 10 pages, 3 figures; Proceedings of Loops'11, Madrid, submitted to Journal of Physics: Conference Series (JPCS

The no-boundary measure in string theory: Applications to moduli stabilization, flux compactification, and cosmic landscape

We investigate the no-boundary measure in the context of moduli stabilization. To this end, we first show that for exponential potentials, there are no classical histories once the slope exceeds a critical value. We also investigate the probability distributions given by the no-boundary wave function near maxima of the potential. These results are then applied to a simple model that compactifies 6D to 4D (HBSV model) with fluxes. We find that the no-boundary wave function effectively stabilizes the moduli of the model. Moreover, we find the a priori probability for the cosmological constant in this model. We find that a negative value is preferred, and a vanishing cosmological constant is not distinguished by the probability measure. We also discuss the application to the cosmic landscape. Our preliminary arguments indicate that the probability of obtaining anti de Sitter space is vastly greater than for de Sitter.Comment: 27 pages, 8 figure