Gravitational Lensing Statistics Research Articles

Observational constraints upon quintessence models arising from moduli fields

We study observational constraints on cosmological models with a quintessence arising from moduli fields. The scalar field potential is given by a double exponential potential V=V 0 exp(−A e 2 κφ ) . After reviewing the properties of the solutions, from a dynamical systems phase space analysis, we consider the constraints on parameter values imposed by luminosity distances from the 60 Type IA supernovae published by Perlmutter et al., and also from gravitational lensing statistics of distant quasars. We also update the constraints on models with a single exponential potential V= V 0e − λκφ .

Measuring Cosmological Parameters from the Evolution of Cluster X‐Ray Temperatures

We have determined the cluster X-ray temperature function from two flux- and redshift-limited samples of clusters. The first sample is comprised of 25 clusters with average redshift 0.05. The local temperature function derived from it supersedes the one we published previously. Fourteen clusters with average redshift 0.38 comprise the second sample. We perform maximum likelihood fits of cluster evolution models to these data in order to constrain cosmological parameters. For an open model with zero cosmological constant we find that the density parameter is Ω0 = 0.49 ± 0.12, the rms mass density fluctuation averaged over 8 h-1 Mpc spheres is σ8 = 0.72 ± 0.10, and the effective index of the mass density fluctuation spectrum on cluster scales is n = -(1.72 ± 0.34), where all errors are symmetrized at 68% confidence. The corresponding results for the case where a cosmological constant produces a flat universe are 0.44 ± 0.12, 0.77 ± 0.15, and -(1.68 ± 0.38). These results agree with those determined from a variety of different independent methods, including supernovae, galaxy-galaxy correlations, fluctuations in the microwave background, gravitational lens statistics, and cluster peculiar velocities.

GRAVITATIONAL LENSING STATISTICS AND CONSTRAINTS ON THE COSMOLOGICAL CONSTANT REVISITED

We re-analyze constraints on the cosmological constant that can be obtained by examining the statistics of strong gravitational lensing of distant quasars by intervening galaxies, focusing on uncertainties in galaxy models (including velocity dispersion, luminosity functions, core radii and magnification bias effects) and on the parameters of the galaxy distribution and luminosity functions. In the process we derive new results on magnification biasing for galaxy lenses with nonzero core radii, and on how to infer the proper velocity dispersions appropriate for use in lensing statistics. We argue that the existing data do not disfavor a large cosmological constant. In fact, for a set of reasonable parameter choices, using the results of five optical quasar lensing surveys we find that a maximum likelihood analysis favors a value of Ω0 in the range ≈ 0.25–0.55 in a flat universe. An open cosmology is not favored by the same statistical analysis. Systematic uncertainties are likely to be dominant, however, as these results are sensitive to uncertainties in our understanding of galaxy luminosity functions, and dark matter velocity dispersions, as well as the choice of lensing survey, and to a lesser extent the existence of core radii. Further observational work will be required before it is possible to definitively distinguish between cosmological models on the basis of gravitational lensing statistics.

Gravitational lensing statistics with extragalactic surveys. IV. Joint constraints on λ and Ω from gravitational lensing statistics and CMB anisotropies

Gravitational lensing statistics with extragalactic surveys. IV. Joint constraints on λ and Ω from gravitational lensing statistics and CMB anisotropies

Determining the Cosmic Equation of State from Gravitational Lensing

An independent method is proposed to determine the equation of state, ωx ≡ px/ρx, for the dark energy component in the universe. This method is based on gravitational lensing statistics. An analytically simple expression for the optical depth of gravitational lensing in general Friedmann-Robertson-Walker cosmologies with dark energy component is derived. It is shown that for a flat universe the optical depth depends sensitively on the redshift to the source zs and the equation of state ωx, which makes the method proposed here efficient and robust.

Cosmological parameters

There is some consensus emerging on the values of the basic parameters of classical cosmology. The baryon number density estimated from the light element abundance or X-ray gas in galaxy clusters tends towards 5% of closure density; the dark matter content based on a number of independent methods appears to be somewhat less than half the closure density; Hubble constant obtained from local measurements, gravitational lens or Sunyaev Zeldovich method are all probably centred around 60 km/sec/Mpc and the age of the Universe is generally agree to be around 14 Gyr — all specified with bearable error bars. The supernova projects and CMBR anisotropy together favour a finite cosmological constant, and gravitational lens statistics support the same conclusion.

An Upper Limit on ΩmUsing Lensed Arcs

We use current observations on the number statistics of gravitationally lensed optical arcs toward galaxy clusters to derive an upper limit on the cosmological mass density of the universe. The gravitational lensing statistics from foreground clusters combine properties of both cluster evolution, which is sensitive to the matter density, and volume change, which is sensitive to the cosmological constant. The uncertainties associated with the predicted number of lensing events, however, currently do not allow one to distinguish between flat and open cosmological models with and without a cosmological constant. Still, after accounting for known errors, and assuming that clusters in general have dark matter core radii of the order ~35 h-1 kpc, we find that the cosmological mass density, Ωm, is less than 0.56 at the 95% confidence. Such a dark matter core radius is consistent with cluster potentials determined recently by detailed numerical inversions of strong and weak lensing imaging data. If no core radius is present, the upper limit on Ωmincreases to 0.62 (95% confidence level). The estimated upper limit on Ωm is consistent with various cosmological probes that suggest a low matter density for the universe.

New Limits on Ω[TINF]Λ[/TINF] and Ω[TINF][ITAL]M[/ITAL][/TINF] from Old Galaxies at High Redshift

The ages of two old galaxies (53W091, 53W069) at high redshifts are used to constrain the value of the cosmological constant in a flat universe (ΛCDM) and the density parameter ΩM in Friedmann-Robertson-Walker models with no Λ term. In the case of ΛCDM models, the quoted galaxies yield two lower limits for the vacuum energy density parameter, ΩΛ ≥ 0.42 and ΩΛ ≥ 0.5, respectively. Although compatible with the limits from statistics of gravitational lensing and cosmic microwave background, these lower bounds are more stringent than the ones recently determined using Type Ia supernovae as standard candles. For matter-dominated universes (ΩΛ = 0), the existence of these galaxies imply that the universe is open with the matter density parameter constrained by ΩM ≤ 0.45 and ΩM ≤ 0.37, respectively. In particular, these results disagree completely with the analysis of field galaxies, which gives a lower limit ΩM ≥ 0.40.

Gravitational lensing statistics with extragalactic surveys

Gravitational lensing statistics with extragalactic surveys

Gravitational lensing statistics with extragalactic surveys. I. A lower limit on the cosmological constant

Gravitational lensing statistics with extragalactic surveys. I. A lower limit on the cosmological constant

Gravitational Lensing as a Probe of Quintessence

A large number of cosmological studies now suggest that roughly two-thirds of the critical energy density of the Universe exists in a component with negative pressure. If the equation of state of such an energy component varies with time, it should in principle be possible to identify such a variation using cosmological probes over a wide range in redshift. Proper detection of any time variation, however, requires cosmological probes beyond the currently studied range in redshift of $\sim$ 0.1 to 1. We extend our analysis to gravitational lensing statistics at high redshift and suggest that a reliable sample of lensed sources, out to a redshift of $\sim$ 5, can be used to constrain the variation of the equation of state, provided that both the redshift distribution of lensed sources and the selection function involved with the lensed source discovery process are known. An exciting opportunity to catalog an adequate sample of lensed sources (quasars) to probe quintessence is now available with the ongoing Sloan Digital Sky Survey. Writing $w(z)\approx w_0 + z (dw/dz)_0$, we study the expected accuracy to which the equation of state today $w_0$ and its rate of change $(dw/dz)_0$ can simultaneously be constrained. Such a determination can rule out some missing-energy candidates, such as classes of quintessence models or a cosmological constant.

New Limits on a Cosmological Constant from Statistics of Gravitational Lensing

We present new limits on cosmological parameters from the statistics of gravitational lensing, based on the recently revised knowledge of the luminosity function and internal dynamics of E/S0 galaxies that are essential in lensing high-redshift QSOs. We find that the lens models using updated Schechter parameters for such galaxies, derived from the recent redshift surveys combined with morphological classification, are found to give smaller lensing probabilities than were calculated earlier. Inconsistent adoption of these parameters from a mixture of various galaxy surveys gives rise to systematic biases in the results. We also show that less compact dwarf-type galaxies that largely dominate the faint part of the Schechter form luminosity function contribute little to lensing probabilities, so that earlier lens models overestimate incidents of small separation lenses. Applications of the lens models to the existing lens surveys indicate that reproduction of both the lensing probability of optical sources and the image separations of optical and radio lenses is significantly improved in the revised lens models. The likelihood analyses allow us to conclude that a flat universe with ?0=0.3 and ?0+?0=1 is preferable, and a matter-dominated flat universe with ?0=0 is ruled out at the 98% confidence level. These new limits are unaffected by the inclusion of uncertainties in the lens properties.

Do Lensing Statistics Rule out a Cosmological Constant?

We present new calculations of the gravitational lensing statistics following recent revised knowledge of the luminosity function and internal velocity dispersion of E/S0 galaxies which work as effective lenses for background high-redshift QSOs. We show that the theoretical prediction of the lensing statistics is much smaller than previously expected. In sharp contrast with the earlier statistics supporting an Ω0 = 1 universe, the reported small lensing probability from the Hubble Space Telescope (HST) snapshot lens survey is in best agreement with a low-density, flat universe with Ω0 ≃ 0.2 and Ω0 + λ0 = 1. The age of this universe, combined with the HST measurement of a high value of the Hubble constant H0, can be reconciled with the age of the oldest globular clusters in the Milky Way (ApJ, 1997, Vol. 489, in press).

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation of state of x-matter which can express a wide range of matter from pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component, in addition to the equation of state w0 = px0/ρx0. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.

Do Lensing Statistics Rule Out a Cosmological Constant?

We present new calculations of gravitational lensing statistics in view of recent revisions in our knowledge of the luminosity function and internal velocity dispersion of E/S0 galaxies that work as effective lenses for background high-redshift QSOs. We show that the theoretical prediction of the lensing statistics is much smaller than previously expected. In sharp contrast to earlier statistics supporting an Ω0 = 1 universe, the small lensing probability reported from the Hubble Space Telescope (HST) Snapshot Lens Survey is in best agreement with a low-density, flat universe with Ω0 0.2 and Ω0 + λ0 = 1. The age of this universe, combined with the HST measurement of a high value for the Hubble constant H0, can be reconciled with the age of the oldest globular clusters in the Milky Way.

Curvature of the Universe and Observed Gravitational Lens Image Separations versus Redshift

In a flat, k = 0, cosmology with galaxies that approximate singular isothermal spheres, gravitational lens image separations should be uncorrelated with source redshift. But in an open, k = -1, cosmology, such gravitational lens image separations become smaller with increasing source redshift. The observed separations do become smaller with increasing source redshift, but the effect is even stronger than that expected in an Ω = 0 cosmology. The observations are thus not compatible with the standard gravitational lensing statistics model in a flat universe. We try various open and flat cosmologies, galaxy mass profiles, galaxy merging and evolution models, and lensing aided by clusters to explain the correlation. We find the data are not compatible with any of these possibilities within the 95% confidence limit, leaving us with a puzzle. If we regard the observed result as a statistical fluke, it is worth noting that we are about twice as likely to observe it in an open universe (with 0 -2.0.

Strong Gravitational Lensing and Velocity Function as Tools to Probe Cosmological Parameters: Current Constraints and Future Predictions

Constraints on cosmological models from strong gravitational lensing statistics are investigated. We pay particular attention to the role of the velocity function in the calculation of the lensing probability. The velocity function derived from the observed galaxy luminosity function, which is used in most previous work, is unable to predict the large separation lensing events. In this paper, we also use the Press-Schechter theory to construct a velocity function theoretically. Model predictions are compared with the observed velocity function and the HST snapshot survey. Comparison with the latter observation shows that the predictions based on the theoretical velocity function are consistent with the observed large separation events in COBE normalized low-density models, especially with a non-vanishing cosmological constant. Adopting the COBE normalization, however, we could find no model which simultaneously satisfies both the observed velocity function and the HST snapshot survey. We systematically investigate various uncertainties in the gravitational lensing statistics including finite core radius, the distance formula, magnification bias, and dust obscuration. The results are very sensitive to these effects as well as theoretical models for the velocity function, implying that current limits on the cosmological parameters should be interpreted with caution. Predictions for future surveys are also presented.

Cosmology with ultralight pseudo Nambu-Goldstone bosons.

We explore the cosmological implications of an ultra-light pseudo-Nambu-Goldstone boson. With global spontaneous symmetry breaking scale $f \simeq 10^{18}$ GeV and explicit breaking scale comparable to MSW neutrino masses, $M \sim 10^{-3}$ eV, such a field, which acquires a mass $m_\phi \sim M^2/f \sim H_0$, would have become dynamical at recent epochs and currently dominate the energy density of the universe. The field acts as an effective cosmological constant for several expansion times and then relaxes into a condensate of coherent non-relativistic bosons. Such a model can reconcile dynamical estimates of the density parameter, $\Omega_m \sim 0.2$, with a spatially flat universe, and can yield an expansion age $H_0 t_0 \simeq 1$ while remaining consistent with limits from gravitational lens statistics.

Cosmological Parameters and Gravitational Lensing Statistics

Annals of the New York Academy of SciencesVolume 759, Issue 1 p. 600-603 Cosmological Parameters and Gravitational Lensing Statistics PHILLIP HELBIG, PHILLIP HELBIG Hamburger Sternwarte · Gojenbergsweg 112 D-21029 Hamburg · GermanySearch for more papers by this author PHILLIP HELBIG, PHILLIP HELBIG Hamburger Sternwarte · Gojenbergsweg 112 D-21029 Hamburg · GermanySearch for more papers by this author First published: September 1995 https://doi.org/10.1111/j.1749-6632.1995.tb17617.xAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volume759, Issue1Seventeenth Texas Symposium on Relativistic Astrophysics and CosmologySeptember 1995Pages 600-603 RelatedInformation

Evidence for dark matter in MG 1654+134

view Abstract Citations (141) References (43) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Evidence for Dark Matter in MG 1654+134 Kochanek, Christopher S. Abstract The radio ring lens MG 1654+134 strongly constrains the structure and mass of the 19 mag lens galaxy at its center. The best-fit effective radius for a de Vaucouleurs model of the lens galaxy is R_e_ = 2.0" (1.5" < R_e_ < 3.0") marginally consistent with fits to the observed lens galaxy. The B band mass-to-light ratio interior to the ring that the galaxy would have today is (M/L)_B_ = (20.4 +/- 2.8)(f_e_/1.4)h, where a passively evolving early type galaxy fades by a factor of f_e_~ 1.4 between the lens redshift and the present. This (M/L)_B_ is inconsistent with stellar dynamical models of nearby ellipticals, but it is consistent with estimates from the statistics of gravitational lens numbers and separations. Isothermal models fit the ring with a halo velocity dispersion of σ_DM_ = (216+/-2) km s^-1^, consistent with the fundamental plane, the stellar dynamics of ellipticals in dark matter halos [predicted dispersion (212+/-12)(f_e_/14)^0.29^ km s^-1^], and the statistics of gravitational lenses. This strongly supports the conclusion from lens statistics that early type galaxies do not have constant mass- to-light ratios even on scales comparable to the effective radius. Density distributions with ρ is proportional to (r^2^ +s^2^)^(α - 3)/2^ fit the data only in the restricted range 0.9 <~ α <~ 1.1 where α = 1 is an isothermal model. Centrally concentrated models such as the Plummer or modified Hubble models require large, finite core radii (800 h^-1^ and 600 h^-1^ pc, respectively) but fail to fit the structure of the ring. Isothermal models only have upper limits of order 100 h^-1^ pc on the core radius. The major axis of the mass distribution is 7^deg^ + 10^deg^ from the major axis of the luminosity distribution. The models clearly distinguish between different angular structures for the lens model, and a quadrupole expansion of an ellipsoidal density distribution fits the data better than a similar monopole in an external shear. Publication: The Astrophysical Journal Pub Date: June 1995 DOI: 10.1086/175721 Bibcode: 1995ApJ...445..559K Keywords: Astronomical Models; Dark Matter; Galactic Structure; Gravitational Lenses; Kinematics; Density Distribution; Luminosity; Mass Distribution; Mass To Light Ratios; Red Shift; Astrophysics; COSMOLOGY: GRAVITATIONAL LENSING; GALAXIES: STRUCTURE; GALAXIES: KINEMATICS AND DYNAMICS full text sources ADS | data products SIMBAD (4) NED (1)