Cosmic distance ladder | EPFL Graph Search

The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A direct distance measurement of an astronomical object is possible only for those objects that are "close enough" (within about a thousand parsecs) to Earth. The techniques for determining distances to more distant objects are all based on various measured correlations between methods that work at close distances and methods that work at larger distances. Several methods rely on a standard candle, which is an astronomical object that has a known luminosity. The ladder analogy arises because no single technique can measure distances at all ranges encountered in astronomy. Instead, one method can be used to measure nearby distances, a second can be used to measure nearby to intermediate distances, and so on. Each rung of the ladder provides information that can be used to determine the distances at the next higher

Topological defects and gravity in theories with extra dimensions

Ewald Rössl

Recent proposals of large and infinite extra dimensions triggered a strong research activity in theories in which our universe is considered as a sub-manifold of some higher-dimensional space-time, a so-called 3-brane. In this context, it is generally assumed that some mechanism is at work which binds Standard Model particles to the 3-brane, an effect often referred to as the localization of matter on the brane. Gravity, however, is allowed to propagate in general also in the extra dimensions. As demonstrated by Randall and Sundrum in 1999, it is also possible to localize gravity itself on a 3-brane. In the setup they proposed. the 3-brane is realized as a singular domain wall separating two patches of 3-dimensional anti-de-Sitter (AdS5) space-time. The potential between two test masses on the brane at distances larger than the AdS5-radius was shown to be the usual 4-dimensional Newtonian 1/r potential with strongly suppressed corrections. The model of Randall and Sundrum, usually referred to as the Randall-Sundrum II setup, constitutes the center of interest for this thesis. The main goal of this work is to find possible generalizations to higher dimensions of the simple setup considered by Randall and Sundrum. One of the motivations for such a generalization is that a realistic theory should possibly be able to explain the chiral nature of 4-dimensional fermions on the brane. One way to explain chiral fermions from higher dimensions is to consider 3-braves identified with the cores of topological defects located in a higher-dimensional transverse space. Naturally a richer topological structure of the field configuration in transverse space provides the possibility of a more realistic spectrum of chiral fermions localized on the 3-brane. After two introductory chapters on extra dimensions and non-factorizable geometries which are relevant for the Randall-Sundrum II model, we briefly discuss basics of topological defects in the following third chapter. In the rest of the third chapter we consider various solutions to higher-dimensional Einstein equations coupled to a series of physically different sources and discuss their properties of localization of gravity. Due to their asymptotic nature, these solutions are only valid far from the cores of the defects in transverse space. Therefore, it seems reasonable to complement the consideration by presenting a particular numerical example of a solution to the Einstein equations coupled to a set of scalar and gauge fields: this solution describes a 3-brave realized as a 't Hooft-Polyakov monopole residing in the 3-dimensional transverse space of a 7-dimensional space-time. The last chapter of this work is dedicated to the study of a modification of the original Randall-Sundrum II model of another kind. The motivation is given by the geodesic incompleteness of the latter scenario with respect to time-like and light-like geodesics. We will describe a model which resembles the Randall-Sundrurn II model with respect to its properties of gravity localization but with the advantage that the underlying space-time manifold is geodesically complete. Parts of the calculations related to the properties of gravity at low energies in this model are rather technical in nature and we therefore preferred to assemble them in several appendices. We finally add some concluding remarks and discuss possible further developments.

EPFL2004

Gravitational lenses

Christel Vuissoz

The Hubble constant H0 is one of the most important parameters in cosmology, as it encodes the age of the Universe and is necessary for any distance determination at a cosmological scale. It is, however, only poorly constrained by traditional methods. The current favored value, H0 = 72±8 km s-1 Mpc-1, is provided by the HST Hubble constant Key Project (Freedman et al. 2001), which combines several Cepheid-calibrated distance indicators. This roughly 10% error nevertheless denotes only the statistical uncertainty in the determination of H0, while the possible systematical errors in the first step of the distance ladder (the distance to the Large Magellanic Cloud) may be of the same order of magnitude. Time delays between gravitationally lensed images of distant quasars can yield a more precise measurement of the Hubble constant, on a truly cosmic scale, and independently of any local distance calibrator. At the beginning of this thesis, time delays had been measured in only ten lensed systems, nine of which gave H0 estimates. However before 2004, no concerted and long term action has succeeded to apply the time delay method at a level of precision really competitive with other techniques. The major difficulties arise from the modeling of the lens mass distribution, and from the uncertainty on the time delay measurement itself, which was typically of about 10% in past monitoring programs. COSMOGRAIL (COSmological MOnitoring of GRAvItational Lenses) is an international collaboration initiated in April 2004 at the Laboratory of Astrophysics of EPFL, and which aims at measuring precise time delays for most known lensed quasars, in order to determine the Hubble constant down to an uncertainty of a few percent. This thesis took place at the beginning of COSMOGRAIL and consisted in setting up this large photometric monitoring. It addressed both issues of carrying out accurate photometry of faint blended sources and of obtaining well sampled light curves, in order to measure precise time delays. As part of the COSMOGRAIL project, I have been managing the monitoring of over twenty gravitationally lensed quasars with the 1-2m telescopes involved both in the Northern and Southern hemispheres, and organizing the data. The first crucial work of this thesis was then to develop an automated reduction pipeline able to produce an homogeneous data set from images acquired with very different telescopes. This pipeline was also needed to perform aperture photometry of all lensed quasars, in order to study their variability and define the monitoring priorities. The powerful MCS deconvolution algorithm (Magain, Courbin, & Sohy 1998) was greatly used in this work and allowed to highly improve the image resolution, with the aim of obtaining accurate photometric measurements of the individual quasar lensed images. I have finally tested and improved three different numerical techniques to determine time delays between the quasar components from their light curves. In this thesis, time delays have been determined in four systems. The first one was measured in the doubly imaged quasar SDSS J1650+4251, after two years of monitoring with the 1.5m telescope of Maidanak Observatory, in Uzbekistan. The quadruply lensed system RXS J1131–1231 was then studied and three time delays determined from 3-year observations with the Swiss Euler 1.2m telescope located at La Silla, in Chile. The photometric monitoring of the quadruple WFI J2033–4723 was also carried out with the Euler telescope, and data were then merged with those obtained by a second monitoring group, with the SMARTS 1.3m telescope at the Cerro Tololo Interamerican Observatory (CTIO), also located in Chile. Two time delays were measured in this system, after three years of observations, the close pair A1 – A2 remaining unresolved. Three time delays were determined in the quadruply imaged quasar HE0435–1223, after four years of optical monitoring with Euler, Mercator and Maidanak telescopes, to which photometric measurements by SMARTS 1.3m telescope were added. Euler and SMARTS merged data for the doubly imaged quasar QJ0158–4325 were also analysed, the size of the source accretion disk was measured, but we failed to determine a time delay due to the high amplitude of the microlensing variability in this system. The accuracies on time delay measurements reached in this thesis are of the order of 3-4% and show a clear improvement from the typical 10% uncertainties of past monitoring programs. These results were finally converted into estimates of the Hubble constant following different models of the lensing mass potential. The H0 mean value obtained when considering the individual determinations from twelve gravitationally lensed quasars with known time delays is H0 = 60 ± 7 km s-1 Mpc-1. This result is consistent with the current favored value, and above all promising, as including additional systems to this ensemble will surely provide tighter bounds on H0. In conclusion, the increasing number of time delay measurements and improvements in lens modeling should reduce the errors on the Hubble constant estimate provided by gravitational lensing. Conversely, the determination of more time delays should put further constraints on lens galaxy density profiles when using a prior on H0 from other studies.

EPFL2008

Precise measurements of time delays in gravitationally lensed quasars for competitive and independent determination of the Hubble constant

Vivien François Bonvin

During these last decades, by virtue of observations, the Standard Cosmological Model has emerged, providing a description of the Universe's evolution using a minimal set of independent constraints - the cosmological parameters. Among them is the expansion rate of the Universe, the so-called Hubble constant or H0, first measured by Lemaître in 1927. The century that followed this cornerstone measurement saw numerous attempts to refine the initial value, and for good reason: a precise and independent measurement of H0 will bring strong constraints on the cosmological models. It could notably help the astronomers to better understand the nature of dark energy, thus making it one of the most sought-after prizes in modern cosmology. My work at the Laboratory of Astrophysics of EPFL is embedded in this context. I am part of the COSMOGRAIL and H0LiCOW collaborations, aiming to measure the Hubble constant with the highest level of precision using time-delay cosmography, a method based on the theory of strong gravitational lensing. This effect occurs when an observer looks at a light source located behind a massive foreground galaxy. The mass of the galaxy acts similarly to an optical lens and focuses the light rays emitted by the source. As a consequence, multiple lensed images of the source appear around the lens galaxy. If the luminosity of the source changes over time, the variations will be seen in all the lensed images but with a temporal delay due to the different travel paths of the light rays. By carefully monitoring the luminosity variations of each lensed image, one can precisely measure the temporal delays between them. Combined to high-resolution observations of the foreground galaxy and its surroundings, it is possible to directly measure the Hubble constant upon the sole assumption that the General Relativity is correct. Since more than 13 years, COSMOGRAIL monitors dozens of lensed quasars to produce high-quality light curves and time-delay measurements. During these last four years, I took care of the monitoring schedule, continuous data reduction and time-delay measurements through the development of curve-shifting techniques. I produced light curves and measured time delays on a variety of lenses. After more than a decade of endeavours, COSMOGRAIL and H0LiCOW finally revealed their measurement of the expansion rate of the Universe from a blind analysis of three lensed sources. I had the privilege to be the lead author of the publication presenting our measurement of the Hubble constant, H0=71.9 -3.0+2.4 km/s/Mpc 3.8% precision in the Standard Cosmological Model. Such a precision allows a direct comparison with the results of the distance ladder technique in the local Universe and the Planck satellite Cosmic Microwave Background observations in the distant Universe, both of which being currently in a significant tension of unknown source.

EPFL2017