Towards new background independent representations for Loop Quantum Gravity

Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened assumptions seem physically reasonable and retain the key requirement of explicit background independence. For simplicity, we restrict attention to the case of gauge group U(1).Comment: 22 pages, minor change

Background independent quantizations: the scalar field I

We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer variables. The quantization, in our formulation, amounts to introducing the `quantum' polymer *-star algebra and looking for positive linear functionals, called states. The assumed in our paper homeomorphism invariance allows to determine a complete class of the states. Except one, all of them are new. In this letter we outline the main steps and conclusions, and present the results: the GNS representations, characterization of those states which lead to essentially self adjoint momentum operators (unbounded), identification of the equivalence classes of the representations as well as of the irreducible ones. The algebra and topology of the problem, the derivation, all the technical details and more are contained in the paper-part II.Comment: 13 pages, minor corrections were made in the revised versio

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

Astrometric planet search around southern ultracool dwarfs II: Astrometric reduction methods and a deep astrometric catalogue

We describe the astrometric reduction of images obtained with the FORS2/VLT camera in the framework of an astrometric planet search around 20 M/L-transition dwarfs. We present the correction of systematic errors, the achieved astrometric performance, and a new astrometric catalogue containing the faint reference stars in 20 fields located close to the Galactic plane. We detected three types of systematic errors in the FORS2 astrometry: the relative motion of the camera's two CCD chips, errors that are correlated in space, and an error contribution of yet unexplained origin. The relative CCD motion has probably a thermal origin and usually is 0.001-0.010 px (~0.1-1 mas), but sometimes amounts to 0.02-0.05 px (3-6 mas). This instability and space-correlated errors are detected and mitigated using reference stars. The third component of unknown origin has an amplitude of 0.03-0.14 mas and is independent of the observing conditions. We find that a consecutive sequence of 32 images of a well-exposed star over 40 min at 0.6" seeing results in a median r.m.s. of the epoch residuals of 0.126 mas. Overall, the epoch residuals are distributed according to a normal law with a chi2~1. We compiled a catalogue of 12000 stars with I-band magnitudes of 16-22 located in 20 fields, each covering ~2x2'. It contains I-band magnitudes, ICRF positions with 40-70 mas precision, and relative proper motions and absolute trigonometric parallaxes with a precision of 0.1 mas/yr and 0.1 mas at the bright end, respectively.Comment: 17 pages, 19 figures, 4 tables, accepted for publication in A&A on March 14, 201

Astrometric orbit of a low-mass companion to an ultracool dwarf

Little is known about the existence of extrasolar planets around ultracool dwarfs. Furthermore, binary stars with Sun-like primaries and very low-mass binaries composed of ultracool dwarfs show differences in the distributions of mass ratio and orbital separation that can be indicative of distinct formation mechanisms. Using FORS2/VLT optical imaging for high precision astrometry we are searching for planets and substellar objects around ultracool dwarfs to investigate their multiplicity properties for very low companion masses. Here we report astrometric measurements with an accuracy of two tenths of a milli-arcsecond over two years that reveal orbital motion of the nearby L1.5 dwarf DENIS-P J082303.1-491201 located at 20.77 +/- 0.08 pc caused by an unseen companion that revolves about its host on an eccentric orbit in 246.4 +/- 1.4 days. We estimate the L1.5 dwarf to have 7.5 +/- 0.7 % of the Sun's mass that implies a companion mass of 28 +/- 2 Jupiter masses. This new system has the smallest mass ratio (0.36 +/- 0.02) of known very low-mass binaries with characterised orbits. With this discovery we demonstrate 200 micro-arcsecond astrometry over an arc-minute field and over several years that is sufficient to discover sub-Jupiter mass planets around ultracool dwarfs. We also show that the achieved parallax accuracy of < 0.4 % makes it possible to remove distance as a dominant source of uncertainty in the modelling of ultracool dwarfs.Comment: 9 pages, 8 figures, accepted for publication in Astronomy and Astrophysics. The reduced astrometry data will be made publically available through the CD

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

Astrometry with the VLTI: calibration of the Fringe Sensor Unit for the PRIMA astrometric camera

The future PRIMA facility at the Very Large Telescope Interferometer (VLTI) in astrometric mode offers the possibility to perform relative narrow-angle astrometry with 10 micro-arcsecond accuracy. This is achieved with a dual-beam interferometer concept, where a reference star and the scientific target, confined in a 60 arcsecond field, are observed simultaneously. The angular separation of the two stellar objects gives rise to an optical delay in the interferometer, which is measured by the Fringe Sensor Unit (FSU) and an internal laser metrology. PRIMA is using two FSU fringe detectors, each observing the interference of stellar beams coming from one of the two objects and measuring the corresponding phase and group delay. The astrometric observable, yielding the angular separation, is deduced from the group delay difference observed between the two objects. In addition, the FSU phase delay estimate is used as error signal for the fringe stabilisation loop of the VLTI. Both functions of the FSU require high precision fringe phase measurements with a goal of 1 nm rms (corresponding to λ/2000). These can only be achieved by applying a calibration procedure prior to the observing run. We discuss the FSU measurement principle and the applied algorithms. The calibration strategy and the methods used to derive the calibration parameters are presented. Special attention is given to the achieved measurement linearity and repeatability. The quality of the FSU calibration is crucial in order to achieve the ultimate accuracy and to fulfill the primary objective of PRIMA astrometry: the detection and characterisation of extrasolar planetary system

Astrometric planet search around southern ultracool dwarfs III. Discovery of a brown dwarf in a 3-year orbit around DE0630-18

Using astrometric measurements obtained with the FORS2/VLT camera, we are searching for low-mass companions around 20 nearby ultracool dwarfs. With a single-measurement precision of 0.1 milli-arcseconds, our survey is sensitive to a wide range of companion masses from planetary companions to binary systems. Here, we report the discovery and orbit characterisation of a new ultracool binary at a distance of 19.5 pc from Earth that is composed of the M8.5-dwarf primary DE0630-18 and a substellar companion. The nearly edge-on orbit is moderately eccentric (e=0.23) with an orbital period of 1120 d, which corresponds to a relative separation in semimajor axis of approximately 1.1 AU. We obtained a high-resolution optical spectrum with UVES/VLT and measured the system's heliocentric radial velocity. The spectrum does not exhibit lithium absorption at 670.8 nm, indicating that the system is not extremely young. A preliminary estimate of the binary's physical parameters tells us that it is composed of a primary at the stellar-substellar limit and a massive brown-dwarf companion. DE0630-18 is a new very low-mass binary system with a well-characterised orbit.Comment: 4 pages, 7 figures. Accepted for publication in A&