Search

We present seven epochs of spectroscopy on the quadruply imaged quasar SDSS J1004+4112, spanning observed-frame time delays from 1 to 322 days. The spectra reveal differences in the emission lines between the lensed images. Specifically, component A showed a strong enhancement in the blue wings of several high-ionization lines relative to component B, which lasted at least 28 days (observed frame) then faded. Since the predicted time delay between A and B is <30 days, our time coverage suggests that the event was not intrinsic to the quasar. We attribute these variations to microlensing of part of the broad emission line region of the quasar, apparently resolving structure in the source plane on a scale of ~10^{16} cm at z=1.734. In addition, we observed smaller differences in the emission line profiles between components A and B that persisted throughout the time span, which may also be due to microlensing or millilensing. Further spectroscopic monitoring of this system holds considerable promise for resolving the structure of the broad emission line region in quasars., Comment: 20 pages, 4 figures (2 color), 1 table, submitted to ApJ

The time dependence of the dark energy density can be an important clue to the nature of dark energy in the universe. We show that future supernova data from dedicated telescopes (such as SNAP), when combined with data of nearby supernovae, can be used to determine how the dark energy density $\rho_X(z)$ depends on redshift, if $\rho_X(z)$ is not too close to a constant. For quantitative comparison, we have done an extensive study of a number of dark energy models. Based on these models we have simulated data sets in order to show that we can indeed reconstruct the correct sign of the time dependence of the dark energy density, outside of a degeneracy region centered on $1+w_0 = -w_1 z_{max}/3$ (where $z_{max}$ is the maximum redshift of the survey, e.g., $z_{max}=1.7$ for SNAP). We emphasize that, given the same data, one can obtain much more information about the dark energy density directly (and its time dependence) than about its equation of state., Comment: submitted to PRD

We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass tracer is chosen to be the number of member galaxies assigned to a cluster. Such a survey can strongly constrain $\sigma_8$ ($\Delta\sigma_8\approx 0.05$), the power law index $\alpha$ where $= 1+(m/M_1)^\alpha$ ($\Delta\alpha\approx0.03$), and perhaps even the Hubble parameter ($\Delta h\approx 0.07$). We find cluster abundances and bias not well suited for constraining $\Omega_m$ or the amplitude $M_1$. We also find that without bias information $\sigma_8$ and $\alpha$ are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass tracer used in the survey., Comment: 27 pages, 11 figures, references added

We present estimates of cosmological parameters from the application of the Karhunen-Loeve transform to the analysis of the 3D power spectrum of density fluctuations using Sloan Digital Sky Survey galaxy redshifts. We use Omega_m*h and f_b = Omega_b/Omega_m to describe the shape of the power spectrum, sigma8 for the (linearly extrapolated) normalization, and beta to parametrize linear theory redshift space distortions. On scales k < 0.16 h/Mpc, our maximum likelihood values are Omega_m*h = 0.264 +/-0.043, f_b = 0.286 +/- 0.065, sigma8 = 0.966 +/- 0.048, and beta = 0.45 +/- 0.12. When we take a prior on Omega_b from WMAP, we find Omega_m*h = 0.207 +/- 0.030, which is in excellent agreement with WMAP and 2dF. This indicates that we have reasonably measured the gross shape of the power spectrum but we have difficulty breaking the degeneracy between Omega_m*h and f_b because the baryon oscillations are not resolved in the current spectroscopic survey window function., Comment: LaTeX, 8 pages, 3 figures; figures updated, references added, minor changes to text; accepted by ApJ

We report the discovery of SDSSJ115517.35+634622.0, a previously unknown gravitationally lensed quasar. The lens system exhibits two images of a $z = 2.89$ quasar, with an image separation of $1{\farcs}832 \pm 0.007$ . Near-IR imaging of the system reveals the presence of the lensing galaxy between the two quasar images. Based on absorption features seen in the Sloan Digital Sky Survey (SDSS) spectrum, we determine a lens galaxy redshift of $z = 0.1756$. The lens is rather unusual in that one of the quasar images is only $0{\farcs}22\pm0{\farcs}07$ ($\sim 0.1 R_{\rm eff}$) from the center of the lens galaxy and photometric modeling indicates that this image is significantly brighter than predicted by a SIS model. This system was discovered in the course of an ongoing search for strongly lensed quasars in the dataset from the SDSS., Comment: 18 pages, 6 figures. Accepted for publication in AJ

We report the discovery of the two-image gravitationally lensed quasar SDSS J1335+0118. The object was selected as a lens candidate from the Sloan Digital Sky Survey. The imaging and spectroscopic follow-up observations confirm that the system exhibits two gravitationally lensed images of a quasar at z=1.57. The image separation is 1.56''. We also detect an extended component between the two quasar images, likely the lensing galaxy. Preliminary mass modeling predicts the differential time delay \Delta t ~ 30 h^{-1} day assuming the redshift of the lens galaxy is 0.5., Comment: 6 pages, 4 figures, accepted for publication in PASJ

We report the discovery of a new gravitationally lensed quasar from the Sloan Digital Sky Survey, SDSS J090334.92+502819.2. This object was targeted for SDSS spectroscopy as a Luminous Red Galaxy (LRG), but manual examination of the spectrum showed the presence of a quasar at z= 3.6 in addition to a red galaxy at z=0.388, and the SDSS image showed a second possible quasar image nearby. Follow-up imaging and spectroscopy confirmed the lensing hypothesis. In images taken at the ARC 3.5-meter telescope, two quasars are separated by 2.8 arc-seconds; the lensing galaxy is clearly seen and is blended with one of the quasar images. Spectroscopy taken at the Keck II telescope shows that the quasars have identical redshifts of z=3.6 and both show the presence of the same broad absorption line-like troughs. We present simple lens models which account for the geometry and magnifications. The lens galaxy lies near two groups of galaxies and may be a part of them. The models suggest that the groups may contribute considerable shear and may have a strong effect on the lens configuration., Comment: submitted to the Astronomical Journal. 27 pages, 7 figures

Understanding the clustering of galaxies has long been a goal of modern observational cosmology. Utilizing our photometric redshift technique a volume limited sample containing more than 2 million galaxies is constructed from the SDSS galaxy catalog. In the largest such analysis to date, we study the angular clustering as a function of luminosity and spectral type. Using Limber's equation we calculate the clustering length for the full data set as r0=5.77+/-0.10 Mpc/h. We find that r0 increases with luminosity by a factor of 1.6 over the sampled luminosity range, in agreement with previous redshift surveys. We also find that both the clustering length and the slope of the correlation function depend on the galaxy type. In particular, by splitting the galaxies in four groups by their rest-frame type we find a bimodal behavior in their clustering properties. Galaxies with spectral types similar to elliptical galaxies have a correlation length of 6.59 +/- 0.17 Mpc/h and a slope of the angular correlation function of 0.96 +/- 0.05 while blue galaxies have a clustering length of 4.51 +/- 0.19 Mpc/h and a slope of 0.68 +/- 0.09. The two intermediate color groups behave like their more extreme 'siblings', rather than showing a gradual transition in slope. We discuss these correlations in the context of current cosmological models for structure formation., Comment: 11 pages, 12 figures, accepted for publication in Astrophys. J., high resolution version of the paper available at http://www.sdss.jhu.edu/~budavari/papers/astroph-0305603.ps

We report the discovery of a new gravitationally lensed quasar from the Sloan Digital Sky Survey, SDSS J092455.87+021924.9 (SDSS J0924+0219). This object was selected from among known SDSS quasars by an algorithm that was designed to select another known SDSS lensed quasar (SDSS 1226-0006A,B). Five separate components, three of which are unresolved, are identified in photometric follow-up observations obtained with the Magellan Consortium's 6.5m Walter Baade telescope at Las Campanas Observatory. Two of the unresolved components (designated A and B) are confirmed to be quasars with z=1.524; the velocity difference is less than 100 km sec^{-1} according to spectra taken with the W. M. Keck Observatory's Keck II telescope on Mauna Kea. A third stellar component, designated C, has the colors of a quasar with redshift similar to components A and B. The maximum separation of the point sources is 1.78". The other two sources, designated G and D, are resolved. Component G appears to be the best candidate for the lensing galaxy. Although component D is near the expected position of the fourth lensed component in a four image lens system, its properties are not consistent with being the image of a quasar at z~1.5. Nevertheless, the identical redshifts of components A and B and the presence of component C strongly suggest that this object is a gravitational lens. Our observations support the idea that a foreground object reddens the fourth lensed component and that another unmodeled effect (such as micro- or milli-lensing) demagnificates it, but we cannot rule out the possibility that SDSS0924+0219 is an example of the relatively rare class of ``three component'' lens systems., Comment: 24 pages, 6 figures, accepted by AJ

We measure the projected correlation function w_p(r_p) from the Sloan Digital Sky Survey for a flux-limited sample of 118,000 galaxies and for a volume limited subset of 22,000 galaxies with absolute magnitude M_r<-21. Both correlation functions show subtle but systematic departures from the best-fit power law, in particular a change in slope at r_p~1-2 Mpc/h. These departures are stronger for the volume-limited sample, which is restricted to relatively luminous galaxies. We show that the inflection point in w_p(r_p) can be naturally explained by contemporary models of galaxy clustering, according to which it marks the transition from a large scale regime dominated by galaxy pairs in separate dark matter halos to a small scale regime dominated by galaxy pairs in the same dark matter halo. For example, given the dark halo population predicted by an inflationary cold dark matter scenario, the projected correlation function of the volume-limited sample can be well reproduced by a model in which the mean number of M_r<-21 galaxies in a halo of mass M>M_1=4.74 X 10^{13}\msun/h is _M=(M/M_1)^{0.89}, with 75% of the galaxies residing in less massive, single-galaxy halos. This physically motivated model has the same number of free parameters as a power law, and it fits the w_p(r_p) data better, with a \chi^2/d.o.f.=0.93 compared to 6.12 (for 10 degrees of freedom, incorporating the covariance of the correlation function errors). Departures from a power-law correlation function encode information about the relation between galaxies and dark matter halos. Higher precision measurements of these departures for multiple classes of galaxies will constrain galaxy bias and provide new tests of the theory of galaxy formation., Comment: 23 pages, 5 figures. Minor changes to match accepted ApJ version

A primary goal for cosmology and particle physics over the coming decade will be to unravel the nature of the dark energy that drives the accelerated expansion of the Universe. In particular, determination of the equation-of-state of dark energy, w equivalent p/rho, and its time variation, dw/dz, will be critical for developing theoretical understanding of the new physics behind this phenomenon. Type Ia supernovae (SNe) and cosmic microwave background (CMB) anisotropy are each sensitive to the dark energy equation-of-state. SNe alone can determine w(z) with some precision, while CMB anisotropy alone cannot because of a strong degeneracy between the matter density Omega_M and w. However, we show that the Planck CMB mission can significantly improve the power of a deep SNe survey to probe w and especially dw/dz. Because CMB constraints are nearly orthogonal to SNe constraints in the Omega_M-w plane, for constraining w(z) Planck is more useful than precise determination of Omega_M. We discuss how the CMB/SNe complementarity impacts strategies for the redshift distribution of a supernova survey to determine w(z) and conclude that a well-designed sample should include a substantial number of supernovae out to redshifts z ~ 2., Comment: More discussion of CMB systematics and many new references added. Matches the PRD version

Weak lensing of high-redshift Type Ia supernovae induces an external dispersion in their observed standard candle brightnesses, comparable in magnitude to the intrinsic dispersion for redshifts z>1. The same matter fluctuations responsible for the magnification of distant supernovae also generate shear in the images of background galaxies. We investigate the possibility of using lensing shear maps constructed from galaxies surrounding the supernovae as a means of correcting the lensing-induced magnification dispersion. We find that a considerable fraction of the lensing dispersion derives from sub-arcminute scales, which are not probed by shear maps smoothed on arcminute scales. We thus find that weak lensing shear maps will be of only limited value in reducing the weak lensing magnification fluctuations of supernovae., Comment: aastex, 3 figures, 11 pages, submitted to ApJL

We describe the algorithm for selecting quasar candidates for optical spectroscopy in the Sloan Digital Sky Survey. Quasar candidates are selected via their non-stellar colors in "ugriz" broad-band photometry, and by matching unresolved sources to the FIRST radio catalogs. The automated algorithm is sensitive to quasars at all redshifts lower than z=5.8. Extended sources are also targeted as low-redshift quasar candidates in order to investigate the evolution of Active Galactic Nuclei (AGN) at the faint end of the luminosity function. Nearly 95% of previously known quasars are recovered (based on 1540 quasars in 446 square degrees). The overall completeness, estimated from simulated quasars, is expected to be over 90%, whereas the overall efficiency (quasars:quasar candidates) is better than 65%. The selection algorithm targets ultraviolet excess quasars to i^*=19.1 and higher-redshift (z>3) quasars to i^*=20.2, yielding approximately 18 candidates per square degree. In addition to selecting ``normal'' quasars, the design of the algorithm makes it sensitive to atypical AGN such as Broad Absorption Line quasars and heavily reddened quasars., Comment: 62 pages, 15 figures (8 color), 8 tables. Accepted by AJ. For a version with higher quality color figures, see http://archive.stsci.edu/sdss/quasartarget/RichardsGT_qsotarget.preprint.ps

This is the report of the {\em Working Group on Early Universe Cosmology and Tests of Fundamental Physics}, group P4.8 of the of the Snowmass 2001 conference. Here we summarize the impressive array of advances that have taken place in this field, and identify opportunities for even greater progress in the future. Topics include Dark Energy, Cosmic Acceleration, Inflation, Phase Transitions, Baryogenesis, and String/M-theory Cosmology. The introductory section gives an executive summary with six key open questions on which we can expect to make significant progress., Comment: 42 pages, 1 figure, uses RevTeX and BibTeX. Version 2 contains updated bibliography and one very minor text change

We present initial results for counts in cells statistics of the angular distribution of galaxies in early data from the Sloan Digital Sky Survey (SDSS). We analyze a rectangular stripe $2.5^\circ$ wide, covering approximately 160 sq. degrees, containing over $10^6$ galaxies in the apparent magnitude range $18 < r^\prime < 22$, with areas of bad seeing, contamination from bright stars, ghosts, and high galactic extinction masked out. This survey region, which forms part of the SDSS Early Data Release, is the same as that for which two-point angular clustering statistics have recently been computed. The third and fourth moments of the cell counts, $s_3$ (skewness) and $s_4$ (kurtosis), constitute the most accurate measurements to date of these quantities (for $r^\prime < 21$) over angular scales $0.015^\circ-0.3^\circ$. They display the approximate hierarchical scaling expected from non-linear structure formation models and are in reasonable agreement with the predictions of $\Lambda$-dominated cold dark matter models with galaxy biasing that suppresses higher order correlations at small scales. The results are in general consistent with previous measurements in the APM, EDSGC, and Deeprange surveys. These results suggest that the SDSS imaging data are free of systematics to a high degree and will therefore enable determination of the skewness and kurtosis to 1% and less then 10%, as predicted by Colombi, Szapudi, & Szalay (1998)., Comment: 24 pages, submitted to ApJ

We present new measurements of scaling laws relating the luminosity of galaxies to the amplitude and shape of their dark matter halos. Early imaging and spectroscopic data from the Sloan Digital Sky Survey are used to make weak lensing measurements of the surface mass density contrast Delta Sigma_+ around classes of lens objects. This surface mass density contrast as a function of radius is a measure of the galaxy-mass correlation function (GMCF). Because spectroscopic redshifts are available for all lens objects, the mass and distance scales are well constrained. The GMCF measured around ~31,000 lenses is well fit by a power law of the form Delta Sigma_+ = (2.5+0.7-0.6) (R/1 Mpc)^{-0.8+-0.2} h M_sun pc^-2. We compare this GMCF to galaxy luminosity, type, and environment, and find that it varies strongly with all three. We quantify these variations by comparing the normalization of a fit to the inner 260 h^-1 kpc, M_260, to the galaxy luminosity. While M_260 is not strongly related to luminosity in bluest band u', there is a simple, linear relation between M_260 and luminosity in redder bands (g', r', i', and z'). We test the universality of these mass-to-light scalings by independently measuring them for spiral and elliptical galaxies,and for galaxies in a variety of environments. We find remarkable consistency in these determinations in the red bands, especially i' and z'. This consistency across a wide range of systems suggests that the measured scaling represents an excellent cosmic average, and that the integrated star formation history of galaxies is strongly related to the dark matter environments in which they form., Comment: 38 pages, 22 figures, submitted to ApJ 6/14/01 For version with full resolution figures see: http://sdss4.physics.lsa.umich.edu:8080/~mckay/m2l_submitted_6_14_01.ps

The angular distribution of galaxies encodes a wealth of information about large scale structure. Ultimately, the Sloan Digital Sky Survey (SDSS) will record the angular positions of order 10^8 galaxies in five bands, adding significantly to the cosmological constraints. This is the first in a series of papers analyzing a rectangular stripe 2.5x90 degrees from early SDSS data. We present the angular correlation function for galaxies in four separate magnitude bins on angular scales ranging from 0.003 degrees to 15 degrees. Much of the focus of this paper is on potential systematic effects. We show that the final galaxy catalog -- with the mask accounting for regions of poor seeing, reddening, bright stars, etc. -- is free from external and internal systematic effects for galaxies brighter than r* = 22. Our estimator of the angular correlation function includes the effects of the integral constraint and the mask. The full covariance matrix of errors in these estimates is derived using mock catalogs with further estimates using a number of other methods., Comment: 64 pages, 31 figures, new version to match that accepted by ApJ

We compute the angular power spectrum C_l from 1.5 million galaxies in early SDSS data on large angular scales, l<600. The data set covers about 160 square degrees, with a characteristic depth of order 1 Gpc/h in the faintest (21

We present measurements of parameters of the 3-dimensional power spectrum of galaxy clustering from 222 square degrees of early imaging data in the Sloan Digital Sky Survey. The projected galaxy distribution on the sky is expanded over a set of Karhunen-Loeve eigenfunctions, which optimize the signal-to-noise ratio in our analysis. A maximum likelihood analysis is used to estimate parameters that set the shape and amplitude of the 3-dimensional power spectrum. Our best estimates are Gamma=0.188 +/- 0.04 and sigma_8L = 0.915 +/- 0.06 (statistical errors only), for a flat Universe with a cosmological constant. We demonstrate that our measurements contain signal from scales at or beyond the peak of the 3D power spectrum. We discuss how the results scale with systematic uncertainties, like the radial selection function. We find that the central values satisfy the analytically estimated scaling relation. We have also explored the effects of evolutionary corrections, various truncations of the KL basis, seeing, sample size and limiting magnitude. We find that the impact of most of these uncertainties stay within the 2-sigma uncertainties of our fiducial result., Comment: Fig 1 postscript problem corrected

The Sloan Digital Sky Survey is one of the first multicolor photometric and spectroscopic surveys designed to measure the statistical properties of galaxies within the local Universe. In this Letter we present some of the initial results on the angular 2-point correlation function measured from the early SDSS galaxy data. The form of the correlation function, over the magnitude interval 18

Early photometric data from the Sloan Digital Sky Survey (SDSS) contain angular positions for 1.5 million galaxies. In companion papers, the angular correlation function $w(\theta)$ and 2D power spectrum $C_l$ of these galaxies are presented. Here we invert Limber's equation to extract the 3D power spectrum from the angular results. We accomplish this using an estimate of $dn/dz$, the redshift distribution of galaxies in four different magnitude slices in the SDSS photometric catalog. The resulting 3D power spectrum estimates from $w(\theta)$ and $C_l$ agree with each other and with previous estimates over a range in wavenumbers $0.03 < k/{\rm h Mpc}^{-1} < 1$. The galaxies in the faintest magnitude bin ($21 < \rstar < 22$, which have median redshift $z_m=0.43$) are less clustered than the galaxies in the brightest magnitude bin ($18 < \rstar < 19$ with $z_m=0.17$), especially on scales where nonlinearities are important. The derived power spectrum agrees with that of Szalay et al. (2001) who go directly from the raw data to a parametric estimate of the power spectrum. The strongest constraints on the shape parameter $\Gamma$ come from the faintest galaxies (in the magnitude bin $21 < \rstar < 22$), from which we infer $\Gamma = 0.14^{+0.11}_{-0.06}$ (95% C.L.)., Comment: 25 pages, 19 figures

We present the first measurements of clustering in the Sloan Digital Sky Survey (SDSS) galaxy redshift survey. Our sample consists of 29,300 galaxies with redshifts 5,700 km/s < cz < 39,000 km/s, distributed in several long but narrow (2.5-5 degree) segments, covering 690 square degrees. For the full, flux-limited sample, the redshift-space correlation length is approximately 8 Mpc/h. The two-dimensional correlation function \xi(r_p,\pi) shows clear signatures of both the small-scale, ``fingers-of-God'' distortion caused by velocity dispersions in collapsed objects and the large-scale compression caused by coherent flows, though the latter cannot be measured with high precision in the present sample. The inferred real-space correlation function is well described by a power law, \xi(r)=(r/6.1+/-0.2 Mpc/h)^{-1.75+/-0.03}, for 0.1 Mpc/h < r < 16 Mpc/h. The galaxy pairwise velocity dispersion is \sigma_{12} ~ 600+/-100 km/s for projected separations 0.15 Mpc/h < r_p < 5 Mpc/h. When we divide the sample by color, the red galaxies exhibit a stronger and steeper real-space correlation function and a higher pairwise velocity dispersion than do the blue galaxies. The relative behavior of subsamples defined by high/low profile concentration or high/low surface brightness is qualitatively similar to that of the red/blue subsamples. Our most striking result is a clear measurement of scale-independent luminosity bias at r < 10 Mpc/h: subsamples with absolute magnitude ranges centered on M_*-1.5, M_*, and M_*+1.5 have real-space correlation functions that are parallel power laws of slope ~ -1.8 with correlation lengths of approximately 7.4 Mpc/h, 6.3 Mpc/h, and 4.7 Mpc/h, respectively., Comment: 51 pages, 18 figures. Replaced to match accepted ApJ version

We present a lensing study of 42 galaxy clusters imaged in Sloan Digital Sky Survey (SDSS) commissioning data. Cluster candidates are selected optically from SDSS imaging data and confirmed for this study by matching to X-ray sources found independently in the ROSAT all sky survey (RASS). Five color SDSS photometry is used to make accurate photometric redshift estimates that are used to rescale and combine the lensing measurements. The mean shear from these clusters is detected to 2 h-1 Mpc at the 7-sigma level, corresponding to a mass within that radius of 4.2 +/- 0.6 x 10^14 h-1 M_sun. The shear profile is well fit by a power law with index -0.9 +/- 0.3, consistent with that of an isothermal density profile. This paper demonstrates our ability to measure ensemble cluster masses from SDSS imaging data., Comment: 14 pages, 7 figures, Accepted for publication in ApJ

We compute the bispectrum for the \IRAS PSCz catalog and find that the galaxy distribution displays the characteristic signature of gravity. Assuming Gaussian initial conditions, we obtain galaxy biasing parameters $1/b_1=1.20^{+0.18}_{-0.19}$ and $b_2/b_1^2=-0.42\pm0.19$, with no sign of scale-dependent bias for $k\leq 0.3$ h/Mpc. These results impose stringent constraints on non-Gaussian initial conditions. For dimensional scaling models with $\chi^2_N$ statistics, we find N>49, which implies a constraint on primordial skewness $B_3<0.35$., Comment: 4 pages, 3 embedded figures, uses revtex style file, minor changes to reflect published version

We explore the implications of gravitationally lensed QSOs and high-redshift SNe Ia observations for spatially flat cosmological models in which a classically evolving scalar field currently dominates the energy density of the Universe. We consider two representative scalar field potentials that give rise to effective decaying $\Lambda $ (``quintessence'') models: pseudo-Nambu-Goldstone bosons ($V(\phi)=M^4(1+\cos (\phi /f)) $) and an inverse power-law potential ($V(\phi)=M^{4+\alpha}\phi ^{-\alpha}$). We show that a large region of parameter space is consistent with current data if $\Omega_{m0} > 0.15$. On the other hand, a higher lower bound for the matter density parameter suggested by large-scale galaxy flows, $\Omega_{m0} > 0.3$, considerably reduces the allowed parameter space, forcing the scalar field behavior to approach that of a cosmological constant., Comment: 6 pages, 2 figures, submitted to PRD

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 which limit in principle the detection of lensing by voids. We conclude that only voids with radii larger than $\sim 100$ \hm have lensing signal to noise larger than unity., Comment: 12 pages, 7 figures, uses mn-1_4.sty file, submitted to MNRAS

We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, $S_3$, starting from leading-order perturbation theory. When generalized to higher-order ($p>3$) polyspectra or correlation functions, this ansatz leads to a good description of non-linear amplitudes in the strongly non-linear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the non-linear evolution of the bispectrum that interpolates between the weakly and strongly non-linear regimes, analogous to previous expressions for the power spectrum., Comment: 20 pages, 6 figures. Final version accepted by ApJ. Includes new paragraphs on factorizable hierarchical models and agreement of HEPT with the excursion set model for white-noise Gaussian fluctuations

The bispectrum provides a characteristic signature of gravitational instability that can be used to probe the Gaussianity of the initial conditions and the bias of the galaxy distribution. We study how this signature is affected by redshift distortions using perturbation theory and high-resolution numerical simulations. We obtain perturbative results for the multipole expansion of the redshift-space bispectrum which provide a natural way to break the degeneracy between bias and $\Omega$ present in measurements of the redshift-space power spectrum. We propose a phenomenological model that incorporates the perturbative results and also describes the bispectrum in the transition to the non-linear regime. We stress the importance of non-linear effects and show that inaccurate treatment of these can lead to significant discrepancies in the determination of bias from galaxy redshift surveys. At small scales we find that the bispectrum monopole exhibits a strong configuration dependence that reflects the velocity dispersion of clusters. Therefore, the hierarchical model for the three-point function does not hold in redshift-space., Comment: 19 pages, 4 figures. Revised version accepted for publication in ApJ

Recent observations of high-redshift Type Ia supernovae have placed stringent constraints on the cosmological constant $\Lambda$. We explore the implications of these SNe observations for cosmological models in which a classically evolving scalar field currently dominates the energy density of the Universe. Such models have been shown to share the advantages of $\Lambda$ models: compatibility with the spatial flatness predicted inflation; a Universe older than the standard Einstein-de Sitter model; and, combined with cold dark matter, predictions for large-scale structure formation in good agreement with data from galaxy surveys. Compared to the cosmological constant, these scalar field models are consistent with the SNe observations for a lower matter density, $\Omega_{m0} \sim 0.2$, and a higher age, $H_0 t_0 \gtrsim 1$. Combined with the fact that scalar field models imprint a distinctive signature on the cosmic microwave background anisotropy, they remain currently viable and should be testable in the near future., Comment: RevTex style format, 14 pages, 11 eps figures included with epsf, submitted to Phys. Rev. D

The bispectrum, the three-point function of density fluctuations in Fourier space, is the lowest order statistic that carries information about the spatial coherence of large-scale structures. For Gaussian initial conditions, when the density fluctuation amplitude is small, tree-level (leading order) perturbation theory predicts a characteristic dependence of the bispectrum on the shape of the triangle formed by the three wave vectors. This configuration dependence provides a signature of gravitational instability, and departures from it in galaxy catalogs can be interpreted as due to bias, that is, non-gravitational effects. On the other hand, N-body simulations indicate that the reduced three-point function becomes relatively shape-independent in the strongly non-linear regime. In order to understand this non-linear transition and assess the domain of reliability of shape-dependence as a probe of bias, we calculate the one-loop (next-to-leading order) corrections to the bispectrum in perturbation theory. We compare these results with measurements in numerical simulations with scale-free and CDM initial power spectra. We find that the one-loop corrections account very well for the departures from the tree-level results measured in numerical simulations on weakly non-linear scales. In this regime, the reduced bispectrum qualitatively retains its tree-level shape, but the amplitude can change significantly. At smaller scales, the reduced bispectrum in the simulations starts to flatten, an effect which can be partially understood from the one-loop results. In the strong clustering regime, where perturbation theory breaks down entirely, the simulation results confirm that the reduced bispectrum has almost no dependence on triangle shape, in rough agreement with the hierarchical ansatz., Comment: 34 pages, 10 figures. Final version accepted in ApJ. Added discussion in the conclusions about present and future measurements of the bispectrum in galaxy surveys

On-going projects to discover Type Ia supernovae at redshifts z = 0.3 - 1, coupled with improved techniques to narrow the dispersion in SN Ia peak magnitudes, have renewed the prospects for determining the cosmic deceleration parameter q_0. We estimate the expected uncertainty in the Hubble diagram determination of q_0 due to weak lensing by structure in the universe, which stochastically shifts the apparent brightness of distant standard candles. Although the results are sensitive to the density power spectrum on small scales, the induced flux dispersion sigma_m < 0.04 Omega_{m,0}^{1/2} mag for sources at z \leq 0.5, well below the ``intrinsic" spread of nearby SN Ia magnitudes, sigma_M \simeq 0.2 mag. Thus, density inhomogeneities do not significantly impact the current program to measure q_0, in contrast to a recent claim. If, however, light-curve shape and other calibrators can reduce the effective intrinsic spread to 0.1 mag at high z, then weak lensing could increase the observed spread by 30% in an Omega_{m,0}=1 universe for SNe at z > 1., Comment: 14 pages LaTeX with 2 figures; earlier version (Mar. '96) accepted for publication in Comments on Astrophysics. Also available by WWW at http://www-astro-theory.fnal.gov/Publications/00Index.html

While the strategy for the first applications of weak lensing has been to ``go deep'' it is equally interesting to use one's telescope time to instead ``go wide''. The Sloan Survey (SDSS) provides a natural framework for a very wide area weak lensing survey., Comment: To appear in Proceedings of IAU Symposium 173. LaTeX using crckapb style (v1.0). PostScript and seperate figures available at ftp://ftp-astro-theory.fnal.gov/pub/Publications/Conf-95-320-A/

Using a diagrammatic approach to Eulerian perturbation theory, we analytically calculate the variance and skewness of the density and velocity divergence induced by gravitational evolution from Gaussian initial conditions, including corrections *beyond* leading order. Except for the power spectrum, previous calculations in cosmological perturbation theory have been confined to leading order (tree level)-we extend these to include loop corrections. For scale-free initial power spectra, the one-loop variance \sigma^2 = \sigma^2_l + 1.82 \sigma^4_l and the skewness S_3 = 34/7 + 9.8 \sigma^2_l, where \sigma_l is the rms fluctuation of the linear density field. We also compute loop corrections to the variance, skewness, and kurtosis for several non-linear approximation schemes, where the calculation can be easily generalized to 1-point cumulants of higher order and arbitrary number of loops. We find that the Zel'dovich approximation gives the best approximation to the loop corrections of exact perturbation theory, followed by the Linear Potential approximation (LPA) and the Frozen Flow approximation (FFA), in qualitative agreement with the relative behavior of tree-level results. In LPA and FFA, loop corrections are infrared divergent for spectral indices n < 0; this is related to the breaking of Galilean invariance in these schemes., Comment: 53 pages, uuencoded and gzipped postscript file, 20 figures, 25 tables, also available at http://fnas08.fnal.gov/cumu.uu

We analyse the effects of large-scale inhomogeneities upon the observables of a gravitational lens system, focusing on the issue of whether large-scale structure imperils the program to determine the Hubble parameter through measurements of time delays between multiple images in lens systems. We find that the lens equation in a spatially flat Robertson-Walker cosmology with scalar metric fluctuations is equivalent to that for the same lensing system in the absence of fluctuations, but with a different angular position of the source relative to the lens axis. Since the absolute position of the source is not observable, gravitational lens measurements cannot directly reveal the presence of large scale structure. Large-scale perturbations do not modify the functional relationship between observable lens parameters and the Hubble parameter, and therefore do not seriously affect the determination of $H_0$ from lens time delays., Comment: 11 pages, latex, 1 bezier figure included.

We study the prospects for the current microlensing searches, which have recently discovered several candidates, to yield useful information about the flattening of the Galaxy dark matter halo. Models of HI warps and N-body simulations of galaxy formation suggest that disks commonly form in oblate halos with a tilt between the disk and halo symmetry axes. The microlensing optical depth for the Large Magellanic Cloud depends sensitively on the disk-halo tilt angle in the Milky Way. We conclude that a much larger spread in values for $\tau(LMC)$ is consistent with rotation curve constraints than previously thought, and that the ratio $\tau(SMC)/\tau(LMC)$ of the optical depth to the Small and Large Magellanic clouds is not a clean test of halo flattening., Comment: 9 pages plain TeX, 4 figs. by FAX, Fermilab-Pub-93/391-A

We analyze the consequences of models of structure formation for higher-order ($n$-point) galaxy correlation functions in the mildly non-linear regime. Several variations of the standard $\Omega=1$ cold dark matter model with scale-invariant primordial perturbations have recently been introduced to obtain more power on large scales, 20 h$^{-1}$ Mpc, e.g., low-matter-density (non-zero cosmological constant) models, `tilted' primordial spectra, and scenarios with a mixture of cold and hot dark matter. They also include models with an effective scale-dependent bias, such as the cooperative galaxy formation scenario of Bower, etal. (1993). We show that higher-order galaxy correlation functions can provide a useful test of such models and can discriminate between models with true large-scale power in the density field and those where the galaxy power arises from scale-dependent bias: a bias with rapid scale-dependence leads to a dramatic decrease of the hierarchical amplitudes at large scales. Current observational constraints on the three-point amplitudes $Q_3$ and $S_3$ can place limits on the bias parameter(s) and appear to disfavor, but not yet rule out, the hypothesis that scale-dependent bias is responsible for the extra power observed on large scales., Comment: 20 pages (5 figues available on request), LaTeX, FERMILAB-Pub-93-140-A

Aside from primordial gravitational instability of the cosmological fluid, various mechanisms have been proposed to generate large-scale structure at relatively late times, including, e.g., ``late-time'' cosmological phase transitions. In these scenarios, it is envisioned that the universe is nearly homogeneous at the time of last scattering and that perturbations grow rapidly sometime after the primordial plasma recombines. On this basis, it was suggested that large inhomogeneities could be generated while leaving relatively little imprint on the cosmic microwave background (MBR) anisotropy. In this paper, we calculate the minimal anisotropies possible in any ``late-time'' scenario for structure formation, given the level of inhomogeneity observed at present. Since the growth of the inhomogeneity involves time-varying gravitational fields, these scenarios inevitably generate significant MBR anisotropy via the Sachs-Wolfe effect. Moreover, we show that the large-angle MBR anisotropy produced by the rapid post-recombination growth of inhomogeneity is generally greater than that produced by the same inhomogeneity grown via gravitational instability. In ``realistic'' scenarios one can decrease the anisotropy compared to models with primordial adiabatic fluctuations, but only on very small angular scales. The value of any particular measure of the anisotropy can be made small in late-time models, but only by making the time-dependence of the gravitational field sufficiently ``pathological''., Comment: Plain TeX, 25 pages, 6 Figures available on request

The cold dark matter (CDM) model of structure formation, normalized on large scales, leads to excessive pairwise velocity dispersions on small scales. In an attempt to circumvent this problem, we study three scenarios (all with $\Omega=1$) which have more large-scale power and less small-scale power than the CDM model: 1) an admixture of cold and hot dark matter; 2) cold dark matter with a non-scale-invariant, power-law primordial power spectrum; and 3) cold dark matter with coupling of dark matter to a long-range vector field. Despite the {reduced} small-scale power, when such models are evolved in the nonlinear regime to large amplitude, the velocities on small scales are actually {\it increased} over CDM with the same value of $\sigma_8$. This `flip-over', in disagreement with the expectation from linear perturbation theory, arises from the nonlinear coupling of the extra power on large scales with shorter wavelengths. However, due to the extra large-scale power, the recent COBE DMR results indicate smaller amplitudes for these models, $\sigma_8 \sim 0.5 - 0.7$, than for CDM (for which $\sigma_8 \sim 1.2$). Therefore, when normalized to COBE on large scales, such models do lead to reduced velocities on small scales and they produce fewer halos compared with CDM. Quantitatively it seems, however, that models that produce sufficiently low small-scale velocities fail to produce an adequate distribution of halos., Comment: 12 pages, Plain TeX, 3 figures included as postscript files. FERMILAB-Pub-92/217-A, UCLA/92/TEP/27

A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\phi) = \Lambda^4[1 \pm \cos(\phi/f)], naturally gives rise to inflation if $f \sim M_{Pl}$ and $\Lambda \sim M_{GUT}$. We show how this can arise in technicolor-like and superstring models, and work out an explicit string example in the context of multiple gaugino condensation models. We study the cosmology of this model in detail, and find that sufficient reheating to ensure that baryogenesis can take place requires $f > 0.3 M_{Pl}$. The primordial density fluctuation spectrum generated is a non-scale-invariant power law, $P(k) \propto k^{n_s}$, with $n_s \simeq 1 - (M^2_{Pl}/8\pi f^2)$, leading to more power on large length scales than the $n_s = 1$ Harrison-Zeldovich spectrum. The standard CDM model with $0 \la n_s \la 0.6-0.7$ could in principle explain the large-scale clustering observed in the APM and IRAS galaxy surveys as well as large-scale flows, but the COBE microwave anisotropy implies such low amplitudes (or high bias factors, $b>2$) for these CDM models that galaxy formation occurs too late to be viable; combining COBE with sufficiently early galaxy formation or the large-scale flows leads to $n_s >0.6$, or $f > 0.3 M_{Pl}$ as well. For extended and power law inflation models, this constraint is even tighter, $n_s > 0.7$; combined with other bounds on large bubbles in extended inflation, this leaves little room for most extended models., Comment: 42 pages, (12 figures not included but available from the authors)