Gravitational Lensing of stars in the central arcsecond of our Galaxy

In the neighborhood of Sgr A*, several stars (S2, S12, S14, S1, S8, S13) enjoy an accurate determination of their orbital parameters. General Relativity predicts that the central black hole acts as a gravitational lens on these stars, generating a secondary image and two infinite series of relativistic images. For each of these six stars, we calculate the light curves for the secondary and the first two relativistic images, in the Schwarzschild black hole hypothesis, throughout their orbital periods. The curves are peaked around the periapse epoch, but two subpeaks may arise in nearly edge-on orbits, when the source is behind or in front of Sgr A*. We show that for most of these stars the secondary image should be observable during its brightness peak. In particular, S14 is the best candidate, since its secondary image reaches K=23.3 with an angular separation of 0.125 mas from the apparent horizon of the central black hole. The detection of such images by future instruments could represent the first observation of gravitational lensing beyond the weak field approximation.Comment: 28 pages, 9 figures, in press on Ap

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10^8 - 10^9 solar masses in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.Comment: 8 pages, 3 figure

Observing gravitational lensing effects by Sgr A* with GRAVITY

The massive black hole at the Galactic center Sgr A* is surrounded by a cluster of stars orbiting around it. Light from these stars is bent by the gravitational field of the black hole, giving rise to several phenomena: astrometric displacement of the primary image, the creation of a secondary image that may shift the centroid of Sgr A*, magnification effects on both images. The near-to-come second generation VLTI instrument GRAVITY will perform observations in the Near Infrared of the Galactic Center at unprecedented resolution, opening the possibility of observing such effects. Here we investigate the observability limits for GRAVITY of gravitational lensing effects on the S-stars in the parameter space [DLS,gamma,K], where DLS is the distance between the lens and the source, gamma is the alignment angle of the source, and K is the source apparent magnitude in the K-band. The easiest effect to be observed in the next years is the astrometric displacement of primary images. In particular the shift of the star S17 from its Keplerian orbit will be detected as soon as GRAVITY becomes operative. For exceptional configurations it will be possible to detect effects related to the spin of the black hole or Post-Newtonian orders in the deflection.Comment: 29 pages, 9 figures, in press on Ap

Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). 31 pages, 12 figure

Simultaneous follow-up of planetary transits: revised physical properties for the planetary systems HAT-P-16 and WASP-21

Context. By now more than 300 planets transiting their host star have been found, and much effort is being put into measuring the properties of each system. Light curves of planetary transits often contain deviations from a simple transit shape, and it is generally difficult to differentiate between anomalies of astrophysical nature (e.g. starspots) and correlated noise due to instrumental or atmospheric effects. Our solution is to observe transit events simultaneously with two telescopes located at different observatories. Aims. Using this observational strategy, we look for anomalies in the light curves of two transiting planetary systems and accurately estimate their physical parameters. Methods. We present the first photometric follow-up of the transiting planet HAT-P-16 b, and new photometric observations of WASP-21 b, obtained simultaneously with two medium-class telescopes located in different countries, using the telescope defocussing technique. We modeled these and other published data in order to estimate the physical parameters of the two planetary systems. Results. The simultaneous observations did not highlight particular features in the light curves, which is consistent with the low activity levels of the two stars. For HAT-P-16, we calculated a new ephemeris and found that the planet is 1.3 \sigma colder and smaller (Rb = 1.190 \pm 0.037 RJup) than the initial estimates, suggesting the presence of a massive core. Our physical parameters for this system point towards a younger age than previously thought. The results obtained for WASP-21 reveal lower values for the mass and the density of the planet (by 1.0 \sigma and 1.4 \sigma respectively) with respect to those found in the discovery paper, in agreement with a subsequent study. We found no evidence of any transit timing variations in either system.Comment: 8 pages, 6 figures, accepted for publication in A&

Scale-invariance in expanding and contracting universes from two-field models

We study cosmological perturbations produced by the most general two-derivative actions involving two scalar fields, coupled to Einstein gravity, with an arbitrary field space metric, that admit scaling solutions. For contracting universes, we show that scale-invariant adiabatic perturbations can be produced continuously as modes leave the horizon for any equation of state parameter $w \ge 0$. The corresponding background solutions are unstable, which we argue is a universal feature of contracting models that yield scale-invariant spectra. For expanding universes, we find that nearly scale-invariant adiabatic perturbation spectra can only be produced for $w \approx -1$, and that the corresponding scaling solutions are attractors. The presence of a nontrivial metric on field space is a crucial ingredient in our results.Comment: 23 pages, oversight in perturbations calculation corrected, conclusions for expanding models modifie

Tracking Curvaton(s)?

The ratio of the curvaton energy density to that of the dominant component of the background sources may be constant during a significant period in the evolution of the Universe. The possibility of having tracking curvatons, whose decay occurs prior to the nucleosynthesis epoch, is studied. It is argued that the tracking curvaton dynamics is disfavoured since the value of the curvature perturbations prior to curvaton decay is smaller than the value required by observations. It is also argued, in a related context, that the minimal inflationary curvature scale compatible with the curvaton paradigm may be lowered in the case of low-scale quintessential inflation.Comment: 20 pages, 4figure

Inferring statistics of planet populations by means of automated microlensing searches

(abridged) The study of other worlds is key to understanding our own, and not only provides clues to the origin of our civilization, but also looks into its future. Rather than in identifying nearby systems and learning about their individual properties, the main value of the technique of gravitational microlensing is in obtaining the statistics of planetary populations within the Milky Way and beyond. Only the complementarity of different techniques currently employed promises to yield a complete picture of planet formation that has sufficient predictive power to let us understand how habitable worlds like ours evolve, and how abundant such systems are in the Universe. A cooperative three-step strategy of survey, follow-up, and anomaly monitoring of microlensing targets, realized by means of an automated expert system and a network of ground-based telescopes is ready right now to be used to obtain a first census of cool planets with masses reaching even below that of Earth orbiting K and M dwarfs in two distinct stellar populations, namely the Galactic bulge and disk. The hunt for extra-solar planets acts as a principal science driver for time-domain astronomy with robotic-telescope networks adopting fully-automated strategies. Several initiatives, both into facilities as well as into advanced software and strategies, are supposed to see the capabilities of gravitational microlensing programmes step-wise increasing over the next 10 years. New opportunities will show up with high-precision astrometry becoming available and studying the abundance of planets around stars in neighbouring galaxies becoming possible. Finally, we should not miss out on sharing the vision with the general public, and make its realization to profit not only the scientists but all the wider society.Comment: 10 pages in PDF format. White paper submitted to ESA's Exo-Planet Roadmap Advisory Team (EPR-AT); typos corrected. The embedded figures are available from the author on request. See also "Towards A Census of Earth-mass Exo-planets with Gravitational Microlensing" by J.P. Beaulieu, E. Kerins, S. Mao et al. (arXiv:0808.0005

Low-scale Quintessential Inflation

In quintessential inflationary model, the same master field that drives inflation becomes, later on, the dynamical source of the (present) accelerated expansion. Quintessential inflationary models require a curvature scale at the end of inflation around $10^{-6}M_{\rm P}$ in order to explain the large scale fluctuations observed in the microwave sky. If the curvature scale at the end of inflation is much smaller than $10^{-6}M_{\rm P}$, the large scale adiabatic mode may be produced thanks to the relaxation of a scalar degree of freedom, which will be generically denoted, according to the recent terminology, as the curvaton field. The production of the adiabatic mode is analysed in detail in the case of the minimal quintessential inflationary model originally proposed by Peebles and Vilenkin.Comment: 25 pages; 5 figure

A general condition of inflationary cosmology on trans-Planckian physics

We consider a more general initial condition satisfying the minimal uncertainty relationship. We calculate the power spectrum of a simple model in inflationary cosmology. The results depend on perturbations generated below a fundamental scale, e.g. the Planck scale.Comment: 7 pages, References adde