Amplitude Σ8 Research Articles

Cosmic-Eν: An- emulator for the non-linear neutrino power spectrum

ABSTRACT Cosmology is poised to measure the neutrino mass sum Mν and has identified several smaller-scale observables sensitive to neutrinos, necessitating accurate predictions of neutrino clustering over a wide range of length scales. The FlowsForTheMasses non-linear perturbation theory for the the massive neutrino power spectrum, $\Delta ^2_\nu (k)$, agrees with its companion N-body simulation at the $10~{{\ \rm per\ cent}}-15~{{\ \rm per\ cent}}$ level for k ≤ 1 h Mpc−1. Building upon the Mira-Titan IV emulator for the cold matter, we use FlowsForTheMasses to construct an emulator for $\Delta ^2_\nu (k)$, Cosmic-Eν, which covers a large range of cosmological parameters and neutrino fractions Ων, 0h2 ≤ 0.01 (Mν ≤ 0.93 eV). Consistent with FlowsForTheMasses at the 3.5 per cent level, it returns a power spectrum in milliseconds. Ranking the neutrinos by initial momenta, we also emulate the power spectra of momentum deciles, providing information about their perturbed distribution function. Comparing a Mν = 0.15 eV model to a wide range of N-body simulation methods, we find agreement to 3 per cent for k ≤ 3kFS = 0.17 h Mpc−1 and to 19 per cent for k ≤ 0.4 h Mpc−1. We find that the enhancement factor, the ratio of $\Delta ^2_\nu (k)$ to its linear-response equivalent, is most strongly correlated with Ων, 0h2, and also with the clustering amplitude σ8. Furthermore, non-linearities enhance the free-streaming-limit scaling $\partial \log (\Delta ^2_\nu /\Delta ^2_{\rm m}) / \partial \log (M_\nu)$ beyond its linear value of 4, increasing the Mν-sensitivity of the small-scale neutrino density.

Non-Gaussian assembly bias from a semi-analytic galaxy formation model

ABSTRACT We produce z = 1 galaxy catalogues with the semi-analytic code galacticus to study the dependence on the assembly history of the host halos of the non-Gaussian bias parameter bϕ for galaxies selected by colour magnitude and emission line luminosities. Galaxies selected by g–r colour shows a large assembly bias consistent with previous analyses: a larger value of the normalization amplitude σ8 implies a faster mass assembly and therefore older and redder galaxies. For galaxies selected by H α luminosity, we do not detect a significant assembly bias for the redshift and the halo masses considered here. This indicates that the non-Gaussian assembly bias should be less of a concern for future emission line galaxy surveys. We investigate, for the first time, the sensitivity of the non-Gaussian assembly bias to a change in the parameters of the galaxy formation model: these induce variations up to order unity in the measured Δbϕ, but the overall trends with colour or luminosity remain the same. Since these results may be sensitive to the specific galaxy formation model, it will be prudent to extend this analysis to other semi-analytic models in addition to halo mass and redshift.

Starlet higher order statistics for galaxy clustering and weak lensing

We present a first application to photometric galaxy clustering and weak lensing of wavelet-based multi-scale (beyond two points) summary statistics: starlet peak counts and starlet ℓ1-norm. Peak counts are the local maxima in the map, and ℓ1-norm is computed via the sum of the absolute values of the starlet (wavelet) decomposition coefficients of a map, providing a fast multi-scale calculation of the pixel distribution, encoding the information of all pixels in the map. We employ the cosmo-SLICS simulations sources and lens catalogues, and we compute wavelet-based non-Gaussian statistics in the context of combined probes and their potential when applied to the weak-lensing convergence maps and galaxy maps. We obtain forecasts on the matter density parameter Ωm, the reduced Hubble constant h, the matter fluctuation amplitude σ8, and the dark energy equation of state parameter w0. In our setting for this first application, we consider the two probes to be independent. We find that the starlet peaks and the ℓ1-norm represent interesting summary statistics that can improve the constraints with respect to the power spectrum, even in the case of photometric galaxy clustering and when the two probes are combined.

A joint 2- and 3-point clustering analysis of the VIPERS PDR2 catalogue at z ∼ 1: breaking the degeneracy of cosmological parameters

ABSTRACT We measure the galaxy two- and three-point correlation functions at z = [0.5, 0.7] and z = [0.7, 0.9], from the Public Data Release 2 (PDR2) of the VIMOS Public Extragalactic Redshift Survey (VIPERS). We model the two statistics including a non-linear one-loop model for the two-point function and a tree-level model for the three-point function, and perform a joint likelihood analysis. The entire process and non-linear corrections are tested and validated through the use of the 153 highly realistic VIPERS mock catalogues, showing that they are robust down to scales as small as 10 $h^{-1} \, \mathrm{Mpc}$. The mocks are also adopted to compute the covariance matrix that we use for the joint two- and three-point analysis. Despite the limited statistics of the two (volume-limited) subsamples analysed, we demonstrate that such a combination successfully breaks the degeneracy existing at two-point level between clustering amplitude σ8, linear bias b1, and the linear growth rate of fluctuations f. For the latter, in particular, we measure $f(z=0.61)=0.64^{+0.55}_{-0.37}$ and f(z = 0.8) = 1.0 ± 1.0, while the amplitude of clustering is found to be σ8(z = 0.61) = 0.50 ± 0.12 and $\sigma _8(z=0.8)=0.39^{+0.11}_{-0.13}$. These values are in excellent agreement with the extrapolation of a Planck cosmology.

Cosmology intertwined III: [formula omitted] and [formula omitted

The standard Λ Cold Dark Matter cosmological model provides a wonderful fit to current cosmological data, but a few statistically significant tensions and anomalies were found in the latest data analyses. While these anomalies could be due to the presence of systematic errors in the experiments, they could also indicate the need for new physics beyond the standard model. In this Letter of Interest we focus on the tension between Planck data and weak lensing measurements and redshift surveys, in the value of the matter energy density Ωm and the amplitude σ8 (or the growth rate fσ8) of cosmic structure. We list a few promising models for solving this tension, and discuss the importance of trying to fit multiple cosmological datasets with complete physical models, rather than fitting individual datasets with a few handpicked theoretical parameters.

Improvements in cosmological constraints from breaking growth degeneracy

Context. The key probes of the growth of a large-scale structure are its rate f and amplitude σ8. Redshift space distortions in the galaxy power spectrum allow us to measure only the combination fσ8, which can be used to constrain the standard cosmological model or alternatives. By using measurements of the galaxy-galaxy lensing cross-correlation spectrum or of the galaxy bispectrum, it is possible to break the fσ8 degeneracy and obtain separate estimates of f and σ8 from the same galaxy sample. Currently there are very few such separate measurements, but even this allows for improved constraints on cosmological models. Aims. We explore how having a larger and more precise sample of such measurements in the future could constrain further cosmological models. Methods. We considered what can be achieved by a future nominal sample that delivers an ∼1% constraint on f and σ8 separately, compared to the case with a similar precision on the combination fσ8. Results. For the six cosmological parameters of ΛCDM, we find improvements of ∼5–50% on their constraints. For modified gravity models in the Horndeski class, the improvements on these standard parameters are ∼0–15%. However, the precision on the sum of neutrino masses improves by 65% and there is a significant increase in the precision on the background and perturbation Horndeski parameters.

Cosmological parameter estimation from large-scale structure deep learning

We propose a light-weight deep convolutional neural network (CNN) to estimate the cosmological parameters from simulated 3-dimensional dark matter distributions with high accuracy. The training set is based on 465 realizations of a cubic box with a side length of 256 h−1 Mpc, sampled with 1283 particles interpolated over a cubic grid of 1283 voxels. These volumes have cosmological parameters varying within the flat ΛCDM parameter space of 0.16 ≤ Ωm ≤ 0.46 and 2.0 ≤ 109As ≤ 2.3. The neural network takes as an input cubes with 323 voxels and has three convolution layers, three dense layers, together with some batch normalization and pooling layers. In the final predictions from the network we find a 2.5% bias on the primordial amplitude σ8 that cannot easily be resolved by continued training. We correct this bias to obtain unprecedented accuracy in the cosmological parameter estimation with statistical uncertainties of δΩm=0.0015 and δσ8=0.0029, which are several times better than the results of previous CNN works. Compared with a 2-point analysis method using the clustering region of 0–130 and 10–130 h−1 Mpc, the CNN constraints are several times and an order of magnitude more precise, respectively. Finally, we conduct preliminary checks of the error-tolerance abilities of the neural network, and find that it exhibits robustness against smoothing, masking, random noise, global variation, rotation, reflection, and simulation resolution. Those effects are well understood in typical clustering analysis, but had not been tested before for the CNN approach. Our work shows that CNN can be more promising than people expected in deriving tight cosmological constraints from the cosmic large scale structure.

Galaxy bias and σ8 from counts in cells from the SDSS main sample

ABSTRACT The counts-in-cells (CIC) galaxy probability distribution depends on both the dark matter clustering amplitude σ8 and the galaxy bias b. We present a theory for the CIC distribution based on a previous prescription of the underlying dark matter distribution and a linear volume transformation to redshift space. We show that, unlike the power spectrum, the CIC distribution breaks the degeneracy between σ8 and b on scales large enough that both bias and redshift distortions are still linear; thus, we obtain a simultaneous fit for both parameters. We first validate the technique on the Millennium Simulation and then apply it to the Sloan Digital Sky Survey main galaxy sample. We find σ8 = 0.92 ± .08 and $b = 1.39^{+.11}_{-.09}$ consistent with previous complementary results from redshift distortions and from Planck.

Joint analysis of 6dFGS and SDSS peculiar velocities for the growth rate of cosmic structure and tests of gravity

ABSTRACT Measurement of peculiar velocities by combining redshifts and distance indicators is a powerful way to measure the growth rate of a cosmic structure and test theories of gravity at low redshift. Here we constrain the growth rate of the structure by comparing observed Fundamental Plane peculiar velocities for 15 894 galaxies from the 6dF Galaxy Survey (6dFGS) and Sloan Digital Sky Survey (SDSS) with predicted velocities and densities from the 2M++ redshift survey. We measure the velocity scale parameter $\beta \equiv {\Omega _{\rm m}^\gamma }/b = 0.372^{+0.034}_{-0.050}$ and $0.314^{+0.031}_{-0.047}$ for 6dFGS and SDSS, respectively, where Ωm is the mass density parameter, γ is the growth index, and b is the bias parameter normalized to the characteristic luminosity of galaxies, L*. Combining 6dFGS and SDSS, we obtain β = 0.341 ± 0.024, implying that the amplitude of the product of the growth rate and the mass fluctuation amplitude is fσ8 = 0.338 ± 0.027 at an effective redshift z = 0.035. Adopting Ωm = 0.315 ± 0.007, as favoured by Planck and using γ = 6/11 for General Relativity and γ = 11/16 for DGP gravity, we get $S_8(z=0) = \sigma _8 \sqrt{\Omega _{\rm m}/0.3} =0.637 \pm 0.054$ and 0.741 ± 0.062 for GR and DGP, respectively. This measurement agrees with other low-redshift probes of large-scale structure but deviates by more than 3σ from the latest Planck CMB measurement. Our results favour values of the growth index γ > 6/11 or a Hubble constant H0 > 70 km s−1 Mpc−1 or a fluctuation amplitude σ8 < 0.8 or some combination of these. Imminent redshift surveys such as Taipan, DESI, WALLABY, and SKA1-MID will help to resolve this tension by measuring the growth rate of cosmic structure to 1 per cent in the redshift range 0 < z < 1.

Constraining the astrophysics and cosmology from 21 cm tomography using deep learning with the SKA

ABSTRACT Future Square Kilometre Array (SKA) surveys are expected to generate huge data sets of 21 cm maps on cosmological scales from the Epoch of Reionization. We assess the viability of exploiting machine learning techniques, namely, convolutional neural networks (CNNs), to simultaneously estimate the astrophysical and cosmological parameters from 21 cm maps from seminumerical simulations. We further convert the simulated 21 cm maps into SKA-like mock maps using the detailed SKA antennae distribution, thermal noise, and a recipe for foreground cleaning. We successfully design two CNN architectures (VGGNet-like and ResNet-like) that are both efficiently able to extract simultaneously three astrophysical parameters, namely the photon escape fraction (fesc), the ionizing emissivity power dependence on halo mass (Cion), and the ionizing emissivity redshift evolution index (Dion), and three cosmological parameters, namely the matter density parameter (Ωm), the dimensionless Hubble constant (h), and the matter fluctuation amplitude (σ8), from 21 cm maps at several redshifts. With the presence of noise from SKA, our designed CNNs are still able to recover these astrophysical and cosmological parameters with great accuracy ($R^{2} \gt 92{{\ \rm per\ cent}}$), improving to $R^{2} \gt 99{{\ \rm per\ cent}}$ towards low-redshift and low neutral fraction values. Our results show that future 21 cm observations can play a key role to break degeneracy between models and tightly constrain the astrophysical and cosmological parameters, using only few frequency channels.

Fisher for complements: extracting cosmology and neutrino mass from the counts-in-cells PDF

ABSTRACT We comprehensively analyse the cosmology dependence of counts-in-cells statistics. We focus on the shape of the one-point probability distribution function (PDF) of the matter density field at mildly non-linear scales. Based on large-deviation statistics, we parametrize the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the non-linear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass Mν and can disentangle it from the clustering amplitude σ8. Using more than a million PDFs extracted from the Quijote simulations, we determine the response of the matter PDF to changing parameters in the νΛCDM model and successfully cross-validate the theoretical model and the simulation measurements. We present the first νΛCDM Fisher forecast for the matter PDF at multiple scales and redshifts, and its combination with the matter power spectrum. We establish that the matter PDF and the matter power spectrum are highly complementary at mildly non-linear scales. The matter PDF is particularly powerful for constraining the matter density Ωm, clustering amplitude σ8 and the total neutrino mass Mν. Adding the mildly non-linear matter PDF to the mildly non-linear matter power spectrum improves constraints on Ωm by a factor of 5 and σ8 by a factor of 2 when considering the three lowest redshifts. In our joint analysis of the matter PDF and matter power spectrum at three redshifts, the total neutrino mass is constrained to better than 0.01 eV with a total volume of 6 (Gpc h−1)3. We discuss how density-split statistics can be used to translate those encouraging results for the matter PDF into realistic observables in galaxy surveys.

Constraining the Neutrino Mass with the Drifting Coefficient of the Field Cluster Mass Function

Abstract A new diagnostics to break the degeneracy between the total neutrino mass (M ν ) and the primordial power spectrum amplitude (σ 8) using the drifting coefficient of the field cluster mass function is presented. Analyzing the data from the Cosmological Massive Neutrino Simulations, we first determine the numerical mass functions of the field clusters at various redshifts. Then, we compare the numerical results with the analytical model characterized by a single parameter called the drifting coefficient, which measures the drifts of the collapse density threshold, δ c, from the Einstein–de Sitter spherical value, δ sc, at a given mass scale. It is found that the analytic model for the field cluster mass function is found to work excellently even in the presence of massive neutrinos, and that its drifting coefficient evolves differently in the cosmologies with different values of M ν . At low redshifts (z ≲ 0.3) the more massive neutrinos drift δ c further from δ sc, while the opposite trend is found at higher redshifts (z ≳ 0.3). Speculating that this distinct redshift-dependent effect of massive neutrinos on the drifting coefficient of the field cluster mass function might help break the σ 8–M ν degeneracy, we also show that the sensitivity of this new diagnostics to M ν is high enough to discriminate the case of M ν = 0.1 eV from that of massless neutrinos.

Cosmological parameters from the BOSS galaxy power spectrum

We present cosmological parameter measurements from the publicly available Baryon Oscillation Spectroscopic Survey (BOSS) data on anisotropic galaxy clustering in Fourier space. Compared to previous studies, our analysis has two main novel features. First, we use a complete perturbation theory model that properly takes into account the non-linear effects of dark matter clustering, short-scale physics, galaxy bias, redshift-space distortions, and large-scale bulk flows. Second, we employ a Markov-Chain Monte-Carlo technique and consistently reevaluate the full power spectrum likelihood as we scan over different cosmologies. Our baseline analysis assumes minimal ΛCDM, varies the neutrino masses within a reasonably tight range, fixes the primordial power spectrum tilt, and uses the big bang nucleosynthesis prior on the physical baryon density ωb. In this setup, we find the following late-Universe parameters: Hubble constant H0=(67.9± 1.1) km s−1Mpc−1, matter density fraction Ωm=0.295± 0.010, and the mass fluctuation amplitude σ8=0.721± 0.043. These parameters were measured directly from the BOSS data and independently of the Planck cosmic microwave background observations. Scanning over the power spectrum tilt or relaxing the other priors do not significantly alter our main conclusions. Finally, we discuss the information content of the BOSS power spectrum and show that it is dominated by the location of the baryon acoustic oscillations and the power spectrum shape. We argue that the contribution of the Alcock-Paczynski effect is marginal in ΛCDM, but becomes important for non-minimal cosmological models.

Joint constraints on galaxy bias and σ8 through the N-pdf of the galaxy number density

We present a full description of the N-probability density function of the galaxy number density fluctuations. This N-pdf is given in terms, on the one hand, of the cold dark matter correlations and, on the other hand, of the galaxy bias parameter. The method relies on the assumption commonly adopted that the dark matter density fluctuations follow a local non-linear transformation of the initial energy density perturbations. The N-pdf of the galaxy number density fluctuations allows for an optimal estimation of the bias parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if there exists any a priori information on the bias parameter), and of those parameters defining the dark matter correlations, in particular its amplitude (σ8). It also provides the proper framework to perform model selection between two competitive hypotheses. The parameters estimation capabilities of the N-pdf are proved by SDSS-like simulations (both, ideal log-normal simulations and mocks obtained from Las Damas simulations), showing that our estimator is unbiased. We apply our formalism to the 7th release of the SDSS main sample (for a volume-limited subset with absolute magnitudes Mr ⩽ −20). We obtain b̂ = 1.193 ± 0.074 and σ̂8 = 0.862 ± 0.080, for galaxy number density fluctuations in cells of the size of 30h−1Mpc. Different model selection criteria show that galaxy biasing is clearly favoured.

Cosmological parameter estimation from CMB and X-ray cluster after Planck

We investigate constraints on cosmological parameters in three 8-parameter models with the summed neutrino mass as a free parameter,by a joint analysis of CCCP X-ray cluster data, the newly released Planck CMB data as well as some external data sets including baryon acoustic oscillation measurementsfrom the 6dFGS, SDSS DR7 and BOSS DR9 surveys, and Hubble Space Telescope H0 measurement.We find that the combined data strongly favor a non-zero neutrino massesat more than 3σ confidence level in these non-vanilla models.Allowing the CMB lensing amplitude AL to vary, we find AL > 1 at 3σ confidence level.For dark energy with a constant equation of state w, we obtain w < −1 at 3σ confidence level.The estimate of the matter power spectrum amplitude σ8 is discrepant withthe Planck value at 2σ confidence level, which reflects some tensionbetween X-ray cluster data and Planck data in these non-vanilla models.The tension can be alleviated by adding a 9% systematic shift in the cluster mass function.

Galaxy formation in WMAP1 and WMAP7 cosmologies

Using the technique of Angulo & White, we scale the Millennium and Millennium II simulations of structure growth in a Λ cold dark matter (ΛCDM) universe from the cosmological parameters with which they were carried out (based on first-year results from the Wilkinson Microwave Anisotropy Probe, WMAP1) to parameters consistent with the seven-year WMAP data (WMAP7). We implement semi-analytic galaxy formation modelling (SAM) on both simulations in both cosmologies to investigate how the formation, evolution and clustering of galaxies are predicted to vary with cosmological parameters. The increased matter density Ωm and decreased linear fluctuation amplitude σ8 in WMAP7 have compensating effects, so that the abundance and clustering of dark haloes are predicted to be very similar to those in WMAP1 for z ≤ 3. As a result, local galaxy properties can be reproduced equally well in the two cosmologies by slightly altering galaxy formation parameters. The evolution of the galaxy populations is then also similar. In WMAP7, structure forms slightly later. This shifts the peak in cosmic star formation rate to lower redshift, resulting in slightly bluer galaxies at z = 0. Nevertheless, the model still predicts more passive low-mass galaxies than are observed. For rp < 1 Mpc, the z = 0 clustering of low-mass galaxies is weaker for WMAP7 than for WMAP1 and closer to that observed, but the two cosmologies give very similar results for more massive galaxies and on large scales. At z > 1 galaxies are predicted to be more strongly clustered for WMAP7. Differences in galaxy properties, including clustering, in these two cosmologies are rather small out to z ∼ 3. Given that there are still considerable residual uncertainties in galaxy formation models, it is very difficult to distinguish WMAP1 from WMAP7 through observations of galaxy properties or their evolution.

SIMULATION OF STAR FORMATIONS IN COSMOLOGICAL VOLUME (240 Mpc/h) 3

In this paper the Lambda Cold Dark Matter ( ΛCDM) model was used for studying star formation inside a box of size (240Mpc/h) 3 by simulating eight million dark matter particles and eight million gas particles together with cosmological density Ω=0.25, dark energy density ΩΛ=0.75, baryon density Ωb=0.04, fluctuation amplitude σ8=0.9 and Hubble constant H0=100h kms -1 Mpc -1 . The gadget-2 code was used for simulating the particles from early Universe, z=30 (450 million years) to z=0 (13.4 billion years). In the box the structures formation were shown including galaxy clusters, voids and filaments which observed clearly at low redshift, z=0. In the temperature-density planes, the thermal processes of cooled gas show the density and temperature values which were different at each redshift, and the gas cooled in the box at nearly 10 4 K caused star formations at certain redshifts. It was also found that stars were formed from z=7.3 which increased with decreasing redshifts. In addition, the total number of star formed in the box was 226217 stars. Sixteen processors of high performance supercomputer of Nottingham University-England were used in the simulation.

Constraining cosmological parameters with observational data including weak lensing effects

In this Letter, we study the cosmological implications of the 100 square degree Weak Lensing survey (the CFHTLS-Wide, RCS, VIRMOS-DESCART and GaBoDS surveys). We combine these weak lensing data with the cosmic microwave background (CMB) measurements from the WMAP5, BOOMERanG, CBI, VSA, ACBAR, the SDSS LRG matter power spectrum and the Type Ia Supernoave (SNIa) data with the “Union” compilation (307 sample), using the Markov Chain Monte Carlo method to determine the cosmological parameters, such as the equation-of-state (EoS) of dark energy w, the density fluctuation amplitude σ8, the total neutrino mass ∑mν and the parameters associated with the power spectrum of the primordial fluctuations. Our results show that the ΛCDM model remains a good fit to all of these data. In a flat universe, we obtain a tight limit on the constant EoS of dark energy, w=−0.97±0.041 (1σ). For the dynamical dark energy model with time evolving EoS parameterized as wde(a)=w0+wa(1−a), we find that the best-fit values are w0=−1.064 and wa=0.375, implying the mildly preference of Quintom model whose EoS gets across the cosmological constant boundary during evolution. Regarding the total neutrino mass limit, we obtain the upper limit, ∑mν<0.471 eV (95% C.L.) within the framework of the flat ΛCDM model. Due to the obvious degeneracies between the neutrino mass and the EoS of dark energy model, this upper limit will be relaxed by a factor of 2 in the framework of dynamical dark energy models. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, within the ΛCDM model, we find that the upper limit on the ratio of the tensor to scalar is r<0.35 (95% C.L.) and the inflationary models with the slope ns⩾1 are excluded at more than 2σ confidence level. In this Letter we pay particular attention to the contribution from the weak lensing data and find that the current weak lensing data do improve the constraints on matter density Ωm, σ8, ∑mν, and the EoS of dark energy.

From Galaxy‐Galaxy Lensing to Cosmological Parameters

Galaxy-galaxy lensing uses the weak distortion of background sources to measure the mean excess surface density profile, ΔΣ(r), around a sample of foreground lensing galaxies. We develop a method for combining ΔΣ(r) with the galaxy-galaxy correlation function ξgg(r) to constrain the matter density parameter Ωm and the matter fluctuation amplitude σ8, going beyond the linear biasing model to reach the level of accuracy demanded by current and future measurements. We adopt the halo occupation distribution (HOD) framework and test its applicability to this problem by examining the effects of replacing satellite galaxies in the halos of a smoothed particle hydrodynamics (SPH) simulation with randomly selected dark matter particles from the same halos. After accounting for the slight differences between the predicted radial profile of dark matter and satellite galaxies, the residual effects of individual subhalos around satellite galaxies and environmental dependence of the HOD at fixed halo mass are 5% in ΔΣ(r) for 0.1 h-1 Mpc < r < 15 h-1 Mpc. We develop an analytic approximation for calculating ΔΣ(r), improving on previous work with more accurate treatments of halo bias and halo exclusion. We demonstrate its accuracy at the few percent level with tests against a suite of populated N-body simulations. We use the analytic model to investigate the dependence of ΔΣ(r) and the galaxy-matter correlation function ξgm(r) on Ωm and σ8, once HOD parameters for a given cosmological model are pinned down by matching ξgg(r). The linear bias prediction that ξgm(r)/ξgg(r) = constant is accurate for r 2 h-1 Mpc but fails at the 30%-50% level on smaller scales. The linear bias prediction that ΔΣ(r) Ωmσ8 breaks down at r < 10 h-1 Mpc. We present predictions of ΔΣ(r) for SDSS galaxy samples with Mr ≤ - 20 and -21. These can be combined with future lensing measurements for these samples to constrain Ωm and σ8.

The Lyman a forest opacity and the metagalactic hydrogen ionization rate at z 2-4

Estimates of the metagalactic hydrogen ionization rate from the Lyα forest opacity in QSO absorption spectra depend on the complex density distribution of neutral hydrogen along the line of sight. We use a large suite of high-resolution hydrodynamical simulations to investigate in detail the dependence of such estimates on physical and numerical parameters in the context of ΛCDM models. Adopting fiducial values for cosmological parameters together with published values of the temperature of the IGM and the effective optical depth, the metagalactic ionization rates that reproduce the Lyα effective optical depth at z=[2, 3, 4] are , respectively. The errors include estimates of uncertainties in the relevant physical parameters and the numerical accuracy of the simulations. We find the errors are dominated by the uncertainty in the temperature of the low-density IGM. The estimated metagalactic hydrogen ionization rate for the neutral hydrogen distribution in the current concordance ΛCDM model is more than four times the value inferred for that in an Einstein–de Sitter model of the same rms-density-fluctuation amplitude σ8. The estimated ionization rate is also more than double that expected from updated estimates of the emissivity of observed QSOs alone. A substantial contribution from galaxies appears to be required at all redshifts.