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Cosmic flexion, like cosmic shear, is a correlation function whose signal originates from the large-scale structure of the universe. Building on the observational success of cosmic shear, along with the unprecedented quality of large-scale cosmological datasets, the time is ripe to explore the practical constraints from cosmic flexion. Unlike cosmic shear, which has a broad window function for power, cosmic flexion is only measurable on small scales and therefore can uniquely place constraints on the small-scale matter power spectrum. Here, we present a full theoretical formalism for cosmic flexion, including both flexion-flexion and shear-flexion two-point correlations. We present forecasts for measuring cosmic flexion in the Dark Energy Survey (DES), a Stage III cosmological survey, and comment on the future prospects of measuring these cosmological flexion signals in the upcoming era of Stage IV experiments., Comment: 21 pages, 9 figures; accepted for publication in Phys.Rev.D; revisions to Section IV. A and Appendix A, as well as other minor changes from submitted version

We calculate the Bayesian evidences for a class of Ekpyrotic universe models, and compare with a model of single field inflation with a Higgs-type potential. Combining parsimony and observational constraints, this gives us a systematic way to evaluate the degree to which Ekpyrotic models are constrained by CMB data from Planck. We integrate the equations of motion numerically to define a likelihood using Planck 2018 data and sample this likelihood to obtain Bayesian evidences. Priors are justified and used to put Ekpyrotic models and inflation on equal footing. We find reasonable preference for one of the considered Ekpyrotic models over the others, but that even this one is disfavored compared with Higgs inflation., Comment: 24 pages, 6 figures; Added references and corrected typos

We perform a flexion based weak gravitational analysis of the first two Hubble Frontier Field clusters: Abell 2744 and MACS 0416. A parametric method for using projected flexion signals as a probe of cluster member mass is described in detail. The normalization and slope of a $L-\theta_E$ (as a proxy for $L-\sigma$) scaling relation in each cluster is determined using measured flexion signals. A parallel field analysis is undertaken concurrently to provide a baseline measure of method effectiveness. We find an agreement in the Faber-Jackson slope $\ell$ associated with galaxy age and morphology for both clusters, as well as theoretical distinction in the cluster normalization mass.

Goldberg & Gott (2008) developed six error measures to rate flat map projections on their verisimilitude to the sphere: Isotropy, Area, Flexion, Skewness, Distances, and Boundary Cuts. The first two depend on the metric of the projection, the next two on its first derivatives. By these criteria, the Winkel Tripel (used by National Geographic for world maps) was the best scoring of all the known projections with a sum of squares of the six errors of 4.563, normalized relative to the Equirectangular in each error term. We present here a useful Gott-Wagner variant with a slightly better error score of only 4.497. We also present a radically new class of flat double-sided maps (like phonograph records) which have correct topology and vastly improved error scores: 0.881 for the azimuthal equidistant version. We believe it is the most accurate flat map of Earth yet. We also show maps of other solar system objects and sky maps.

Canonically, elliptical galaxies might be expected to have a perfect rotational symmetry, making them ideal targets for flexion studies - however, this assumption hasn't been tested. We have undertaken an analysis of low and high redshift galaxy catalogs of known morphological type with a new gravitational lensing code, Lenser. Using color measurements in the u-r band and fit Sersic index values, objects with characteristics consistent with early-type galaxies are found to have a lower intrinsic scatter in flexion signal than late-type galaxies. We find this measured flexion noise can be reduced by more than a factor of two at both low and high redshift., Comment: 7 pages, 13 figures, submitted to MNRAS

We present the first flexion-focused gravitational lensing analysis of the first of the strong-lensing "cosmic telescope" galaxy clusters, observed as part of the Hubble Frontier Fields initiative. Using HST observations of Abell 2744 (z = 0.308), we apply a modified Analytic Image Model (AIM) technique to measure source galaxy flexion and shear values at a final number density of 82 arcmin$^{-2}$. By using flexion data alone we are able to identify the primary mass structure aligned along the heart of the cluster in addition to a major substructure peak offset 1.43' from the cluster core. We generate two types of nonparametric reconstructions: a flexion aperture mass map, which identifies the central potential and substructure peak with mass signal-to-noise of 3.5$\sigma$ and 2.3$\sigma$ respectively; and a convergence map derived directly from the smoothed flexion field. For the primary peak we find a mass of $1.93\times10^{14}\,h^{-1}\,M_{\odot}$ within a 45" (145h$^{-1}$ kpc) aperture, and for the western substructure we find a mass of $7.12\times10^{13}\,h^{-1}\,M_{\odot}$ within a 25" (80h$^{-1}$ kpc) aperture. The associated peak velocity dispersions were determined to be $\sigma_v$ = 1630 km/s and $\sigma_v$ = 766 km/s, respectively, by fitting nonsingular isothermal sphere profiles to the flexion data. Additionally, we use simultaneous shear measurements to independently reconstruct the broader cluster mass structure, and find that it is unable to reproduce the small-scale structure associated with the flexion reconstructions. Finally, we perform the same analysis on the Abell 2744 parallel sky field, and find no strong phantom signals in the noise reconstructions., Comment: 12 pages, 5 figures. Submitted to MNRAS

Scaling relations of clusters have made them particularly important cosmological probes of structure formation. In this work, we present a comprehensive study of the relation between two profile observables, concentration ($\mathrm{c_{vir}}$) and mass ($\mathrm{M_{vir}}$). We have collected the largest known sample of measurements from the literature which make use of one or more of the following reconstruction techniques: Weak gravitational lensing (WL), strong gravitational lensing (SL), Weak+Strong Lensing (WL+SL), the Caustic Method (CM), Line-of-sight Velocity Dispersion (LOSVD), and X-ray. We find that the concentration-mass (c-M) relation is highly variable depending upon the reconstruction technique used. We also find concentrations derived from dark matter only simulations (at approximately $\mathrm{M_{vir} \sim 10^{14} M_{\odot}}$) to be inconsistent with the WL and WL+SL relations at the $\mathrm{1\sigma}$ level, even after the projection of triaxial halos is taken into account. However, to fully determine consistency between simulations and observations, a volume-limited sample of clusters is required, as selection effects become increasingly more important in answering this. Interestingly, we also find evidence for a steeper WL+SL relation as compared to WL alone, a result which could perhaps be caused by the varying shape of cluster isodensities, though most likely reflects differences in selection effects caused by these two techniques. Lastly, we compare concentration and mass measurements of individual clusters made using more than one technique, highlighting the magnitude of the potential bias which could exist in such observational samples., Comment: 34 pages, 7 figures, 4 tables

We report a mass reconstruction of A1689 using Particle Based Lensing (PBL), a new technique for Strong+Weak lensing that allows a variable resolution depending on the data density and the signal-to-noise. Using PBL we also calculate the covariance matrix for the resulting mass map. The reconstruction of A1689 shows a secondary mass peak in the north-east direction confirming previous optical observations. This indicates that the central region of the cluster is still undergoing a weak merger. We have used this mass map to measure power ratios of the dark matter distribution and compared it to the X-ray distribution. We find that the power in the X-ray distribution is lower suggesting a smoother and rounder gas distribution compared to the dark matter distribution. We fitted an NFW profile to the profile derived from the mass map and we find that the lensing mass within 1 Mpc is $1.5\pm0.33\times 10^{15}M_\odot$. This is higher than the X-ray mass., Comment: submitted to APJ. 21 pages, 6 figures

In a recent publication, the flexion aperture mass statistic was found to provide a robust and effective method by which substructure in galaxy clusters might be mapped. Moreover, we suggested that the masses and mass profile of structures might be constrained using this method. In this paper, we apply the flexion aperture mass technique to HST ACS images of Abell 1689. We demonstrate that the flexion aperture mass statistic is sensitive to small-scale structures in the central region of the cluster. While the central potential is not constrained by our method, due largely to missing data in the central 0.5$^\prime$ of the cluster, we are able to place constraints on the masses and mass profiles of prominent substructures. We identify 4 separate mass peaks, and use the peak aperture mass signal and zero signal radius in each case to constrain the masses and mass profiles of these substructures. The three most massive peaks exhibit complex small-scale structure, and the masses indicated by the flexion aperture mass statistic suggest that these three peaks represent the dominant substructure component of the cluster ($\sim 7\times 10^{14}h^{-1}M_\odot$). Their complex structure indicates that the cluster -- far from being relaxed -- may have recently undergone a merger. The smaller, subsidiary peak is located coincident with a group of galaxies within the cluster, with mass $\sim 1\times10^{14}h^{-1}M_\odot$. These results are in excellent agreement with previous substructure studies of this cluster., Comment: 18 pages, 10 figures, MNRAS accepted (7 Dec 2010)

Using a high resolution radio image, we successfully resolve the two fold image components B and C of the quasar lens system SDSS J1029+2623. The flux anomalies associated with these two components in the optical regime persist, albeit less strongly, in our radio observations, suggesting that the cluster must be modeled by something more than a single central potential. We argue that placing substructure close to one of the components can account for a flux anomaly with negligible changes in the component positions. Our best fit model has a substructure mass of ~10^8 solar masses up to the mass-sheet degeneracy, located roughly 0.1 arcsecs West and 0.1 arcsecs North of component B. We demonstrate that a positional offset between the centers of the source components can explain the differences between the optical and radio flux ratios., Comment: 5 pages, 3 figures, 2 tables, accepted to ApJ Letters

We present a non-parametric measure of the ellipticity and the alignment of the dark matter halos in Abell 901/902 supercluster. This super-cluster is a system of four separate peaks in a $0.5^{\circ}\times0.5^{\circ}$ field of view. We map the mass distribution of each individual peak using an improved version of Particle Based Lensing (PBL) and measure the ellipticity of the dark matter halos associated with two of the peaks directly from the mass map and by fitting them to a singular isothermal ellipse. The parametric and non-parametric measurements are consistent for A901b while the position angle for the Southwest Group is different for the two techniques. We account for this discrepancy to substructure present in the Southwest Peak. We estimate an axis ratio of $0.37\pm 0.1$ for A901b and $0.54^{+0.08}_{-0.09}$ for the Southwest Group., Comment: submitted to APJ, 25 pages, 13 figures

We develop a new approach for studying flux anomalies in quadruply-imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly constrained using only geometric arguments. We apply this technique to 11 known quadruple lens systems in the radio and infrared, and compare our estimates to the Monte Carlo based results of Keeton, Gaudi, and Petters. We show that a robust estimate for a flux ratio from a smoothly varying potential can be found, and at long wavelengths those lenses deviating from from this ratio almost certainly contain significant substructure., Comment: 16 pages, including 8 figures

The advent of affordable parallel computers such as Beowulf PC clusters and, more recently, of multi-core PCs has been highly beneficial for a large number of scientists and smaller institutions that might not otherwise have access to substantial computing facilities. However, there has not been an analogous progress in the development and dissemination of parallel software: scientists need the expertise to develop parallel codes and have to invest a significant amount of time in the development of tools even for the most common data analysis tasks. We describe the Beowulf Analysis Symbolic INterface (BASIN) a multi-user parallel data analysis and visualization framework. BASIN is aimed at providing scientists with a suite of parallel libraries for astrophysical data analysis along with general tools for data distribution and parallel operations on distributed data to allow them to easily develop new parallel libraries for their specific tasks., Comment: 12 pages, 3 figures, Submitted to Computing in Science and Engineering-special issue on Computational Astrophysics

We present Particle-Based Lensing (PBL), a new technique for gravitational lensing mass reconstructions of galaxy clusters. Traditionally, most methods have employed either a finite inversion or gridding to turn observational lensed galaxy ellipticities into an estimate of the surface mass density of a galaxy cluster. We approach the problem from a different perspective, motivated by the success of multi-scale analysis in smoothed particle hydrodynamics. In PBL, we treat each of the lensed galaxies as a particle and then reconstruct the potential by smoothing over a local kernel with variable smoothing scale. In this way, we can tune a reconstruction to produce constant signal-noise throughout, and maximally exploit regions of high information density. PBL is designed to include all lensing observables, including multiple image positions and fluxes from strong lensing, as well as weak lensing signals including shear and flexion. In this paper, however, we describe a shear-only reconstruction, and apply the method to several test cases, including simulated lensing clusters, as well as the well-studied ``Bullet Cluster'' (1E0657-56). In the former cases, we show that PBL is better able to identify cusps and substructures than are grid-based reconstructions, and in the latter case, we show that PBL is able to identify substructure in the Bullet Cluster without even exploiting strong lensing measurements. We also make our codes publicly available., Comment: Accepted for publication in ApJ; Codes available at http://www.physics.drexel.edu/~deb/PBL.htm ; 12 pages,9 figures, section 3 shortened

It is now routine to measure the weak gravitational lensing shear signal from the mean ellipticity of distant galaxies. However, conversion between ellipticity and shear assumes local linearity of the lensing potential (ie that the spatial derivatives of the shear are small), and this condition is not satisfied in some of the most interesting regions of the sky. We extend a derivation of lensing equations to include higher order terms, and assess the level of biases introduced by assuming that first-order weak lensing theory holds in a relatively strong shear regime. We find that, even in a worst-case scenario, a fully linear analysis is accurate to within 1% outside ~1.07 times the Einstein radius of a lens, by deriving an analytic function that can be used to estimate the applicability of any first-order analysis. The effect is too small to explain the discrepancy between weak- and strong-lensing estimates of the mass of the bullet cluster, and should not impact cluster surveys for the forseeable future. In fact, it means that arclets can be used to measure shears closer to a cluster core than has been generally appreciated. However, at the level of accuracy demanded by future lensing surveys, this bias ought to be considered in measurements of the inner slope of cluster mass distributions and the small-scale end of the mass power spectrum. Both of these are central in determining the relationship between baryonic and dark matter., Comment: 5 pages, 1 figure. Matches published version

We present a gravitational lensing analysis of the galaxy cluster Abell 1689, incorporating measurements of the weak shear, flexion, and strong lensing induced in background galaxies. This is the first time that a shapelet technique has been used to reconstruct the distribution of mass in this cluster, and the first time that a flexion signal has been measured using cluster members as lenses. From weak shear measurements alone, we generate a non-parametric mass reconstruction, which shows significant substructure corresponding to groups of galaxies within the cluster. Additionally, our galaxy-galaxy flexion signal demonstrates that the cluster galaxies can be well-fit by a singular isothermal sphere model with a characteristic velocity dispersion of $\sigma_v = 295\pm 40 km/s $. We identify a major, distinct dark matter clump, offset by 40$h^{-1}$kpc from the central cluster members, which was not apparent from shear measurements alone. This secondary clump is present in a parametric mass reconstruction using flexion data alone, and its existence is suggested in a non-parametric reconstruction of the cluster using a combination of strong and weak lensing. As found in previous studies, the mass profile obtained by combining weak and strong lensing data shows a much steeper profile than that obtained from only weak lensing data., Comment: 17 pages, 12 figures, accepted for publication in ApJ

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts allowing us to compare different world map projections. We find that the Winkel-Tripel projection (already adopted for world maps by the National Geographic), has low distortion on most measures and excellent quality overall., Comment: 31 pages, including 27 postscript figures. Accepted to Cartographica. Detailed discussion and code at http://www.physics.drexel.edu/~goldberg/projections

We describe practical approaches to measuring flexion in observed galaxies. In particular, we look at the issues involved in using the Shapelets and HOLICs techniques as means of extracting 2nd order lensing information. We also develop an extension of HOLICs to estimate flexion in the presence of noise, and with a nearly isotropic PSF. We test both approaches in simple simulated lenses as well as a sample of possible background sources from ACS observations of A1689. We find that because noise is weighted differently in shapelets and HOLICs approaches, that the correlation between measurements of the same object is somewhat diminished, but produce similar scatter due to measurement noise., Comment: 10 pages, including 13 postscript figures

Wide-angle, moderately deep redshift surveys such as that conducted as part of the Sloan Digital Sky Survey (SDSS) allow study of the relationship between the structural elements of the large-scale distribution of galaxies -- including groups, cluster, superclusters, and voids -- and the dependence of galaxy formation and evolution on these enviroments. We present a progress report on mapping efforts with the SDSS and discuss recently constructed catalogs of clusters, voids, and void galaxies, and evidence for a 420Mpc/h supercluster or ``Great Wall.'' Analysis of multi-band photometry and moderate-resolution spectroscopy from the SDSS reveals environmental dependence of the star formation history of galaxies that extends over more than a factor of 100 in density, from clusters all the way to the deep interiors of voids. On average, galaxies in the rarified environments of voids exhibit bluer colors, higher specific star formation rates, lower dust content, and more disk-like morphology than objects in denser regions. This trend persists in comparisons of samples in low vs. high-density regions with similar luminosity and morphology, thus this dependence is not simply an extension of the morphology-density relation. Large-scale modulation of the halo mass function and the temperature of the intergalactic medium might explain this dependence of galaxy evolution on the large-scale environment., Comment: 7 pages, invited review to appear in Outskirts of Galaxy Clusters: intense life in the suburbs, Proceedings IAU COlloquium No. 195, 2004, A. Diaferio, ed

We estimate the Mass Function of void galaxies in the second public data release of the Sloan Digital Sky Survey from a sample of 1000 galaxies with local density contrasts of delta_v < -0.6. The galaxy sample is split into ellipticals and spirals using a color-Sersic index criteria. We estimate the virial masses of ellipticals using the measured spectral line-widths along with the observed size. Projection effects and uncertainties in halo properties make mass estimates of spirals more difficult. We use an inversion of the Tully-Fisher relation to estimate the isothermal rotational velocity, and introduce a scaling factor to estimate the halo extent. We then fit the measured mass function against a theoretical Press-Schechter model, and find that the distribution of galaxies in voids appears to be nearly unbiased compared to the mass., Comment: 9 pages, 5 postscript figures. Accepted to Astrophysical Journal; Revisions in response to referee comments

In this paper, we develop a new gravitational lensing inversion technique. While traditional approaches assume that the lensing field varies little across a galaxy image, we note that this variation in the field can give rise to a ``Flexion'' or bending of a galaxy image, which may then be used to detect a lensing signal with increased signal to noise. Since the significance of the Flexion signal increases on small scales, this is ideally suited to galaxy-galaxy lensing. We develop an inversion technique based on the ``Shapelets'' formalism of Refregier (2003). We then demonstrate the proof of this concept by measuring a Flexion signal in the Deep Lens Survey. Assuming an intrinsically isothermal distribution, we find from the Flexion signal alone a velocity width of v_c=221\pm 12 km/s for lens galaxies of r < 21.5, subject to uncertainties in the intrinsic Flexion distribution., Comment: 11 pages, Latex, 4 figures. Accepted by ApJ, changes include revision of errors from previous draft

We present a novel method for simulation of the interior of large cosmic voids, suitable for study of the formation and evolution of objects lying within such regions. Following Birkhoff's theorem, void regions dynamically evolve as universes with cosmological parameters that depend on the underdensity of the void. We derive the values of $\Omega_M$, $\Omega_{\Lambda}$, and $H_0$ that describe this evolution. We examine how the growth rate of structure and scale factor in a void differ from the background universe. Together with a prescription for the power spectrum of fluctuations, these equations provide the initial conditions for running specialized void simulations. The increased efficiency of such simulations, in comparison with general-purpose simulations, allows an improvement of upwards of twenty in the mass resolution. As a sanity check, we run a moderate resolution simulation ($N=128^3$ particles) and confirm that the resulting mass function of void halos is consistent with other theoretical and numerical models., Comment: Accepted to ApJ., Dec. 11, 2003. 9 pages, 3 postscript figures. Changes made to respond to referee's comments

In this paper, we apply the Perturbative Least Action Method to model the Local Group of galaxies for various Cosmological models. We show that though the galaxy masses are theoretically good discriminators of $\Omega_M$ given some observed MW and M31 separation and radial velocity, current estimates of the masses are insufficient to make any cosmological claims. We then discuss additional complications to expand this analysis., Comment: 18 Pages LaTeX, including 5 postscript figures. Submitted to Astrophysical Journal

In this paper, we present a redshift space reconstruction scheme which is analogous to and extends the Perturbative Least Action (PLA) method described by Goldberg & Spergel (2000). We first show that this scheme is effective in reconstructing even nonlinear observations. We then suggest that by varying the cosmology to minimize the quadrupole moment of a reconstructed density field, it may be possible to lower the errorbars on the redshift distortion parameter, $\beta$ as well as to break the degeneracy between the linear bias parameter, $b$, and $\Omega_M$. Finally, we discuss how PLA might be applied to realistic redshift surveys., Comment: 34 Pages LaTeX, including 10 postscript figures. Submitted to Astrophysical Journal

We introduce a new method for generating initial conditions consistent with highly nonlinear observations of density and velocity fields. Using a variant of the Least Action method, called Perturbative Least Action (PLA), we show that it is possible to generate several different sets of initial conditions, each of which will satisfy a set of highly nonlinear observational constraints at the present day. We then discuss a code written to test and apply this method and present the results of several simulations., Comment: 24 pages, 6 postscript figures. Accepted for publication in Astrophysical Journal

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters consist of order 2.5e+05 particles of mass $m_p \simeq 10^{10} \Msun$, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total mass. The weak lensing estimate yields a very good measurement of the total mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to the virial radius). [abridged], Comment: Accepted for publication in The Astrophysical Journal. Complete paper, including 3 large colour figures can also be obtained from http://bu-ast.bu.edu/~brainerd/preprints/

In this paper, we discuss the potential importance of measuring the CMB anisotropy bispectrum. We develop a formalism for computing the bispectrum and for measuring it from microwave background maps. As an example, we compute the bispectrum resulting from the 2nd order Rees-Sciama effect, and find that is undetectable with current and upcoming missions., Comment: 18 Pages, 3 Postscript Figures; Minor changes in response to referee's report

Gravitational fluctuations along the line-of-sight from the surface of last scatter to the observer distort the microwave background in several related ways: The fluctuations deflect the photon path (gravitational lensing), the decay of the gravitational potential produces additional fluctuations (ISW effect) and scattering off of hot gas in clusters produce additional fluctuations (Sunyaev-Zel'dovich effect). Even if the initial fluctuations generated at the surface of last scatter were Gaussian, the combination of these effects produce non-Gaussian features in the microwave sky. We discuss the microwave bispectrum as a tool for measuring a studying this signal. For MAP, we estimate that these measurements will enable us to determine the fraction of ionized gas and to probe the time evolution of the gravitational potential., Comment: 15 Pages, 5 Postscript Figures; Minor Changes in Response to Referee's report

We measure the astrometric shifts of the light centroids for the microlensing events in the OGLE-1 database. Of the 15 consistently detected events, 7 had significant shifts which we were able to measure with a fair degree of confidence. Those events with large shifts are also expected to be unresolved with a background ``blend'', and thus, we suggest that we have identified events in the OGLE-1 catalog which are strongly blended. Though we concentrate on the OGLE-1 database, and use the DoPHOT package in order to perform our analysis, we suggest that this shift is a generic effect, and should be observable in any crowded field., Comment: 18 pages, including 6 postscript figures

We discuss the prospect of deblending microlensing events by observing astrometric shifts of the lensed stars. Since microlensing searches are generally performed in very crowded fields, it is expected that stars will be confusion limited rather than limited by photon statistics. By performing simulations of events in crowded fields, we find that if we assume a dark lens and that the lensed star obeys a power law luminosity function, $n(L)\propto L^{-\beta}$, over half the simulated events show a measurable astrometric shift. Our simulations included 20000 stars in a $256\times 256$ Nyquist sampled CCD frame. For $\beta=2$, we found that 58% of the events were significantly blended $(F_{\ast}/F_{tot}\leq 0.9)$, and of those, 73% had a large astrometric shift $(\geq 0.5 pixels)$. Likewise, for $\beta=3$, we found that 85% of the events were significantly blended, and that 85% of those had large shifts. Moreover, the shift is weakly correlated to the degree of blending, suggesting that it may be possible not only to detect the existence of a blend, but also to deblend events statistically using shift information., Comment: 24 pages, 7 postscript Figures

We estimate the degree to which the baryon density, $\Omega_{b}$, can be determined from the galaxy power spectrum measured from large scale galaxy redshift surveys, and in particular, the Sloan Digital Sky Survey. A high baryon density will cause wiggles to appear in the power spectrum, which should be observable at the current epoch. We assume linear theory on scales $\geq 20h^{-1}Mpc$ and do not include the effects of redshift distortions, evolution, or biasing. With an optimum estimate of $P(k)$ to $k\sim 2\pi/(20 h^{-1} Mpc)$, the $1 \sigma$ uncertainties in $\Omega_{b}$ are roughly 0.07 and 0.016 in flat and open ($\Omega_{0}=0.3$) cosmological models, respectively. This result suggests that it should be possible to test for consistency with big bang nucleosynthesis estimates of $\Omega_{b}$ if we live in an open universe., Comment: 23 Pages, 10 Postscript figures

The formation history of rich clusters is investigated using a hybrid N-body simulation in which high spatial and mass resolution can be achieved self-consistently within a small region of a very large volume. The evolution of three massive clusters is studied via mass accretion, spherically-averaged density profiles, three-dimensional and projected shapes, and degree of substructure. Each cluster consists of order $4\times 10^5$ particles at the present epoch and in the case that rich cluster evolution is well-described by a 1-parameter family, the simulations have sufficient resolution to demonstrate this. At $z=0$ the clusters have similar masses, $M(r \le 1.5h^{-1} Mpc) \sim 2\times 10^{15} h^{-1} M_\odot$, and similar spherically-averaged density profiles, however markedly different formation histories are observed. No single, dominant pattern is apparent in the time variation of the mass accretion rate, the cluster shape, or the degree of substructure. Although not a statistically large sample, these objects suggest that the detailed formation history of rich clusters cannot be characterized by a simple 1-parameter family. These results suggest that the use of observations of rich clusters over a wide range of redshifts to constrain cosmological parameters may not be entirely straightforward., Comment: 28 pages, 8 figures, plain TeX