An investigation of gravitational lens determinations of H0 in quintessence cosmologies

There is growing evidence that the majority of the energy density of the Universe is not baryonic or dark matter, but rather it resides in an exotic component with negative pressure. The nature of this 'quintessence' influences our view of the Universe, modifying angular diameter and luminosity distances. Here, we examine the influence of a quintessence component upon gravitational lens time-delays. As well as a static quintessence component, an evolving equation of state is also considered. It is found that the equation of state of the quintessence component and its evolution influence the value of the Hubble constant derived from gravitational lenses. However, the differences between evolving and non-evolving cosmologies are relatively small. We undertake a suite of Monte Carlo simulations to examine the potential constraints that can be placed on the universal equation of state from the monitoring of gravitational lens systems, and demonstrate that at least an order of magnitude more lenses than currently known will have to be discovered and analysed to accurately probe any quintessence component.     

The Amplitude of Mass Fluctuations and Mass Density of the Universe Constrained by Strong Gravitational Lensing

We investigate the linear amplitude of mass fluctuations in the universe, σ8, and the present mass density parameter of the Universe, Ωm, from statistical strong gravitational lensing. We use the two population model of lens halos with fixed cooling mass scale Mc = 3×1013h-1M⊙ to match the observed lensing probabilities, and leave σ8 orΩm as a free parameter to be constrained by the data. Another varying parameter, the equation of state of dark energy ω, and its typical values of -1, -2/3, -1/2 and -1/3 are investigated. We find that σ8 is degenerate with Ωm in a way similar to that suggested by present day cluster abundance as well as cosmic shear lensing measurements: σ8Ω0.6m≈0.33. However, both σ8≤0.7 and Ωm≤0.2 can be safely ruled out, the best fit is when σ8 = 1.0, Ωm = 0.3 and ω= - 1. This result is different from that obtained by Bahcall & Bode, who gave σ8 = 0.98±0.1 and Ωm = 0.17 ±0.05. For σ8 = 1.0, the higher value ofΩm = 0.35 requires ω = -2/3 and Ωm = 0.40 require     

Bayesian photometric redshifts for weak-lensing applications

The next generation of weak gravitational lensing surveys are capable of generating good measurements of cosmological parameters, provided that, amongst other requirements, adequate redshift information is available for the background galaxies that are measured. It is frequently assumed that photometric redshift techniques provide the means to achieve this. Here, we compare Bayesian and frequentist approaches to photometric redshift estimation, particularly at faint magnitudes. We identify and discuss the biases that are inherent in the various methods, and describe an optimum Bayesian method for extracting redshift distributions from photometric data.     

Constraints on a quintessence model from gravitational lensing statistics

Constraints on an exact quintessence scalar-field model with an exponential potential are derived from gravitational lens statistics. An exponential potential can account for data from both optical quasar surveys and radio-selected sources. Based on the Cosmic Lens All-Sky Survey (CLASS) sample, lensing statistics provides, for the pressureless matter density parameter, an estimate of  Ω_M0= 0.31^+0.12_−0.14  .     

The impact of non-Gaussian errors on weak lensing surveys

The weak lensing power spectrum carries cosmological information via its dependence on the growth of structure and on geometric factors. Since much of the cosmological information comes from scales affected by non-linear clustering, measurements of the lensing power spectrum can be degraded by non-Gaussian covariances. Recently, there have been conflicting studies about the level of this degradation. We use the halo model to estimate it and include new contributions related to the finite size of lensing surveys, following Rimes and Hamilton's study of three-dimensional simulations. We find that non-Gaussian correlations between different multipoles can degrade the cumulative signal-to-noise ratio (S/N) for the power spectrum amplitude by up to a factor of 2 (or 5 for a worst-case model that exceeds current N -body simulation predictions). However, using an eight-parameter Fisher analysis, we find that the marginalized errors on individual parameters are degraded by less than 10 per cent (or 20 per cent for the worst-case model). The smaller degradation in parameter accuracy is primarily because: individual parameters in a high-dimensional parameter space are degraded much less than the volume of the full Fisher ellipsoid; lensing involves projections along the line of sight, which reduce the non-Gaussian effect; some of the cosmological information comes from geometric factors which are not degraded at all. We contrast our findings with those of Lee and Pen who suggested a much larger degradation in information content. Finally, our results give a useful guide for exploring survey design by giving the cosmological information returns for varying survey area, depth and the level of some systematic errors.     

The Hubble constant from galaxy lenses: impacts of triaxiality and model degeneracies

The Hubble constant can be constrained using the time delays between multiple images of gravitationally lensed sources. In some notable cases, typical lensing analyses assuming isothermal galaxy density profiles produce low values for the Hubble constant, inconsistent with the result of the HST Key Project  (72 ± 8 km s⁻¹ Mpc⁻¹)  . Possible systematics in the values of the Hubble constant derived from galaxy lensing systems can result from a number of factors, for example, neglect of environmental effects, assumption of isothermality, or contamination by line-of-sight structures. One additional potentially important factor is the triaxial structure of the lensing galaxy halo; most lens models account for halo shape simply by perturbing the projected spherical lensing potential, an approximation that is often necessary but that is inadequate at the levels of triaxiality predicted in the cold dark matter paradigm. To quantify the potential error introduced by this assumption in estimates of the Hubble parameter, we strongly lens a distant galaxy through a sample of triaxial softened isothermal haloes and use an Markov Chain Monte Carlo method to constrain the lensing halo profile and the Hubble parameter from the resulting multiple image systems. We explore the major degeneracies between the Hubble parameter and several parameters of the lensing model, finding that without a way to accurately break these degeneracies accurate estimates of the Hubble parameter are not possible. Crucially, we find that triaxiality does not significantly bias estimates of the Hubble constant, and offer an analytic explanation for this behaviour in the case of isothermal profiles. Neglected triaxial halo shape cannot contribute to the low Hubble constant values derived in a number of galaxy lens systems.     

Weak gravitational lensing by voids

We consider the prospects for detecting weak gravitational lensing by underdensities (voids) in the large-scale matter distribution. We derive the basic expressions for magnification and distortion by spherical voids. Clustering of the background sources and cosmic variance are the main factors that limit in principle the detection of lensing by voids. We conclude that only voids with radii larger than ∼100  h ⁻¹ Mpc have lensing signal-to-noise ratio larger than unity.     

The Δθ–zs relation for gravitational lenses as a cosmological test

Recently, Park &38; Gott claimed that there is a statistically significant, strong, negative correlation between the image separation Δθ and source redshift z _s for gravitational lenses. This is somewhat puzzling if one believes in a flat ( k  = 0) universe, since in this case the typical image separation is expected to be independent of the source redshift, while one expects a negative correlation in a k  = −1 universe and a positive one in a k  = +1 universe. Park &38; Gott explored several effects that could cause the observed correlation, but no combination of these can explain the observations with a realistic scenario. Here, I explore this test further in three ways. First, I show that in an inhomogeneous universe a negative correlation is expected regardless of the value of k . Secondly, I test whether the Δθ– z _s relation can be used as a test to determine λ₀ and Ω₀, rather than just the sign of k . Thirdly, I compare the results of the test from the Park &38; Gott sample with those using other samples of gravitational lenses, which can illuminate (unknown) selection effects and probe the usefulness of the Δθ– z _s relation as a cosmological test.     

Testing Bekenstein's relativistic Modified Newtonian Dynamics with lensing data

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specifically tensor–vector–scalar (TeVeS) theory, a theory which is consistent with fundamental relativistic principles and the phenomenology of Modified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we analytically derive the deflection angle for the point lens and the Hernquist galaxy profile, and study their patterns in convergence, shear and amplification. Applying our analytical lensing models, we fit galaxy-quasar lenses in the CfA-Arizona Space Telescope Lens Survey (CASTLES) sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all the cases, we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy μ function provides more efficient lensing than the standard MOND μ function. But for a handful of lenses, a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function μ and modification scale a ₀ for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND μ function. We also show that the simplest TeVeS 'minimal-matter' cosmology, a baryonic universe with a cosmological constant, can fit the distance–redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity.     

Direct observation of cosmic strings via their strong gravitational lensing effect – I. Predictions for high-resolution imaging surveys

We use present theoretical estimates for the density of long cosmic strings to predict the number of strong gravitational lensing events in astronomical imaging surveys as a function of the angular resolution and survey area. We show that angular resolution is the single most important factor, and that interesting limits on the dimensionless string tension   G μ/ c ²  can be obtained by existing and planned surveys. At the resolution of the Hubble Space Telescope ( HST ) (0.14 arcsec), it is sufficient to survey of the order of a few square degrees – well within reach of the current HST archive – to probe the regime   G μ/ c ²∼ 10⁻⁷  . If lensing by cosmic strings is not detected, such a survey would improve the limit on the string tension by a factor of two over that available from the cosmic microwave background. Future high resolution imaging surveys, covering a few hundred square degrees or more, either from space in the optical or from large-format radio telescopes on the ground, would be able to further lower this limit to   G μ/ c ²∼ 10⁻⁸  . These limits will not be improved significantly by increasing the solid angle of the survey.