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The (re)introduction of $\Lambda$ into cosmology has spurred debates that touch on central questions in philosophy of science, as well as the foundations of general relativity and particle physics. We provide a systematic assessment of the often implicit philosophical assumptions guiding the methodology of precision cosmology in relation to dark energy. We start by briefly introducing a recent account of scientific progress in terms of risky and constrained lines of inquiry. This allows us to contrast aspects of $\Lambda$ that make it relevantly different from other theoretical entities in science, such as its remoteness from direct observation or manipulability. We lay out a classification for possible ways to explain apparent accelerated expansion but conclude that these conceptually clear distinctions may blur heavily in practice. Finally, we consider the important role played in cosmology by critical tests of background assumptions, approximation techniques, and core principles, arguing that the weak anthropic principle fits into this category. We argue that some core typicality assumptions -- like the Copernican principle and the cosmological principle -- are necessary though not provable, while others -- like the strong anthropic principle and appeals to naturalness or probability in the multiverse -- are not similarly justifiable., Comment: Forthcoming in a special issue of Universe

Indra is a suite of large-volume cosmological $N$-body simulations with the goal of providing excellent statistics of the large-scale features of the distribution of dark matter. Each of the 384 simulations is computed with the same cosmological parameters and different initial phases, with 1024$^3$ dark matter particles in a box of length 1 Gpc/h, 64 snapshots of particle data and halo catalogs, and 505 time steps of the Fourier modes of the density field, amounting to almost a petabyte of data. All of the Indra data are immediately available for analysis via the SciServer science platform, which provides interactive and batch computing modes, personal data storage, and other hosted data sets such as the Millennium simulations and many astronomical surveys. We present the Indra simulations, describe the data products and how to access them, and measure ensemble averages, variances, and covariances of the matter power spectrum, the matter correlation function, and the halo mass function to demonstrate the types of computations that Indra enables. We hope that Indra will be both a resource for large-scale structure research and a demonstration of how to make very large datasets public and computationally accessible., matches published version. Indra is available on SciServer at http://sciserver.org

We propose a new scheme to reconstruct the baryon acoustic oscillations (BAO) signal, which contains key cosmological information, based on deep convolutional neural networks (CNN). Trained with almost no fine-tuning, the network can recover large-scale modes accurately in the test set: the correlation coefficient between the true and reconstructed initial conditions reaches $90\%$ at $k\leq 0.2 h\mathrm{Mpc}^{-1}$, which can lead to significant improvements of the BAO signal-to-noise ratio down to $k\simeq0.4h\mathrm{Mpc}^{-1}$. Since this new scheme is based on the configuration-space density field in sub-boxes, it is local and less affected by survey boundaries than the standard reconstruction method, as our tests confirm. We find that the network trained in one cosmology is able to reconstruct BAO peaks in the others, i.e. recovering information lost to non-linearity independent of cosmology. The accuracy of recovered BAO peak positions is far less than that caused by the difference in the cosmology models for training and testing, suggesting that different models can be distinguished efficiently in our scheme. It is very promising that Our scheme provides a different new way to extract the cosmological information from the ongoing and future large galaxy surveys., Accepted for publication in MNRAS

The standard explanation for galaxy spin starts with the tidal-torque theory (TTT), in which an ellipsoidal dark-matter protohalo, which comes to host the galaxy, is torqued up by the tidal gravitational field around it. We discuss a complementary picture, using the relatively familiar velocity field, instead of the tidal field, whose intuitive connection to the surrounding, possibly faraway matter arrangement is more obscure. In this 'spin from primordial inner motions' (SPIM) concept, implicit in TTT derivations but not previously emphasized, the angular momentum from the gravity-sourced velocity field inside a protohalo largely cancels out, but has some excess from the aspherical outskirts. At first, the net spin scales according to linear theory, a sort of comoving conservation of familiar angular momentum. Then, at collapse, it is conserved in physical coordinates. Small haloes are then typically subject to secondary exchanges of angular momentum. The TTT is useful for analytic estimates. But a literal interpretation of the TTT is inaccurate in detail, without some implicit concepts about smoothing of the velocity and tidal fields. This could lead to misconceptions, for those first learning about how galaxies come to spin. Protohaloes are not perfectly ellipsoidal and do not uniformly torque up, as in a naive interpretation of the TTT; their inner velocity fields retain substantial dispersion. Furthermore, quantitatively, given initial conditions and protohalo boundaries, SPIM is more direct and accurate than the TTT to predict halo spins. We also discuss how SPIM applies to rotating filaments, and the relation between halo mass and spin, in which the total spin of a halo can be thought of as a sum of random contributions., Accepted to OJA (Open Journal of Astrophysics). 3 movies at https://www.youtube.com/playlist?list=PLJxZSP5_6rBmo7Rz8JgnE1eI2bxRGXGCT

The Vainshtein mechanism, present in many models of gravity, is very effective at screening dark matter halos such that the fifth force is negligible and general relativity is recovered within their Vainshtein radii. Vainshtein screening is independent of halo mass and environment, in contrast to e.g. chameleon screening, making it difficult to test. However, our previous studies have found that the dark matter particles in filaments, walls, and voids are not screened by the Vainshtein mechanism. We therefore investigate whether cosmic voids, identified as local density minima using a watershed technique, can be used to test models of gravity that exhibit Vainshtein screening. We measure density, velocity, and screening profiles of stacked voids in cosmological $N$-body simulations using both dark matter particles and dark matter halos as tracers of the density field. We find that the voids are completely unscreened, and the tangential velocity and velocity dispersion profiles of stacked voids show a clear deviation from $\Lambda$CDM at all radii. Voids have the potential to provide a powerful test of gravity on cosmological scales., Comment: 11 pages, 12 figures; matches version accepted to MNRAS

The most common statistic used to analyze large-scale structure surveys is the correlation function, or power spectrum. Here, we show how `slicing' the correlation function on local density brings sensitivity to interesting non-Gaussian features in the large-scale structure, such as the expansion or contraction of baryon acoustic oscillations (BAO) according to the local density. The sliced correlation function measures the large-scale flows that smear out the BAO, instead of just correcting them as reconstruction algorithms do. Thus, we expect the sliced correlation function to be useful in constraining the growth factor, and modified gravity theories that involve the local density. Out of the studied cases, we find that the run of the BAO peak location with density is best revealed when slicing on a $\sim 40$ Mpc/$h$ filtered density. But slicing on a $\sim100$ Mpc/$h$ filtered density may be most useful in distinguishing between underdense and overdense regions, whose BAO peaks are separated by a substantial $\sim 5$ Mpc/$h$ at $z=0$. We also introduce `curtain plots' showing how local densities drive particle motions toward or away from each other over the course of an $N$-body simulation., Matches revision accepted in MNRAS

Multiple modifications of general relativity (GR) have been proposed in the literature in order to understand the nature of the accelerated expansion of the Universe. However, thus far all the predictions of GR have been confirmed with constantly increasing accuracy. In this work, we study the imprints of a particular class of models -- "screened" modified gravity theories -- on cosmic filaments. We have utilized the $N$-body code ISIS/RAMSES to simulate the symmetron model and the Hu-Sawicky $f(R)$ model, and we post-process the output with DisPerSE to identify the filaments of the cosmic web. We investigated how the global properties of the filaments -- such as their lengths, masses, and thicknesses -- as well as their radial density and speed profiles change under different gravity theories. We find that filaments are, on average, shorter and denser in modified gravity models compared to in $\Lambda$CDM. We also find that the speed profiles of the filaments are enhanced, consistent with theoretical expectations. Overall, our results suggest that cosmic filaments can be an effective complementary probe of screened modified gravity theories on Mpc scales., Comment: 11 pages, 17 figures, accepted by A&A

Author(s): Yang, LF; Neyrinck, MC; Aragon-Calvo, MA; Falck, B; Silk, J | Abstract: Warm dark matter (WDM) has been proposed as an alternative to cold dark matter (CDM), to resolve issues such as the apparent lack of satellites around the MilkyWay. Even ifWDMis not the answer to observational issues, it is essential to constrain the nature of the dark matter. The effect of WDM on haloes has been extensively studied, but the small-scale initial smoothing in WDM also affects the present-day cosmic web and voids. It suppresses the cosmic 'subweb' inside voids, and the formation of both void haloes and subvoids. In N-body simulations run with different assumed WDM masses, we identify voids with the ZOBOV algorithm, and cosmic-web components with the ORIGAMI algorithm. As dark-matter warmth increases (i.e. particle mass decreases), void density minima grow shallower, while void edges change little. Also, the number of subvoids decreases. The density field in voids is particularly insensitive to baryonic physics, so if void density profiles and minima could be measured observationally, they would offer a valuable probe of the nature of dark matter. Furthermore, filaments and walls become cleaner, as the substructures in between have been smoothed out; this leads to a clear, mid-range peak in the density PDF.

We study the nature of voids defined as single-stream regions that have not undergone shell-crossing. We use ORIGAMI to determine the cosmic web morphology of each dark matter particle in a suite of cosmological $N$-body simulations, which explicitly calculates whether a particle has crossed paths with others along multiple sets of axes and does not depend on a parameter or smoothing scale. The theoretical picture of voids is that of expanding underdensities with borders defined by shell-crossing. We find instead that locally underdense single-stream regions are not bounded on all sides by multi-stream regions, thus they percolate, filling the simulation volume; we show that the set of multi-stream particles also percolates. This percolation persists to high resolution, where the mass fraction of single-stream voids is low, because the volume fraction remains high; we speculate on the fraction of collapsed mass in the continuum limit of infinite resolution. By introducing a volume threshold parameter to define underdense void "cores", we create a catalog of ORIGAMI voids which consist entirely of single-stream particles and measure their percolation properties, volume functions, and average densities., 17 pages, 20 figures; matches version published in MNRAS. ORIGAMI code available at http://icg.port.ac.uk/~falckb/

The cosmic web is one of the most striking features of the distribution of galaxies and dark matter on the largest scales in the Universe. It is composed of dense regions packed full of galaxies, long filamentary bridges, flattened sheets and vast low density voids. The study of the cosmic web has focused primarily on the identification of such features, and on understanding the environmental effects on galaxy formation and halo assembly. As such, a variety of different methods have been devised to classify the cosmic web -- depending on the data at hand, be it numerical simulations, large sky surveys or other. In this paper we bring twelve of these methods together and apply them to the same data set in order to understand how they compare. In general these cosmic web classifiers have been designed with different cosmological goals in mind, and to study different questions. Therefore one would not {\it a priori} expect agreement between different techniques however, many of these methods do converge on the identification of specific features. In this paper we study the agreements and disparities of the different methods. For example, each method finds that knots inhabit higher density regions than filaments, etc. and that voids have the lowest densities. For a given web environment, we find substantial overlap in the density range assigned by each web classification scheme. We also compare classifications on a halo-by-halo basis; for example, we find that 9 of 12 methods classify around a third of group-mass haloes (i.e. $M_{\rm halo}\sim10^{13.5}h^{-1}M_{\odot}$) as being in filaments. Lastly, so that any future cosmic web classification scheme can be compared to the 12 methods used here, we have made all the data used in this paper public., Comment: 24 pages, 8 figures, 2 tables. Submitted to MN. Comments Welcome

In view of future high-precision large-scale structure surveys, it is important to quantify the percent and subpercent level effects in cosmological $N$-body simulations from which theoretical predictions are drawn. One such effect involves deciding whether to zero all modes above the one-dimensional Nyquist frequency, the so-called "corner" modes, in the initial conditions. We investigate this effect by comparing power spectra, density distribution functions, halo mass functions, and halo profiles in simulations with and without these modes. For a simulation with a mass resolution of $m_p \sim 10^{11}\,h^{-1}\,M_{\odot}$, we find that at $z>6$, the difference in the matter power spectrum is large at wavenumbers above $\sim 80$\% of $k_{\rm{Ny}}$, reducing to below 2\% at all scales by $z\sim 3$. Including corner modes results in a better match between low- and high-resolution simulations at wavenumbers around the Nyquist frequency of the low-resolution simulation, but the effect of the corner modes is smaller than the effect of particle discreteness. The differences in mass functions are 3\% for the smallest halos at $z=6$ for the $m_p \sim 10^{11}\,h^{-1}\,M_{\odot}$ simulation, but we find no significant difference in the stacked profiles of well-resolved halos at $z \leq 6$. Thus removing power at $|\mathbf{k}|>k_{\rm{Ny}}$ in the initial conditions of cosmological simulations has a small effect on small scales and high redshifts, typically below a few percent., 10 pages, 15 figures, matches version accepted to ApJ

[abridged] We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends (FOF), spherical-overdensity (SO) and phase-space based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allows halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Via a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30-40 particles. However, also here the phase space finders excelled by resolving substructure down to 10-20 particles. By comparing the halo finders using a high resolution cosmological volume we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity, and peak of the rotation curve).

Measurements of the equation of state of dark energy from surveys of thousands of Type Ia Supernovae (SNe Ia) will be limited by spectroscopic follow-up and must therefore rely on photometric identification, increasing the chance that the sample is contaminated by Core Collapse Supernovae (CC SNe). Bayesian methods for supernova cosmology can remove contamination bias while maintaining high statistical precision but are sensitive to the choice of parameterization of the contaminating distance distribution. We use simulations to investigate the form of the contaminating distribution and its dependence on the absolute magnitudes, light curve shapes, colors, extinction, and redshifts of core collapse supernovae. We find that the CC luminosity function dominates the distance distribution function, but its shape is increasingly distorted as the redshift increases and more CC SNe fall below the survey magnitude limit. The shapes and colors of the CC light curves generally shift the distance distribution, and their effect on the CC distances is correlated. We compare the simulated distances to the first year results of the SDSS-II SN survey and find that the SDSS distance distributions can be reproduced with simulated CC SNe that are ~1 mag fainter than the standard Richardson et al. (2002) luminosity functions, which do not produce a good fit. To exploit the full power of the Bayesian parameter estimation method, parameterization of the contaminating distribution should be guided by the current knowledge of the CC luminosity functions, coupled with the effects of the survey selection and magnitude-limit, and allow for systematic shifts caused by the parameters of the distance fit., 17 pages, 5 figures; accepted for publication in the Astrophysical Journal

In order to determine the observable signatures of modified gravity theories, it is important to consider the effect of baryonic physics. We use a modified version of the ISIS code to run cosmological hydrodynamic simulations to study degeneracies between modified gravity and radiative hydrodynamical processes. Of these, one was the standard $\Lambda$CDM model and four were variations of the Symmetron model. For each model we ran three variations of baryonic processes: non-radiative hydrodynamics; cooling and star formation; and cooling, star formation, and supernova feedback. We construct stacked gas density, temperature, and dark matter density profiles of the halos in the simulations, and study the differences between them. We find that both radiative variations of the models show degeneracies between their processes and at least two of the three parameters defining the Symmetron model., Comment: 9 pages, 4 figures, matches version accepted to A&A

Theories which modify general relativity to explain the accelerated expansion of the Universe often use screening mechanisms to satisfy constraints on Solar System scales. We investigate the effects of the cosmic web and the local environmental density of dark matter halos on the screening properties of the Vainshtein and chameleon screening mechanisms. We compare the cosmic web morphology of dark matter particles, mass functions of dark matter halos, mass and radial dependence of screening, velocity dispersions and peculiar velocities, and environmental dependence of screening mechanisms in $f(R)$ and nDGP models. Using the ORIGAMI cosmic web identification routine we find that the Vainshtein mechanism depends on the cosmic web morphology of dark matter particles, since these are defined according to the dimensionality of their collapse, while the chameleon mechanism shows no morphology dependence. The chameleon screening of halos and their velocity dispersions depend on halo mass, and small halos and subhalos can be environmentally screened in the chameleon mechanism. On the other hand, the screening of halos in the Vainshtein mechanism does not depend on mass nor environment, and their velocity dispersions are suppressed. The peculiar velocities of halos in the Vainshtein mechanism are enhanced because screened objects can still feel the fifth force generated by external fields, while peculiar velocities of chameleon halos are suppressed when the halo centers are screened., 17 pages, 11 figures, matches version accepted to JCAP; ORIGAMI code available at http://icg.port.ac.uk/~falckb

Structures like galaxies and filaments of galaxies in the Universe come about from the origami-like folding of an initially flat three-dimensional manifold in 6D phase space. The ORIGAMI method identifies these structures in a cosmological simulation, delineating the structures according to their outer folds. Structure identification is a crucial step in comparing cosmological simulations to observed maps of the Universe. The ORIGAMI definition is objective, dynamical and geometric: filament, wall and void particles are classified according to the number of orthogonal axes along which dark-matter streams have crossed. Here, we briefly review these ideas, and speculate on how ORIGAMI might be useful to find cosmic voids., Comment: Talk summary to appear in the Proceedings of the 13th Marcel Grossmann Meeting (MG13), Stockholm, July 2012. 3 pages, 3 figures

Self-consistent ${\it N}$-body simulations of modified gravity models are a key ingredient to obtain rigorous constraints on deviations from General Relativity using large-scale structure observations. This paper provides the first detailed comparison of the results of different ${\it N}$-body codes for the $f(R)$, DGP, and Symmetron models, starting from the same initial conditions. We find that the fractional deviation of the matter power spectrum from $\Lambda$CDM agrees to better than $1\%$ up to $k \sim 5-10~h/{\rm Mpc}$ between the different codes. These codes are thus able to meet the stringent accuracy requirements of upcoming observational surveys. All codes are also in good agreement in their results for the velocity divergence power spectrum, halo abundances and halo profiles. We also test the quasi-static limit, which is employed in most modified gravity ${\it N}$-body codes, for the Symmetron model for which the most significant non-static effects among the models considered are expected. We conclude that this limit is a very good approximation for all of the observables considered here., Comment: 31 pages, 16 figures. Version to appear in MNRAS

We investigate the formation, growth, merger history, movement, and destruction of cosmic voids detected via the watershed transform code VIDE in a cosmological N-body dark matter {\Lambda}CDM simulation. By adapting a method used to construct halo merger trees, we are able to trace individual voids back to their initial appearance and record the merging and evolution of their progenitors at high redshift. For the scales of void sizes captured in our simulation, we find that the void formation rate peaks at scale factor 0.3, which coincides with a growth in the void hierarchy and the emergence of dark energy. Voids of all sizes appear at all scale factors, though the median initial void size decreases with time. When voids become detectable they have nearly their present-day volumes. Almost all voids have relatively stable growth rates and suffer only infrequent minor mergers. Dissolution of a void via merging is very rare. Instead, most voids maintain their distinct identity as annexed subvoids of a larger parent. The smallest voids are collapsing at the present epoch, but void destruction ceases after scale factor 0.3. In addition, voids centers tend to move very little, less than 0.01 of their effective radii per ln a, over their lifetimes. Overall, most voids exhibit little radical dynamical evolution; their quiet lives make them pristine probes of cosmological initial conditions and the imprint of dark energy., Comment: 11 pages, 12 figures, MNRAS accepted, minor revisions from referee comments

We investigate the dependence of the Vainshtein screening mechanism on the cosmic web morphology of both dark matter particles and halos as determined by ORIGAMI. Unlike chameleon and symmetron screening, which come into effect in regions of high density, Vainshtein screening instead depends on the dimensionality of the system, and screened bodies can still feel external fields. ORIGAMI is well-suited to this problem because it defines morphologies according to the dimensionality of the collapsing structure and does not depend on a smoothing scale or density threshold parameter. We find that halo particles are screened while filament, wall, and void particles are unscreened, and this is independent of the particle density. However, after separating halos according to their large scale morphological environment, we find no difference in the screening properties of halos in filaments versus halos in clusters. We find that the fifth force enhancement of dark matter particles in halos is greatest well outside the virial radius. We confirm the theoretical expectation that even if the internal field is suppressed by the Vainshtein mechanism, the object still feels the fifth force generated by the external fields, by measuring peculiar velocities and velocity dispersions of halos. Finally, we investigate the morphology and gravity model dependence of halo spins, concentrations, and shapes., Comment: 21 pages, 14 figures, matches version accepted to JCAP; ORIGAMI code available at http://icg.port.ac.uk/~falckb

The ever increasing size and complexity of data coming from simulations of cosmic structure formation demands equally sophisticated tools for their analysis. During the past decade, the art of object finding in these simulations has hence developed into an important discipline itself. A multitude of codes based upon a huge variety of methods and techniques have been spawned yet the question remained as to whether or not they will provide the same (physical) information about the structures of interest. Here we summarize and extent previous work of the "halo finder comparison project": we investigate in detail the (possible) origin of any deviations across finders. To this extent we decipher and discuss differences in halo finding methods, clearly separating them from the disparity in definitions of halo properties. We observe that different codes not only find different numbers of objects leading to a scatter of up to 20 per cent in the halo mass and Vmax function, but also that the particulars of those objects that are identified by all finders differ. The strength of the variation, however, depends on the property studied, e.g. the scatter in position, bulk velocity, mass, and the peak value of the rotation curve is practically below a few per cent, whereas derived quantities such as spin and shape show larger deviations. Our study indicates that the prime contribution to differences in halo properties across codes stems from the distinct particle collection methods and -- to a minor extent -- the particular aspects of how the procedure for removing unbound particles is implemented. We close with a discussion of the relevance and implications of the scatter across different codes for other fields such as semi-analytical galaxy formation models, gravitational lensing, and observables in general., Comment: 28 pages containing 13 figures & 4 tables + 9 pages appendix containing another 4 tables + 4 pages of references, accepted for publication in MNRAS

We describe the challenges arising from tracking dark matter particles in state of the art cosmological simulations. We are in the process of running the Indra suite of simulations, with an aggregate count of more than 35 trillion particles and 1.1PB of total raw data volume. However, it is not enough just to store the particle positions and velocities in an efficient manner -- analyses also need to be able to track individual particles efficiently through the temporal history of the simulation. The required inverted indices can easily have raw sizes comparable to the original simulation.We explore various strategies on how to create an efficient index for such data, using additional insight from the physical properties of the particle motions for a greatly compressed data representation. The basic particle data are stored in a relational database in course-grained containers corresponding to leaves of a fixed depth oct-tree labeled by their Peano-Hilbert index. Within each container the individual objects are sorted by their Lagrangian identifier. Thus each particle has a multi-level address: the PH key of the container and the index of the particle within the sorted array (the slot).Given the nature of the cosmological simulations and choice of the PH-box sizes, in consecutive snapshots particles can only cross into spatially adjacent boxes. Also, the slot number of a particle in adjacent snapshots is adjusted up or down by typically a small number. As a result, a special version of delta encoding over the multi-tier address already results in a dramatic reduction of data that needs to be stored. We follow next with an efficient bit-compression, adapting to the statistical properties of the two-part addresses, achieving a final compression ratio better than a factor of 9. The final size of the full inverted index is projected to be 22.5 TB for a petabyte ensemble of simulations.

We present the ORIGAMI method of identifying structures, particularly halos, in cosmological N-body simulations. Structure formation can be thought of as the folding of an initially flat three-dimensional manifold in six-dimensional phase space. ORIGAMI finds the outer folds that delineate these structures. Halo particles are identified as those that have undergone shell-crossing along 3 orthogonal axes, providing a dynamical definition of halo regions that is independent of density. ORIGAMI also identifies other morphological structures: particles that have undergone shell-crossing along 2, 1, or 0 orthogonal axes correspond to filaments, walls, and voids respectively. We compare this method to a standard Friends-of-Friends halo-finding algorithm and find that ORIGAMI halos are somewhat larger, more diffuse, and less spherical, though the global properties of ORIGAMI halos are in good agreement with other modern halo-finding algorithms., 11 pages, 14 figures; matches version accepted to ApJ

We investigate the use of a logarithmic density variable in estimating the Lagrangian displacement field, motivated by the success of a logarithmic transformation in restoring information to the matter power spectrum. The logarithmic relation is an extension of the linear relation, motivated by the continuity equation, in which the density field is assumed to be proportional to the divergence of the displacement field; we compare the linear and logarithmic relations by measuring both of these fields directly in a cosmological N-body simulation. The relative success of the logarithmic and linear relations depends on the scale at which the density field is smoothed. Thus we explore several ways of measuring the density field, including Cloud-In-Cell smoothing, adaptive smoothing, and the (scale-independent) Delaunay tessellation, and we use both a Fourier space and a geometrical tessellation approach to measuring the divergence. We find that the relation between the divergence of the displacement field and the density is significantly tighter with a logarithmic density variable, especially at low redshifts and for very small (~2 Mpc/h) smoothing scales. We find that the grid-based methods are more reliable than the tessellation-based method of calculating both the density and the divergence fields, though in both cases the logarithmic relation works better in the appropriate regime, which corresponds to nonlinear scales for the grid-based methods and low densities for the tessellation-based method., 6 pages, 3 figures, accepted to ApJ

Supernova cosmology without spectroscopic confirmation is an exciting new frontier which we address here with the Bayesian Estimation Applied to Multiple Species (BEAMS) algorithm and the full three years of data from the Sloan Digital Sky Survey II Supernova Survey (SDSS-II SN). BEAMS is a Bayesian framework for using data from multiple species in statistical inference when one has the probability that each data point belongs to a given species, corresponding in this context to different types of supernovae with their probabilities derived from their multi-band lightcurves. We run the BEAMS algorithm on both Gaussian and more realistic SNANA simulations with of order 10^4 supernovae, testing the algorithm against various pitfalls one might expect in the new and somewhat uncharted territory of photometric supernova cosmology. We compare the performance of BEAMS to that of both mock spectroscopic surveys and photometric samples which have been cut using typical selection criteria. The latter typically are either biased due to contamination or have significantly larger contours in the cosmological parameters due to small data-sets. We then apply BEAMS to the 792 SDSS-II photometric supernovae with host spectroscopic redshifts. In this case, BEAMS reduces the area of the (\Omega_m,\Omega_\Lambda) contours by a factor of three relative to the case where only spectroscopically confirmed data are used (297 supernovae). In the case of flatness, the constraints obtained on the matter density applying BEAMS to the photometric SDSS-II data are \Omega_m(BEAMS)=0.194\pm0.07. This illustrates the potential power of BEAMS for future large photometric supernova surveys such as LSST., Comment: 25 pages, 15 figures, submitted to ApJ