Scaling the universe: Gravitational lenses and the Hubble constant

Gravitational lenses, besides being interesting in their own right, have been demonstrated to be suitable as “gravitational standard rulers” for the measurement of the rate of expansion of the Universe (Ho), as well as to constrain the values of the cosmological parameters such as Ωo and Λo that control the evolution of the volume of the Universe with cosmic time.

Determination of the Hubble constant

Establishing accurate extragalactic distances has provided an immense challenge to astronomers since the 1920s. The situation has improved dramatically as better detectors have become available, and as several new, promising techniques have been developed. For the first time in the history of this difficult field, relative distances to galaxies are being compared on a case-by-case basis, and their quantitative agreement is being established. New instrumentation, the development of new techniques for measuring distances, and recent measurements with the Hubble Space telescope all have resulted in new distances to galaxies with precision at the ±5–20% level. The current statistical uncertainty in some methods for measuring H0 is now only a few percent; with systematic errors, the total uncertainty is approaching ±10%. Hence, the historical factor-of-two uncertainty in the value of the H0 is now behind us.

Direction dependence in supernova data: constraining isotropy

We revise and extend the extreme value statistic, introduced in Gupta et al., to study direction dependence in the high-redshift supernova data, arising either from departures, from the cosmological principle or due to direction-dependent statistical systematics in the data. We introduce a likelihood function that analytically marginalizes over the,Hubble constant and use it to extend our previous statistic. We also introduce a new statistic that is sensitive to direction dependence arising from living off-centre inside a large void as well as from previously mentioned reasons for anisotropy. We show that for large data sets, this statistic has a limiting form that can be computed analytically. We apply our statistics to the gold data sets from Riess et al., as in our previous work. Our revision and extension of the previous statistic show that the effect of marginalizing over the Hubble constant instead of using its best-fitting value on our results is only marginal. However, correction of errors in our previous work reduces the level of non-Gaussianity in the 2004 gold data that were found in our earlier work. The revised results for the 2007 gold data show that the data are consistent with isotropy and Gaussianity. Our second statistic confirms these results.

Non-Gaussianity and direction-dependent systematics in HST Key Project data

Two new statistics, namely Delta(chi 2) and Delta(chi), based on the extreme value theory, were derived by Gupta et al. We use these statistics to study the direction dependence in the HST Key Project data, which provides one of the most precise measurements of the Hubble constant. We also study the non-Gaussianity in this data set using these statistics. Our results for Delta(chi 2) show that the significance of direction-dependent systematics is restricted to well below the 1 sigma confidence limit; however, the presence of non-Gaussian features is subtle. On the other hand, the Delta(chi). statistic, which is more sensitive to direction dependence, shows direction dependence systematics to be at a slightly higher confidence level, and the presence of non-Gaussian features at a level similar to the Delta(chi 2) statistic.

Black holes in the early universe, in compact binaries, and as energy sources inside solar-type stars

This thesis consists of three separate studies of roles that black holes might play in our universe.

In the first part we formulate a statistical method for inferring the cosmological parameters of our universe from LIGO/VIRGO measurements of the gravitational waves produced by coalescing black-hole/neutron-star binaries. This method is based on the cosmological distance-redshift relation, with "luminosity distances" determined directly, and redshifts indirectly, from the gravitational waveforms. Using the current estimates of binary coalescence rates and projected "advanced" LIGO noise spectra, we conclude that by our method the Hubble constant should be measurable to within an error of a few percent. The errors for the mean density of the universe and the cosmological constant will depend strongly on the size of the universe, varying from about 10% for a "small" universe up to and beyond 100% for a "large" universe. We further study the effects of random gravitational lensing and find that it may strongly impair the determination of the cosmological constant.

In the second part of this thesis we disprove a conjecture that black holes cannot form in an early, inflationary era of our universe, because of a quantum-field-theory induced instability of the black-hole horizon. This instability was supposed to arise from the difference in temperatures of any black-hole horizon and the inflationary cosmological horizon; it was thought that this temperature difference would make every quantum state that is regular at the cosmological horizon be singular at the black-hole horizon. We disprove this conjecture by explicitly constructing a quantum vacuum state that is everywhere regular for a massless scalar field. We further show that this quantum state has all the nice thermal properties that one has come to expect of "good" vacuum states, both at the black-hole horizon and at the cosmological horizon.

In the third part of the thesis we study the evolution and implications of a hypothetical primordial black hole that might have found its way into the center of the Sun or any other solar-type star. As a foundation for our analysis, we generalize the mixing-length theory of convection to an optically thick, spherically symmetric accretion flow (and find in passing that the radial stretching of the inflowing fluid elements leads to a modification of the standard Schwarzschild criterion for convection). When the accretion is that of solar matter onto the primordial hole, the rotation of the Sun causes centrifugal hangup of the inflow near the hole, resulting in an "accretion torus" which produces an enhanced outflow of heat. We find, however, that the turbulent viscosity, which accompanies the convective transport of this heat, extracts angular momentum from the inflowing gas, thereby buffering the torus into a lower luminosity than one might have expected. As a result, the solar surface will not be influenced noticeably by the torus's luminosity until at most three days before the Sun is finally devoured by the black hole. As a simple consequence, accretion onto a black hole inside the Sun cannot be an answer to the solar neutrino puzzle.

An early-time infrared and optical study of the Type Ia Supernova 1998bu in M96

We present first-season infrared (IR) and optical photometry and spectroscopy of the Type Ia Supernova 1998bu in M96. We also report optical polarimetry of this event. SN 1998bu is one of the closest type Ia supernovae of modern times, and the distance of its host galaxy is well determined. We find that SN 1998bu is both photometrically and spectroscopically normal. However, the extinction to this event is unusually high, with A(V) = 1.0 +/- 0.11. We find that SN 1998bu peaked at an intrinsic M-V = -19.37 +/- 0.23. Adopting a distance modulus of 30.25 (Tanvir et al.) and using Phillips et al.'s relations for the Hubble constant, we obtain H-0 = 70.4 +/- 4.3 km s(-1) Mpc(-1). Combination of our IR photometry with those of Jha et al. provides one of the most complete early-phase IR light curves for a SN Ia published so far. In particular, SN 1998bu is the first normal SN Ia for which good pre-t(Bmax) IR coverage has been obtained. It reveals that the J, H and K light curves peak about 5 days earlier than the flux in the B-band curve.

DENSITY PROFILE, VELOCITY ANISOTROPY, AND LINE-OF-SIGHT EXTERNAL CONVERGENCE OF SLACS GRAVITATIONAL LENSES

Data from 58 strong-lensing events surveyed by the Sloan Lens ACS Survey are used to estimate the projected galaxy mass inside their Einstein radii by two independent methods: stellar dynamics and strong gravitational lensing. We perform a joint analysis of these two estimates inside models with up to three degrees of freedom with respect to the lens density profile, stellar velocity anisotropy, and line-of-sight (LOS) external convergence, which incorporates the effect of the large-scale structure on strong lensing. A Bayesian analysis is employed to estimate the model parameters, evaluate their significance, and compare models. We find that the data favor Jaffe`s light profile over Hernquist`s, but that any particular choice between these two does not change the qualitative conclusions with respect to the features of the system that we investigate. The density profile is compatible with an isothermal, being sightly steeper and having an uncertainty in the logarithmic slope of the order of 5% in models that take into account a prior ignorance on anisotropy and external convergence. We identify a considerable degeneracy between the density profile slope and the anisotropy parameter, which largely increases the uncertainties in the estimates of these parameters, but we encounter no evidence in favor of an anisotropic velocity distribution on average for the whole sample. An LOS external convergence following a prior probability distribution given by cosmology has a small effect on the estimation of the lens density profile, but can increase the dispersion of its value by nearly 40%.

Observational constraints on the dark energy and dark matter mutual coupling

We examine different phenomenological interaction models for Dark Energy and Dark Matter by performing statistical joint analysis with observational data arising from the 182 Gold type la supernova samples, the shift parameter of the Cosmic Microwave Background given by the three-year Wilkinson Microwave Anisotropy Probe observations, the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey and age estimates of 35 galaxies. Including the time-dependent observable, we add sensitivity of measurement and give complementary results for the fitting. The compatibility among three different data sets seem to imply that the coupling between dark energy and dark matter is a small positive value, which satisfies the requirement to solve the coincidence problem and the second law of thermodynamics, being compatible with previous estimates. (c) 2008 Elsevier B.V. All rights reserved.

Observational constraints on holographic tachyonic dark energy in interaction with dark matter

We discuss an interacting tachyonic dark energy model in the context of the holographic principle. The potential of the holographic tachyon field in interaction with dark matter is constructed. The model results are compared with CMB shift parameter, baryonic acoustic oscilations, lookback time and the Constitution supernovae sample. The coupling constant of the model is compatible with zero, but dark energy is not given by a cosmological constant.

Age constraints and fine tuning in variable-mass particle models

VAMP (variable-mass particle) scenarios, in which the mass of the cold dark matter particles is a function of the scalar field responsible for the present acceleration of the Universe, have been proposed as a solution to the cosmic coincidence problem, since in the attractor regime both dark energy and dark matter scale in the same way. We find that only a narrow region in parameter space leads to models with viable values for the Hubble constant and dark energy density today. In the allowed region, the dark energy density starts to dominate around the present epoch and consequently such models cannot solve the coincidence problem. We show that the age of the Universe in this scenario is considerably higher than the age for noncoupled dark energy models, and conclude that more precise independent measurements of the age of the Universe would be useful in distinguishing between coupled and noncoupled dark energy models.

Constraining H-0 in general dark energy models from Sunyaev-Zeldovich/X-ray technique and complementary probes

In accelerating dark energy models, the estimates of the Hubble constant, Ho, from Sunyaev-Zerdovich effect (SZE) and X-ray surface brightness of galaxy clusters may depend on the matter content (Omega(M)), the curvature (Omega(K)) and the equation of state parameter GO. In this article, by using a sample of 25 angular diameter distances of galaxy clusters described by the elliptical beta model obtained through the SZE/X-ray technique, we constrain Ho in the framework of a general ACDM model (arbitrary curvature) and a flat XCDM model with a constant equation of state parameter omega = p(x)/rho(x). In order to avoid the use of priors in the cosmological parameters, we apply a joint analysis involving the baryon acoustic oscillations (BA()) and the (MB Shift Parameter signature. By taking into account the statistical and systematic errors of the SZE/X-ray technique we obtain for nonflat ACDM model H-0 = 74(-4.0)(+5.0) km s(-1) Mpc(-1) (1 sigma) whereas for a fiat universe with constant equation of state parameter we find H-0 = 72(-4.0)(+5.5) km s(-1) Mpc(-1)(1 sigma). By assuming that galaxy clusters are described by a spherical beta model these results change to H-0 = 6(-7.0)(+8.0) and H-0 = 59(-6.0)(+9.0) km s(-1) Mpc(-1)(1 sigma), respectively. The results from elliptical description are in good agreement with independent studies from the Hubble Space Telescope key project and recent estimates based on the Wilkinson Microwave Anisotropy Probe, thereby suggesting that the combination of these three independent phenomena provides an interesting method to constrain the Bubble constant. As an extra bonus, the adoption of the elliptical description is revealed to be a quite realistic assumption. Finally, by comparing these results with a recent determination for a, flat ACDM model using only the SZE/X-ray technique and BAO, we see that the geometry has a very weak influence on H-0 estimates for this combination of data.

New constraints on H-0 and Omega(m) from SZE/X-ray data and baryon acoustic oscillations

The Hubble constant, H-0, sets the scale of the size and age of the Universe and its determination from independent methods is still worthwhile to be investigated. In this article, by using the Sunyaev-Zeldovich effect and X-ray surface brightness data from 38 galaxy clusters observed by Bonamente et al. (Astrophys J 647:25, 2006), we obtain a new estimate of H-0 in the context of a flat Lambda CDM model. There is a degeneracy on the mass density parameter (Omega(m)) which is broken by applying a joint analysis involving the baryon acoustic oscillations (BAO) as given by Sloan Digital Sky Survey. This happens because the BAO signature does not depend on H-0. Our basic finding is that a joint analysis involving these tests yield H-0 = 76.5(-3.33)(+3.35) km/s/mpc and Omega(m) = 0.27(-0.02)(+0.03). Since the hypothesis of spherical geometry assumed by Bonamente et al. is questionable, we have also compared the above results to a recent work where a sample of galaxy clusters described by an elliptical profile was used in analysis.

Holographic field theory models of dark energy in interaction with dark matter

We discuss two Lagrangian interacting dark energy models in the context of the holographic principle. The potentials of the interacting fields are constructed. The models are compared with CMB distance information, baryonic acoustic oscillations, lookback time and the Constitution supernovae sample. For both models, the results are consistent with a nonvanishing interaction in the dark sector of the Universe and the sign of coupling is consistent with dark energy decaying into dark matter, alleviating the coincidence problem-with more than 3 standard deviations of confidence for one of them. However, this is because the noninteracting holographic dark energy model is a bad fit to the combination of data sets used in this work as compared to the cosmological constant with cold dark matter model, so that one needs to introduce the interaction in order to improve this model.

Early-type galaxies as probes of galaxy formation and cosmology

The goal of this thesis is to analyze the possibility of using early-type galaxies to place evolutionary and cosmological constraints, by both disentangling what is the main driver of ETGs evolution between mass and environment, and developing a technique to constrain H(z) and the cosmological parameters studying the ETGs age-redshift relation. The (U-V) rest-frame color distribution is studied as a function of mass and environment for two sample of ETGs up to z=1, extracted from the zCOSMOS survey with a new selection criterion. The color distributions and the slopes of the color-mass and color-environment relations are studied, finding a strong dependence on mass and a minor dependence on environment. The spectral analysis performed on the D4000 and Hδ features gives results validating the previous analysis. The main driver of galaxy evolution is found to be the galaxy mass, the environment playing a subdominant but non negligible role. The age distribution of ETGs is also analyzed as a function of mass, providing strong evidences supporting a downsizing scenario. The possibility of setting cosmological constraints studying the age-redshift relation is studied, discussing the relative degeneracies and model dependencies. A new approach is developed, aiming to minimize the impact of systematics on the “cosmic chronometer” method. Analyzing theoretical models, it is demonstrated that the D4000 is a feature correlated almost linearly with age at fixed metallicity, depending only minorly on the models assumed or on the SFH chosen. The analysis of a SDSS sample of ETGs shows that it is possible to use the differential D4000 evolution of the galaxies to set constraints to cosmological parameters in an almost model-independent way. Values of the Hubble constant and of the dark energy EoS parameter are found, which are not only fully compatible, but also with a comparable error budget with the latest results.

Measuring cosmological parameters

In this review, the status of measurements of the matter density (Ωm), the vacuum energy density or cosmological constant (ΩΛ), the Hubble constant (H0), and the ages of the oldest measured objects (t0) are summarized. Three independent types of methods for measuring the Hubble constant are considered: the measurement of time delays in multiply imaged quasars, the Sunyaev–Zel’dovich effect in clusters, and Cepheid-based extragalactic distances. Many recent independent dynamical measurements are yielding a low value for the matter density (Ωm ≈ 0.2–0.3). A wide range of Hubble constant measurements appear to be converging in the range of 60–80 km/sec per megaparsec. Areas where future improvements are likely to be made soon are highlighted—in particular, measurements of anisotropies in the cosmic microwave background. Particular attention is paid to sources of systematic error and the assumptions that underlie many of the measurement methods.