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We develop a set of machine-learning based cosmological emulators, to obtain fast model predictions for the $C(\ell)$ angular power spectrum coefficients characterising tomographic observations of galaxy clustering and weak gravitational lensing from multi-band photometric surveys (and their cross-correlation). A set of neural networks are trained to map cosmological parameters into the coefficients, achieving a speed-up $\mathcal{O}(10^3)$ in computing the required statistics for a given set of cosmological parameters, with respect to standard Boltzmann solvers, with an accuracy better than $0.175\%$ ($<0.1\%$ for the weak lensing case). This corresponds to $\sim 2\%$ or less of the statistical error bars expected from a typical Stage IV photometric surveys. Such overall improvement in speed and accuracy is obtained through ($\textit{i}$) a specific pre-processing optimisation, ahead of the training phase, and ($\textit{ii}$) a more effective neural network architecture, compared to previous implementations.

Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are invaluable tools to generate large suites of mock halo catalogues. In this paper, we first show that the main limitation of current semi-analytical schemes to simulate the displacement of CDM is their inability to model the evolution of overdensities in the initial density field, a limit that can be circumvented by detecting halo particles in the initial conditions. We thus propose `MUltiscale Spherical Collapse Lagrangian Evolution Using Press-Schechter' (muscle-ups), a new scheme that reproduces the results from Lagrangian perturbation theory on large scales, while improving the modelling of overdensities on small scales. In muscle-ups, we adapt the extended Press and Schechter (EPS) formalism to Lagrangian algorithms of the displacement field. For regions exceeding a collapse threshold in the density smoothed at a radius $R$, we consider all particles within a radius $R$ collapsed. Exploiting a multi-scale smoothing of the initial density, we build a halo catalogue on the fly by optimizing the selection of halo candidates. This allows us to generate a density field with a halo mass function that matches one measured in $N$-body simulations. We further explicitly gather particles in each halo together in a profile, providing a numerical, Lagrangian-based implementation of the halo model. Compared to previous semi-analytical Lagrangian methods, we find that muscle-ups improves the recovery of the statistics of the density field at the level of the probability density function (PDF), the power spectrum, and the cross correlation with the $N$-body result., Comment: 19 pages, 11 figures. Modest changes to the text to match the referee's comments, results unchanged. Comments are welcome

We present a public code to generate random fields with an arbitrary probability distribution function (PDF) and an arbitrary correlation function. The algorithm is cosmology-independent, applicable to any stationary stochastic process over a three dimensional grid. We implement it in the case of the matter density field, showing its benefits over the lognormal approximation, which is often used in cosmology for generation of mock catalogues. We find that the covariance of the power spectrum from the new fast realizations is more accurate than that from a lognormal model. As a proof of concept, we also apply the new simulation scheme to the divergence of the Lagrangian displacement field. We find that information from the correlation function and the PDF of the displacement-divergence provides modest improvement over other standard analytical techniques to describe the particle field in the simulation. This suggests that further progress in this direction should come from multi-scale or non-local properties of the initial matter distribution., Comment: 14 pages, 17 figures. The code for ITAM is available at https://github.com/tos-1/ITAM . The code for MUSCLE is at https://github.com/tos-1/MUSCLE . Minor modifications to match the accepted MNRAS version

We use mock galaxy data from the VIMOS Public Extragalactic Redshift Survey (VIPERS) to test the performance of the Multi-Tracer Optimal Estimator (MTOE) of Abramo et al. as a tool to measure the monopoles of the power spectra of multiple tracers of the large-scale structure, $P^{(0)}_\alpha(k)$. We show that MTOE provides more accurate measurements than the standard technique of Feldman, Kaiser & Peacock (FKP), independently of the tracer-selection strategy adopted, on both small and large scales. The largest improvements on individual $P^{(0)}_\alpha(k)$ are obtained using a colour-magnitude selection on small scales, due to MTOE being naturally better equipped to deal with shot noise: we report an average error reduction with respect to FKP of $\sim$ 40$\%$ at $k \, [h$ Mpc$^{-1}]\gtrsim 0.3$. On large scales ($k[h$ Mpc$^{-1}]\lesssim0.1$), the gain in accuracy resulting from cosmic-variance cancellation is $\sim$ 10$\%$ for the ratios of $P^{(0)}_\alpha(k)$. We have carried out a Monte-Carlo Markov Chain analysis to determine the impact of these gains on several quantities derived from $P^{(0)}_\alpha(k)$. If we push the measurement to scales $0.3 < k \, [h$ Mpc$^{-1}]< 0.5$, the average improvements are $\sim$ 30 $\%$ for the amplitudes of the monopoles, $\sim$ 70 $\%$ for the monopole ratios, and $\sim$ 20 $\%$ for the galaxy biases. Our results highlight the potential of MTOE to shed light upon the physics that operate both on large and small cosmological scales. The effect of MTOE on cosmological constraints using VIPERS data will be addressed in a separate paper., Comment: 19 pages, 13 figures; submitted to MNRAS

We recommend a conceptual design study for a spectroscopic facility in the southern hemisphere comprising a large diameter telescope, fiber system, and spectrographs collectively optimized for massively-multiplexed spectroscopy. As a baseline, we propose an 11.4-meter aperture, optical spectroscopic survey telescope with a five square degree field of view. Using current technologies, the facility could be equipped with 15,000 robotically-controlled fibers feeding spectrographs over 360

We test a theoretical description of the void size distribution function against direct estimates from halo catalogues of the DEMNUni suite of large cosmological simulations. Besides standard $\Lambda$CDM, we consider deviations of the dark energy equation of state from $w=-1$, corresponding to four combinations in the popular Chevallier-Polarski-Linder parametrisation: $w_0=-0.9;-1.1$, $w_a=-0.3;0.3$. The theoretical void size function model, relying on the Sheth & van de Weygaert double barrier excursion set formalism, provides an accurate description of the simulation measurements for the different dark energy models considered, within the statistical errors. The model remains accurate for any value of the threshold for void formation $\delta_\mathrm{v}$. Its robust consistency with simulations demonstrates that the theoretical void size function can be applied to real data as a sensitive tool to constrain dark energy., Comment: 15 pages, 5 figures and 2 tables

We test the history of structure formation from redshift 1 to today by matching galaxies from VIPERS and SDSS with dark matter haloes in the MultiDark SMDPL N-body simulation. We first show that the standard subhalo abundance matching (SHAM) recipe implemented with MultiDark characterizes the clustering of galaxies well both at redshift 0 for SDSS and at redshift 1 for VIPERS. This is an important validation of the SHAM model at high redshift. We then remap the simulation timesteps to test alternative growth histories and infer the growth index $\gamma=0.6\pm0.3$. This analysis demonstrates the power of using N-body simulations to forward model galaxy surveys for cosmological inference., Comment: Matches published version. Data and code to reproduce the analysis are available at https://github.com/darklight-cosmology/vipers-sham

The nature of dark energy remains a profound mystery 20 years after the discovery of cosmic acceleration. A very high number density galaxy redshift survey over a wide area (HD GRS Wide) spanning the redshift range of 0.5

We estimate the velocity field in a large set of $N$-body simulations including massive neutrino particles, and measure the auto-power spectrum of the velocity divergence field as well as the cross-power spectrum between the cold dark matter density and the velocity divergence. We perform these measurements at four different redshifts and within four different cosmological scenarios, covering a wide range in neutrino masses. We find that the nonlinear correction to the velocity power spectra largely depend on the degree of nonlinear evolution with no specific dependence on the value of neutrino mass. We provide a fitting formula, based on the value of the r.m.s. of the matter fluctuations in spheres of $8h^{-1}$Mpc, describing the nonlinear corrections with 3\% accuracy on scales below $k=0.7\; h$ Mpc$^{-1}$., Comment: 8 pages, 5 figures, accepted by A&A, typos corrected in equation 12

The recent discovery of gravitational waves marks the culmination of a sequence of successful tests of the general theory of relativity (GR) since its formulation in 1915. Yet these tests remain confined to the scale of stellar systems or the strong gravity regime. A departure from GR on larger, cosmological scales has been advocated by the proponents of modified gravity theories as an alternative to the Cosmological Constant to account for the observed cosmic expansion history. While indistinguishable in these terms by construction, such models on the other hand yield distinct values for the linear growth rate of density perturbations and, as a consequence, for the associated galaxy peculiar velocity field. Measurements of the resulting anisotropy of galaxy clustering, when spectroscopic redshifts are used to derive distances, have thus been proposed as a powerful probe of the validity of GR on cosmological scales. However, despite significant effort in modelling such redshift space distortions, systematic errors remain comparable to current statistical uncertainties. Here, we present the results of a different forward-modelling approach, which fully exploits the sensitivity of the galaxy velocity field to modifications of GR. We use state-of-the-art, high-resolution N-body simulations of a standard GR and a compelling f(R) model, one of GR's simplest variants, to build simulated catalogues of stellar-mass-selected galaxies through a robust match to the Sloan Digital Sky Survey observations. We find that, well within the uncertainty of this technique, f(R) fails to reproduce the observed redshift-space clustering on scales 1-10 Mpc/h. Instead, the standard LCDM GR model agrees impressively well with the data. This result provides a strong confirmation, on cosmological scales, of the robustness of Einstein's general theory of relativity., Comment: 35 Pages, 8 figures. Published in Nature Astronomy. This is the submitted version according to the journal policy. Full article available here (https://rdcu.be/7DiG)

The clustering ratio is defined as the ratio between the correlation function and the variance of the smoothed overdensity field. In LCDM cosmologies not accounting for massive neutrinos, it has already been proved to be independent from bias and redshift space distortions on a range of linear scales. It therefore allows for a direct comparison of measurements (from galaxies in redshift space) to predictions (for matter in real space). In this paper we first extend the applicability of such properties of the clustering ratio to cosmologies that include massive neutrinos, by performing tests against simulated data. We then investigate the constraining power of the clustering ratio when cosmological parameters such as the total neutrino mass and the equation of state of dark energy are left free. We analyse the joint posterior distribution of the parameters that must satisfy, at the same time, the measurements of the galaxy clustering ratio in the SDSS DR12, and the angular power spectrum of temperature and polarization anisotropies of the CMB measured by the Planck satellite. We find the clustering ratio to be very sensitive to the CDM density parameter, but not very much so to the total neutrino mass. Lastly, we forecast the constraining power the clustering ratio will achieve with forthcoming surveys, predicting the amplitude of its errors in a Euclid-like galaxy survey. In this case, we find it is expected to improve the constraint at 95% level on the CDM density by 40% and on the total neutrino mass by 14%., Comment: 17 pages, 12 figures

(Abridged) We consider the scientific case for a large aperture (10-12m class) optical spectroscopic survey telescope with a field of view comparable to that of LSST. Such a facility could enable transformational progress in several areas of astrophysics, and may constitute an unmatched capability for decades. Deep imaging from LSST and Euclid will provide accurate photometry for spectroscopic targets beyond the reach of 4m class instruments. Such a facility would revolutionise our understanding of the assembly and enrichment history of the Milky Way and the role of dark matter through chemo-dynamical studies of tens of millions of stars in the Local Group. Emission and absorption line spectroscopy of redshift z=2-5 galaxies can be used to directly chart the evolution of the cosmic web and examine its connection with activity in galaxies. The facility will also have synergistic impact, e.g. in following up live and transpired transients found with LSST, as well as providing targets and the local environmental conditions for follow-up studies with E-ELT and future space missions. Although our study is exploratory, we highlight a specific telescope design with a 5 square degree field of view and an additional focus that could host a next-generation panoramic IFU. We discuss some technical challenges and operational models and recommend a conceptual design study aimed at completing a more rigorous science case in the context of a costed technical design., Comment: 50 pages including Appendices, 12 figures. One of several reports, commissioned internally at ESO, taking a first look at possible future projects for the era beyond E-ELT construction

We consider the application of relative self-calibration using overlap regions to spectroscopic galaxy surveys that use slit-less spectroscopy. This method is based on that developed for the SDSS by Padmanabhan at al. (2008) in that we consider jointly fitting and marginalising over calibrator brightness, rather than treating these as free parameters. However, we separate the calibration of the detector-to-detector from the full-focal-plane exposure-to-exposure calibration. To demonstrate how the calibration procedure will work, we simulate the procedure for a potential implementation of the spectroscopic component of the wide Euclid survey. We study the change of coverage and the determination of relative multiplicative errors in flux measurements for different dithering configurations. We use the new method to study the case where the flat-field across each exposure or detector is measured precisely and only exposure-to-exposure or detector-to-detector variation in the flux error remains. We consider several base dither patterns and find that they strongly influence the ability to calibrate, using this methodology. To enable self-calibration, it is important that the survey strategy connects different observations with at least a minimum amount of overlap, and we propose an "S"-pattern for dithering that fulfills this requirement. The final survey strategy adopted by Euclid will have to optimise for a number of different science goals and requirements. The large-scale calibration of the spectroscopic galaxy survey is clearly cosmologically crucial, but is not the only one., Comment: 23 pages, 19 figures, Accepted for publication in MNRAS, 2017

Euclid is a European Space Agency medium class mission selected for launch in 2020 within the Cosmic Vision 2015 2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and redshifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission., Comment: This article provides an update of arXiv:1206.1225, with different authors. Forecasts are not updated in this version

The set-up of the initial conditions in cosmological N-body simulations is usually implemented by rescaling the desired low-redshift linear power spectrum to the required starting redshift consistently with the Newtonian evolution of the simulation. The implementation of this practical solution requires more care in the context of massive neutrino cosmologies, mainly because of the non-trivial scale-dependence of the linear growth that characterises these models. In this work we consider a simple two-fluid, Newtonian approximation for cold dark matter and massive neutrinos perturbations that can reproduce the cold matter linear evolution predicted by Boltzmann codes such as CAMB or CLASS with a 0.1% accuracy or below for all redshift relevant to nonlinear structure formation. We use this description, in the first place, to quantify the systematic errors induced by several approximations often assumed in numerical simulations, including the typical set-up of the initial conditions for massive neutrino cosmologies adopted in previous works. We then take advantage of the flexibility of this approach to rescale the late-time linear power spectra to the simulation initial redshift, in order to be as consistent as possible with the dynamics of the N-body code and the approximations it assumes. We implement our method in a public code providing the initial displacements and velocities for cold dark matter and neutrino particles that will allow accurate, i.e. one-percent level, numerical simulations for this cosmological scenario., Comment: 16 pages, 6 figures, 1 table (MNRAS, accepted). Code at https://github.com/matteozennaro/reps

We investigate the use of the cross-correlation between galaxies and galaxy groups to measure redshift-space distortions (RSD) and thus probe the growth rate of cosmological structure. This is compared to the classical approach based on using galaxy auto-correlation. We make use of realistic simulated galaxy catalogues that have been constructed by populating simulated dark matter haloes with galaxies through halo occupation prescriptions. We adapt the classical RSD dispersion model to the case of the group-galaxy cross-correlation function and estimate the RSD parameter $\beta$ by fitting both the full anisotropic correlation function $\xi(r_p,\pi)$ and its multipole moments. In addition, we define a modified version of the latter statistics by truncating the multipole moments to exclude strongly non-linear distortions at small transverse scales. We fit these three observable quantities in our set of simulated galaxy catalogues and estimate statistical and systematic errors on $\beta$ for the case of galaxy-galaxy, group-group, and group-galaxy correlation functions. When ignoring off-diagonal elements of the covariance matrix in the fitting, the truncated multipole moments of the group-galaxy cross-correlation function provide the most accurate estimate, with systematic errors below 3% when fitting transverse scales larger than $10Mpc/h$. Including the full data covariance enlarges statistical errors but keep unchanged the level of systematic error. Although statistical errors are generally larger for groups, the use of group-galaxy cross-correlation can potentially allow the reduction of systematics while using simple linear or dispersion models., Comment: 18 pages, 16 figures

We introduce the idea of {\it effective} dark matter halo catalog in $f(R)$ gravity, which is built using the {\it effective} density field. Using a suite of high resolution N-body simulations, we find that the dynamical properties of halos, such as the distribution of density, velocity dispersion, specific angular momentum and spin, in the effective catalog of $f(R)$ gravity closely mimic those in the $\Lambda$CDM model. Thus, when using effective halos, an $f(R)$ model can be viewed as a $\Lambda$CDM model. This effective catalog therefore provides a convenient way for studying the baryonic physics, the galaxy halo occupation distribution and even semi-analytical galaxy formation in $f(R)$ cosmologies., Comment: 5 pages, 4 figures, revised version, accepted for publication in PRL

As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation $\vec{r}$, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean $\mu$ and dispersion $\sigma$. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. We also show how this description naturally allows for the Taylor expansion of $1+\xi_S(\vec{s})$ around $1+\xi_R(r)$, which leads to the Kaiser linear formula when truncated to second order, expliciting its connection with the moments of the velocity distribution functions. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators., Comment: 11 pages, 3 figures, 2 tables

Galaxy clusters provide unique laboratories to study astrophysical processes on large scales and are important probes for cosmology. X-ray observations are currently the best means of detecting and characterizing galaxy clusters. In this paper we describe the construction of the REFLEX II galaxy cluster survey based on the southern part of the ROSAT All-Sky Survey. REFLEX II extends the REFLEX I survey by a factor of about two down to a flux limit of $1.8 \times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ (0.1 - 2.4 keV). We describe the determination of the X-ray parameters, the process of X-ray source identification, and the construction of the survey selection function. The REFLEX II cluster sample comprises currently 915 objects. A standard selection function is derived for a lower source count limit of 20 photons in addition to the flux limit. The median redshift of the sample is $z = 0.102$. Internal consistency checks and the comparison to several other galaxy cluster surveys imply that REFLEX II is better than 90\% complete with a contamination less than 10\%., Comment: Astronomy and Astrophysics Vol. 555, A30 - 15 pages, 20 figures

Euclid is a European Space Agency medium class mission selected for launch in 2019 within the Cosmic Vision 2015-2025 programme. The main goal of Euclid is to understand the origin of the accelerated expansion of the Universe. Euclid will explore the expansion history of the Universe and the evolution of cosmic structures by measuring shapes and redshifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid's Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission., Comment: 236 pages, minor edits to match the journal version 2013

We discuss the ability of the planned Euclid mission to detect deviations from General Relativity using its extensive redshift survey of more than 50 Million galaxies. Constraints on the gravity theory are placed measuring the growth rate of structure within 14 redshift bins between z=0.7 and z=2. The growth rate is measured from redshift-space distortions, i.e. the anisotropy of the clustering pattern induced by coherent peculiar motions. This is performed in the overall context of the Euclid spectroscopic survey, which will simultaneously measure the expansion history of the universe, using the power spectrum and its baryonic features as a standard ruler, accounting for the relative degeneracies of expansion and growth parameters. The resulting expected errors on the growth rate in the different redshift bins, expressed through the quantity f\sigma_8, range between 1.3% and 4.4%. We discuss the optimisation of the survey configuration and investigate the important dependence on the growth parameterisation and the assumed cosmological model. We show how a specific parameterisation could actually drive the design towards artificially restricted regions of the parameter space. Finally, in the framework of the popular "\gamma -parameterisation", we show that the Euclid spectroscopic survey alone will already be able to provide substantial evidence (in Bayesian terms) if the growth index differs from the GR value \gamma=0.55 by at least \sim 0.13. This will combine with the comparable inference power provided by the Euclid weak lensing survey, resulting in Euclid's unique ability to provide a decisive test of modified gravity., Comment: 18 pages, 15 figures, accepted by MNRAS

We use the galaxy angular power spectrum at $z\sim0.5-1.2$ from the Canada-France-Hawaii-Telescope Legacy Survey Wide fields (CFHTLS-Wide) to constrain separately the total neutrino mass $\sum{m_\nu}$ and the effective number of neutrino species $N_{\rm{eff}}$. This survey has recently benefited from an accurate calibration of the redshift distribution, allowing new measurements of the (non-linear) matter power spectrum in a unique range of scales and redshifts sensitive to neutrino free streaming. Our analysis makes use of a recent model for the effect of neutrinos on the weakly non-linear matter power spectrum derived from accurate N-body simulations. We show that CFHTLS, combined with WMAP7 and a prior on the Hubble constant provides an upper limit of $\sum{m_\nu}<0.29\,$eV and $N_{\rm{eff}} =4.17^{+1.62}_{-1.26}$ (2$\,\sigma$ confidence levels). If we omit smaller scales which may be affected by non-linearities, these constraints become $\sum{m_\nu}<0.41\,$eV and $N_{\rm{eff}} =3.98^{+2.02}_{-1.20}$ (2$\,\sigma$ confidence levels). Finally we show that the addition of other large scale structures probes can further improve these constraints, demonstrating that high redshift large volumes surveys such as CFHTLS are complementary to other cosmological probes of the neutrino mass., Comment: 15 pages, 8 figures, 3 tables

We investigate the impact of statistical and systematic errors on measurements of linear redshift-space distortions (RSD) in future cosmological surveys, analyzing large catalogues of dark-matter halos from the BASICC simulation. These allow us to estimate the dependence of errors on typical survey properties, as volume, galaxy density and mass (i.e. bias factor) of the adopted tracer. We find that measures of the specific growth rate \beta=f/b using the Hamilton/Kaiser harmonic expansion of the redshift-space correlation function \xi(r_p,\pi) on scales larger than 3/h Mpc are typically under-estimated by up to 10% for galaxy sized halos. This is significantly larger than the corresponding statistical errors, which amount to a few percent, indicating the importance of non-linear improvements to the Kaiser model to obtain accurate measurements of the growth rate. We compare the statistical errors to predictions obtained with the Fisher information matrix, based on the usual FKP prescription for the errors on the power spectrum. We show that this produces parameter errors fairly similar to the standard deviations from the halo catalogues, but only if applied to strictly linear scales in Fourier space (k<0.2 h/Mpc). Finally, we present an accurate scaling formula describing the relative error on {\beta} as a function of the survey parameters, which closely matches the simulation results in all explored regimes. This provides a handy and plausibly more realistic alternative to the Fisher matrix approach, to quickly and accurately predict RSD statistical errors expected from future surveys., Comment: 19 pages, 15 figures

We investigate the impact of different observational effects affecting a precise and accurate measurement of the growth rate of fluctuations from the anisotropy of clustering in galaxy redshift surveys. We focus on redshift measurement errors, on the reconstruction of the underlying real-space clustering and on the apparent degeneracy existing with the geometrical distortions induced by the cosmology-dependent conversion of redshifts into distances. We use a suite of mock catalogues extracted from large N-body simulations, focusing on the analysis of intermediate, mildly non-linear scales and apply the standard linear dispersion model to fit the anisotropy of the observed correlation function. We verify that redshift errors up to ~0.2% have a negligible impact on the precision with which the specific growth rate beta can be measured. Larger redshift errors introduce a positive systematic error, which can be alleviated by adopting a Gaussian distribution function of pairwise velocities. This is, in any case, smaller than the systematic error of up to 10% due to the limitations of the linear dispersion model, which is studied in a separate paper. We then show that 50% of the statistical error budget on beta depends on the deprojection procedure through which the real-space correlation function is obtained. Finally, we demonstrate that the degeneracy with geometric distortions can in fact be circumvented. This is obtained through a modified version of the Alcock-Paczynski test in redshift-space, which successfully recovers the correct cosmology by searching for the solution that optimizes the description of dynamical redshift distortions. For a flat cosmology, we obtain largely independent, robust constraints on beta and OmegaM. In a volume of 2.4(Gpc/h)^3, the correct OmegaM is obtained with ~12% error and negligible bias, once the real-space correlation function is properly reconstructed., Comment: 16 pages, 12 figures. Accepted for publication in MNRAS

The 40% Arecibo Legacy Fast ALFA (ALFALFA) survey catalog (\alpha.40) of approximately 10,150 HI-selected galaxies is used to analyze the clustering properties of gas-rich galaxies. By employing the Landy-Szalay estimator and a full covariance analysis for the two-point galaxy-galaxy correlation function, we obtain the real-space correlation function and model it as a power law, \xi(r) = (r/r_0)^(-\gamma), on scales less than 10 h^{-1} Mpc. As the largest sample of blindly HI-selected galaxies to date, \alpha.40 provides detailed understanding of the clustering of this population. We find \gamma = 1.51 +/- 0.09 and r_0 = 3.3 +0.3, -0.2 h^{-1} Mpc, reinforcing the understanding that gas-rich galaxies represent the most weakly clustered galaxy population known; we also observe a departure from a pure power law shape at intermediate scales, as predicted in \Lambda CDM halo occupation distribution models. Furthermore, we measure the bias parameter for the \alpha.40 galaxy sample and find that HI galaxies are severely antibiased on small scales, but only weakly antibiased on large scales. The robust measurement of the correlation function for gas-rich galaxies obtained via the \alpha.40 sample constrains models of the distribution of HI in simulated galaxies, and will be employed to better understand the role of gas in environmentally-dependent galaxy evolution., Comment: 30 pages, 10 figures, accepted by ApJ

We investigate the ability of state-of-the-art redshift-space distortions models for the galaxy anisotropic two-point correlation function \xi(r_p, \pi), to recover precise and unbiased estimates of the linear growth rate of structure f, when applied to catalogues of galaxies characterised by a realistic bias relation. To this aim, we make use of a set of simulated catalogues at z = 0.1 and z = 1 with different luminosity thresholds, obtained by populating dark-matter haloes from a large N-body simulation using halo occupation prescriptions. We examine the most recent developments in redshift-space distortions modelling, which account for non-linearities on both small and intermediate scales produced respectively by randomised motions in virialised structures and non-linear coupling between the density and velocity fields. We consider the possibility of including the linear component of galaxy bias as a free parameter and directly estimate the growth rate of structure f. Results are compared to those obtained using the standard dispersion model, over different ranges of scales.We find that the model of Taruya et al. (2010), the most sophisticated one considered in this analysis, provides in general the most unbiased estimates of the growth rate of structure, with systematic errors within 4% over a wide range of galaxy populations spanning luminosities between L > L* and L > 3L*. The scale-dependence of galaxy bias plays a role on recovering unbiased estimates of f when fitting quasi non-linear scales. Its effect is particularly severe for most luminous galaxies, for which systematic effects in the modelling might be more difficult to mitigate and have to be further investigated. [...], Comment: 17 pages, 16 figures, Accepted for publication in MNRAS

A space-based galaxy redshift survey would have enormous power in constraining dark energy and testing general relativity, provided that its parameters are suitably optimized. We study viable space-based galaxy redshift surveys, exploring the dependence of the Dark Energy Task Force (DETF) figure-of-merit (FoM) on redshift accuracy, redshift range, survey area, target selection, and forecast method. Fitting formulae are provided for convenience. We also consider the dependence on the information used: the full galaxy power spectrum P(k, P(k) marginalized over its shape, or just the Baryon Acoustic Oscillations (BAO). We find that the inclusion of growth rate information (extracted using redshift space distortion and galaxy clustering amplitude measurements) leads to a factor of ~ 3 improvement in the FoM, assuming general relativity is not modified. This inclusion partially compensates for the loss of information when only the BAO are used to give geometrical constraints, rather than using the full P(k) as a standard ruler. We find that a space-based galaxy redshift survey covering ~20,000 deg^2 over 0.5< z < 2 with \sigma_z/(1+z)<= 0.001 exploits a redshift range that is only easily accessible from space, extends to sufficiently low redshifts to allow both a vast 3-D map of the universe using a single tracer population, and overlaps with ground-based surveys to enable robust modeling of systematic effects. We argue that these parameters are close to their optimal values given current instrumental and practical constraints., Comment: 13 pages, 5 figures. Version with slightly modified text. Accepted by MNRAS

The clustering of galaxies observed in future redshift surveys will provide a wealth of cosmological information. Matching the signal at different redshifts constrains the dark energy driving the acceleration of the expansion of the Universe. In tandem with these geometrical constraints, redshift-space distortions (RSD) depend on the build up of large-scale structure. As pointed out by many authors measurements of these effects are intrinsically coupled. We investigate this link, and argue that it strongly depends on the cosmological assumptions adopted when analysing data. Using representative assumptions for the parameters of the Euclid survey in order to provide a baseline future experiment, we show how the derived constraints change due to different model assumptions. We argue that even the assumption of a Friedman-Robertson-Walker (FRW) space-time is sufficient to reduce the importance of the coupling to a significant degree. Taking this idea further, we consider how the data would actually be analysed and argue that we should not expect to be able to simultaneously constrain multiple deviations from the standard $\Lambda$CDM model. We therefore consider different possible ways in which the Universe could deviate from the $\Lambda$CDM model, and show how the coupling between geometrical constraints and structure growth affects the measurement of such deviations., Comment: 11 pages, 5 figures. Matches published version. For the fisher matrix code email Lado Samushia

The Chandra COSMOS Survey (C-COSMOS) is a large, 1.8 Ms, Chandra} program that has imaged the central 0.5 sq.deg of the COSMOS field (centered at 10h, +02deg) with an effective exposure of ~160ksec, and an outer 0.4sq.deg. area with an effective exposure of ~80ksec. The limiting source detection depths are 1.9e-16 erg cm(-2) s(-1) in the Soft (0.5-2 keV) band, 7.3e(-16) erg cm^-2 s^-1 in the Hard (2-10 keV) band, and 5.7e(-16) erg cm(-2) s(-1) in the Full (0.5-10 keV) band. Here we describe the strategy, design and execution of the C-COSMOS survey, and present the catalog of 1761 point sources detected at a probability of being spurious of <2e(-5) (1655 in the Full, 1340 in the Soft, and 1017 in the Hard bands). By using a grid of 36 heavily (~50%) overlapping pointing positions with the ACIS-I imager, a remarkably uniform (to 12%) exposure across the inner 0.5 sq.deg field was obtained, leading to a sharply defined lower flux limit. The widely different PSFs obtained in each exposure at each point in the field required a novel source detection method, because of the overlapping tiling strategy, which is described in a companion paper. (Puccetti et al. Paper II). This method produced reliable sources down to a 7-12 counts, as verified by the resulting logN-logS curve, with sub-arcsecond positions, enabling optical and infrared identifications of virtually all sources, as reported in a second companion paper (Civano et al. Paper III). The full catalog is described here in detail, and is available on-line., Comment: Revised to omit egregious bold facing and fix missing ',' in author list

These are the findings of the Joint Dark Energy Mission (JDEM) Figure of Merit (FoM) Science Working Group (SWG), the FoMSWG. JDEM is a space mission planned by NASA and the DOE for launch in the 2016 time frame. The primary mission is to explore the nature of dark energy. In planning such a mission, it is necessary to have some idea of knowledge of dark energy in 2016, and a way to quantify the performance of the mission. In this paper we discuss these issues.

We present the first results of the measurements of angular auto-correlation functions (ACFs) of X-ray point sources detected in the XMM-Newton observations of the 2 deg2 COSMOS field (XMM-COSMOS). A significant positive signals have been detected in the 0.5-2 (SFT) band, in the angle range of 0.5-24 arcminutes, while the positive signals were at the 2 and 3 sigma levels in the 2-4.5 (MED) and 4.5-10 (UHD) keV bands respectively. Correctly taking integral constraints into account is a major limitation in interpreting our results. With power-law fits to the ACFs without the integral constraint term, we find correlation lengths of theta_c=1.9+-0.3, 0.8+0.5-0.4 and 6+-2 arcseconds for the SFT, MED, and UHD bands respectively for gamma=1.8. The inferred comoving correlation lengths, also taking into account the bias by the source merging due to XMM-Newton PSF, are 9.8+-0.7, 5.8+1.4-1.7 and 12+-2 h-1 Mpc at the effective redshifts of 1.1, 0.9, and 0.6 for the SFT, MED, and UHD bands respectively. If we include the integral constraint term in the fitting process,assuming that the power-law extends to the scale length of the entire XMM-COSMOSfield, the correlation lengths become larger by 20%-90%. Comparing the inferred rms fluctuations of the spatial distribution of AGNs with those of the underlying mass, the bias parameters of the X-ray source clustering at these effective redshifts are in the range b(AGN)=1.5-4. (Edited to simple ascii.), Comment: 17 pages, 3 figures Accepted for Astrophysical Journal Supplement series (COSMOS Special issue)

New observational constraints on the cosmic matter density $\Omega_m$ and an effectively redshift-independent equation of state parameter $w_x$ of the dark energy are obtained while simultaneously testing the strong and null energy conditions of general relativity on macroscopic scales. The combination of REFLEX X-ray cluster and type-Ia supernova data shows that for a flat Universe the strong energy condition might presently be violated whereas the null energy condition seems to be fulfilled. This provides another observational argument for the present accelerated cosmic expansion and the absence of exotic physical phenomena related to a broken null energy condition. The marginalization of the likelihood distributions is performed in a manner to include a large fraction of the recently discussed possible systematic errors involved in the application of X-ray clusters as cosmological probes. This yields for a flat Universe, $\Omega_m=0.29^{+0.08}_{-0.12}$ and $w_x=-0.95^{+0.30}_{-0.35}$ ($1\sigma$ errors without cosmic variance). The scatter in the different analyses indicates a quite robust result around $w_x=-1$, leaving little room for the introduction of new energy components described by quintessence-like models or phantom energy. The most natural interpretation of the data is a positive cosmological constant with $w_x=-1 or something like it., Comment: 11 pages, 5 figures, Astron. Astrophys. (in press)

For the first time the large-scale clustering and the mean abundance of galaxy clusters are analysed simultaneously to get precise constraints on the normalized cosmic matter density $\Omega_m$ and the linear theory RMS fluctuations in mass $\sigma_8$. A self-consistent likelihood analysis is described which combines, in a natural and optimal manner, a battery of sensitive cosmological tests where observational data are represented by the (Karhunen-Lo\'{e}ve) eigenvectors of the sample correlation matrix. This method breaks the degeneracy between $\Omega_m$ and $\sigma_8$. The cosmological tests are performed with the ROSAT ESO Flux-Limited X-ray (REFLEX) cluster sample. The computations assume cosmologically flat geometries and a non-evolving cluster population mainly over the redshift range $0

The Karhunen-Lo\'{e}ve (KL) eigenvectors and eigenvalues of the sample correlation matrix are used to analyse the spatial fluctuations of the REFLEX clusters of galaxies. The method avoids the disturbing effects of correlated power spectral densities which affects all previous cluster measurements on Gpc scales. Comprehensive tests use a large set of independent REFLEX-like mock cluster samples extracted from the Hubble Volume Simulation. It is found that unbiased measurements on Gpc scales are possible with the REFLEX data. The distribution of the KL eigenvalues are consistent with a Gaussian random field on the 93.4% confidence level. Assuming spatially flat cold dark matter models, the marginalization of the likelihood contours over different sample volumes, fiducial cosmologies, mass/X-ray luminosity relations and baryon densities, yields the 95.4% confidence interval for the matter density of $0.03<\Omega_mh^2<0.19$. The N-body simulations show that cosmic variance, although difficult to estimate, is expected to increase the confidence intervals by about 50%., Comment: 11 pages, 7 figures, accepted for publication in MNRAS

We describe the main features of the BMW survey of serendipitous X-ray clusters, based on the still unexploited ROSAT-HRI archival observations. The sky coverage, surface density and first deep optical CCD images of the candidates indicate that this sample can represent an excellent complement to the existing PSPC deep cluster surveys and will provide us with a fully independent probe of the evolution of the cluster abundance, in addition to significantly increasing the number of clusters known at z>0.6., Comment: 6 pages,4 figures.To appear in the proceedings of the "X-Ray Astronomy 2000" conference (Sept. 2000, Palermo, Italy), PASP Conference Series, ed. R. Giacconi, L. Stella and S. Serio

We present a measure of the power spectrum on scales from 15 to 800 Mpc/h using the ROSAT-ESO Flux-Limited X-Ray(REFLEX) galaxy cluster catalogue. The REFLEX survey provides a sample of the 452 X-ray brightest southern clusters of galaxies with the nominal flux limit S=3.0 10^{-12}erg/s/cm2 for the ROSAT energy band (0.1-2.4)keV. Several tests are performed showing no significant incompletenesses of the REFLEX clusters with X-ray luminosities brighter than 10^{43}erg/s up to scales of about 800 Mpc/h. They also indicate that cosmic variance might be more important than previous studies suggest. We regard this as a warning not to draw general cosmological conclusions from cluster samples with a size smaller than REFLEX. Power spectra, P(k), of comoving cluster number densities are estimated for flux- and volume-limited subsamples. The most important result is the detection of a broad maximum within the comoving wavenumber range 0.022

I review the current status of studies of the large-scale structure of the Universe using redshift surveys of galaxies and clusters of galaxies. I first summarise the advances we have made in our knowledge of the cosmography of the z<0.2 Universe during the last 25 years, as well as the status of the major surveys in progress. The question of how the "a priori" selection of some classes of objects "biases" the mapping of the underlying mass density field is discussed in some detail. I then emphasise the advantages of using clusters of galaxies selected in the X-ray band as tracers of large--scale structure, summarising the most recent results of the REFLEX survey, which is under completion. The strong potential of using X-ray clusters to study the evolution of structure to large redshifts is underlined. I then summarise some of the most recent statistical results on the clustering of galaxies and clusters, using the two-point correlation function xi(s) and the power spectrum P(k). In particular, I concentrate on the increased information available on the detailed shape of these functions on large scales, lambda~100/h Mpc. I argue that significant evidence is accumulating from different observations that P(k) has a well-defined and possibly narrow peak around k~0.05 h/Mpc. I conclude with a glimpse into the future of large-scale structure surveys at high redshifts, describing the features of the VIRMOS deep survey, which will soon start collecting redshifts with the ESO VLT for ~150,000 galaxies at a typical depth of z=1., Comment: Invited review delivered at the XIX Texas Symposium on Relativistic Astrophysics, Paris, December 1998; 38 pages Latex with 16 colour figures; uses texas.sty (included) and psfig.sty; higher-resolution versions of Figs.3, 4 and 15 available at ftp://antares.merate.mi.astro.it/pub/guzzo/Texas

We present a new algorithm to search for distant clusters of galaxies on catalogues deriving from imaging data, as those of the ESO Imaging Survey. We discuss the advantages of our technique relative to the ones developed before and present preliminary results of its application to the I--band data of the survey's patch A., Comment: 4 pages (1 figure included), To appear in `Wide-Field Surveys in Cosmology', proceedings of the XIVth IAP meeting

I critically discuss in a pedagogical and phenomenological way a few crucial tests challenging the claims by Pietronero and collaborators that there is no evidence from available galaxy catalogues that the Universe is actually homogeneous above a certain scale. In a series of papers, these authors assert that observations are consistent with a fractal distribution of objects extending to the limit of the present data. I show that while galaxies are indeed clustered in a scale-free way on small and intermediate scales, this behaviour does not continue indefinitely. Although the specific wavelength at which the galaxy distribution apparently turns to homogeneity is dangerously close to the size of the largest samples presently available, there are serious hints suggesting that this turnover is real and that its effects are detected in the behaviour of statistical estimators. The most recent claims of a continuing fractal hierarchy up to scales of several hundreds Mpc seem to be abscribable to the use of incomplete samples or to an improper treatment of otherwise high- quality data sets. The fractal perspective, nevertheless, can represent a fruitful way to look at the clustering properties of galaxies, when properly coupled to the traditional gravitational instability scenario. In the last part of this paper I therefore try to clarify, at a very simple level, some of the confusion existing on the actual scaling properties of the galaxy distribution. In this context, I shall discuss how these can provide hints on the evolution of the large-scale structure of the Universe, when one properly takes into account the effect of both initial conditions and nonlinear gravitational growth in producing the presently observed distribution., Comment: 27 pages, New Astronomy, in press (2, 517). Full html version available at http://pigeon.elsevier.nl/journals/newast/jnl/menu.htm . Original colour figures available also at ftp://antares.merate.mi.astro.it/pub/guzzo/NA

We study the distortions induced by peculiar velocities on the redshift-space correlation function of galaxies of different morphological types in the Pisces-Perseus redshift survey. Redshift-space distortions affect early- and late-type galaxies in different ways. In particular, at small separations, the dominant effect comes from virialized cluster cores, where ellipticals are the dominant population. The net result is that a meaningful comparison of the clustering strength of different morphological types can be performed only in real space, i.e., after projecting out the redshift distortions on the two-point correlation function xi(r_p,pi). A power-law fit to the projected function w_p(r_p) on scales smaller than 10/h Mpc gives r_o = 8.35_{-0.76}^{+0.75} /h Mpc, \gamma = 2.05_{-0.08}^{+0.10} for the early-type population, and r_o = 5.55_{-0.45}^{+0.40} /h Mpc, \gamma = 1.73_{-0.08}^{+0.07} for spirals and irregulars. These values are derived for a sample luminosity brighter than M_{Zw} = -19.5. We detect a 25% increase of r_o with luminosity for all types combined, from M_{Zw} = -19 to -20. In the framework of a simple stable-clustering model for the mean streaming of pairs, we estimate sigma_12(1), the one-dimensional pairwise velocity dispersion between 0 and 1 /h Mpc, to be 865^{+250}_{-165} km/s for early-type galaxies and 345^{+95}_{-65} km/s for late types. This latter value should be a fair estimate of the pairwise dispersion for ``field'' galaxies; it is stable with respect to the presence or absence of clusters in the sample, and is consistent with the values found for non-cluster galaxies and IRAS galaxies at similar separations., Comment: 17 LaTeX pages including 3 tables, plus 11 PS figures. Uses AASTeX macro package (aaspp4.sty) and epsf.sty. To appear on ApJ, 489, Nov 1997

I review the present status of the mapping of the large-scale structure of the Universe through wide-angle redshift surveys. In the first part of the paper, I discuss the current state of the art, describing in some detail the recently completed ESO Slice Project (ESP). I then briefly recall some of the basic motivations for performing larger surveys. Then, in the final section, I present in detail three large redshift survey projects that in the years from now to the end of the Century are expected to satisfy this demand., Comment: 14 pages, standard uu-pack including LaTeX file and 8 postscript figures; fig.6 also available in jpg format at http://www.merate.mi.astro.it/~guzzo/KP/sky.html; to appear in proceedings "Mapping, Measuring and Modelling the Universe", Valencia, September 1995, eds. P.Coles & V.Martinez, APS

We discuss the rationale and the present status of a large redshift survey aiming at measuring distances for all the clusters of galaxies detected by the ROSAT X--ray All--Sky Survey in the southern hemisphere, with flux larger than $\sim 2\times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$. The survey is being performed using three ESO telescopes in parallel. The final sample will contain about 700 clusters. It will represent a unique database for the study of the spatial distribution of clusters, their X--ray luminosity function and their intrinsic physical properties. Serendipitous results obtained so far include two new gravitational arc systems in two clusters of galaxies. These findings, obtained on rather short exposures, confirm the advantage of searching for arcs in X--ray selected clusters., Comment: to appear in "Wide-Field Spectroscopy and the Distant Universe", 35th Herstmonceux Conference, 8 pages uuencoded-compressed- tarred LaTeX, 2 figures available from guzzo@astmim.mi.astro.it, ESOKP-002

We show how, based on considerations on the observed form of the galaxy 2-point spatial correlation function xi(r), a very simplified -- yet surprisingly effective -- model for the linear density fluctuations power spectrum can be constructed. We first relate the observed large-scale shape of xi(r) to a power-law form for the power spectrum, P(k)\propto k^{-2.2}. For a plausible value of the bias parameter b = 1/sigma_8 ~ 1.8, one has (delta_rho / rho)_{rms} ~ 1 r ~ 3.5/h Mpc, suggesting that the change of slope observed in xi(r) around this scale marks the transition between the linear and nonlinear gravitational regimes. Under this working hypothesis, we use a simple analytical form to fit the large-scale correlations constraints together with the COBE CMB anisotropy measurement, thus constructing a simple phenomenological model for the linear power spectrum. Despite its simplicity, the model fits remarkably well directly estimated power spectra from different optical galaxy samples, and when evolved through an N-body simulation it provides a good match to the observed galaxy correlations. One of the most interesting features of the model is the small-scale one-dimensional velocity dispersion produced: sigma_{1d} = 450 Km s^{-1} at 0.5/h Mpc and sigma_{1d} = 350 Km s^{-1} for separations larger than ~ 2/h Mpc., Comment: ApJL in press, 10 pages in plain TeX, 3 figures available from guzzo@astmim.mi.astro.it, SISSA 110/93/A