Uros Seljak

Cosmological constraints from the SDSS luminous red galaxies

We measure the large-scale real-space power spectrum P(k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loeve eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.01h/Mpc 0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial.

Constraints on local primordial non-Gaussianity from large scale structure

Recent work has shown that the local non-Gaussianity parameter fNL induces a scale dependent bias, whose amplitude is growing with scale. Here we first rederive this result within the context of the peak–background split formalism and show that it only depends on the assumption of universality of the mass function, assuming that the halo bias only depends on the mass. We then use the extended Press–Schechter formalism to argue that this assumption may be violated and that the scale dependent bias will depend on other properties, such as the merging history of halos. In particular, in the limit of recent mergers we find that the effect is suppressed. Next we use these predictions in conjunction with a compendium of large scale data to put a limit on the value of fNL. When combining all data assuming that the halo occupation depends only on the halo mass, we get a limit of -29 (-65)<fNL<+70 (+93) at 95% (99.7%) confidence. While we use a wide range of data sets, our combined result is dominated by the signal from the SDSS photometric quasar sample. If the latter are modeled as recent mergers then the limits weaken to -31 (-96)<fNL<+70 (+96). These limits are comparable to the strongest current limits from the Wilkinson Anisotropy Probe (WMAP) five-year analysis, with no evidence of a positive signal in fNL. While the method needs to be thoroughly tested against large scale structure simulations with realistic quasar and galaxy formation models, our results indicate that this is a competitive method relative to the cosmic microwave background one and should be further pursued both observationally and theoretically.

Ray-tracing Simulations of Weak Lensing by Large-Scale Structure

We investigate weak lensing by large-scale structure using ray tracing through N-body simulations. Photon trajectories are followed through high-resolution simulations of structure formation to make simulated maps of shear and convergence on the sky. Tests with varying numerical parameters are used to calibrate the accuracy of computed lensing statistics on angular scales from ~1 to a few degrees. Various aspects of the weak-lensing approximation are also tested. We show that the nonscalar component of the shear generated by the multiple deflections is small. For fields a few degrees on a side, the shear power spectrum is almost entirely in the nonlinear regime and agrees well with nonlinear analytical predictions. Sampling fluctuations in power-spectrum estimates are investigated by comparing several ray-tracing realizations of a given model. For survey areas smaller than 1° on a side, the main source of scatter is nonlinear coupling to modes larger than the survey. We develop a method that uses this effect to estimate Ωm from the scatter in power-spectrum estimates for subregions of a larger survey. We show that the power spectrum can be measured accurately on scales corresponding to 1-10 h-1 Mpc with realistic number densities of source galaxies with large intrinsic ellipticities. Non-Gaussian features in the one-point distribution function of the weak-lensing convergence (reconstructed from the shear) are also sensitive to Ωm. We suggest several techniques for estimating Ωm in the presence of noise and compare their statistical power, robustness, and simplicity. With realistic number densities of source galaxies, Ωm can be determined to within 0.1-0.2 from a deep survey of several square degrees.

Confirmation of general relativity on large scales from weak lensing and galaxy velocities

Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, EG, that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to ‘galaxy bias’ (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of EG different from the general relativistic prediction because, in these theories, the ‘gravitational slip’ (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure and the strength of the gravitational lensing effect. Here we report that EG = 0.39u2009±u20090.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of EGu2009≈u20090.4. The measured value excludes a model within the tensor–vector–scalar gravity theory, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f() theory, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

A joint analysis of Planck and BICEP2 B modes including dust polarization uncertainty

We analyze BICEP2 and Planck data using a model that includes CMB lensing, gravity waves, and polarized dust. Recently published Planck dust polarization maps have highlighted the difficulty of estimating the amount of dust polarization in low intensity regions, suggesting that the polarization fractions have considerable uncertainties and may be significantly higher than previous predictions. In this paper, we start by assuming nothing about the dust polarization except for the power spectrum shape, which we take to be C{sub l}{sup BB,dust} ∝ l{sup -2.42}. The resulting joint BICEP2+Planck analysis favors solutions without gravity waves, and the upper limit on the tensor-to-scalar ratio is r 0.14 are excluded with 99.5% confidence). We address the cross-correlation analysis of BICEP2 at 150 GHz with BICEP1 at 100 GHz as a testmorexa0» of foreground contamination. We find that the null hypothesis of dust and lensing with 0r= gives Δ χ{sup 2} < 2 relative to the hypothesis of no dust, so the frequency analysis does not strongly favor either model over the other. We also discuss how more accurate dust polarization maps may improve our constraints. If the dust polarization is measured perfectly, the limit can reach r < 0.05 (or the corresponding detection significance if the observed dust signal plus the expected lensing signal is below the BICEP2 observations), but this degrades quickly to almost no improvement if the dust calibration error is 20% or larger or if the dust maps are not processed through the BICEP2 pipeline, inducing sampling variance noise.«xa0less

A halo mass—concentration relation from weak lensing

We perform a statistical weak lensing analysis of dark matter profiles around tracers of halo mass from galaxy-size to cluster-size halos. In this analysis we use 170 640 isolated ∼L∗ galaxies split into ellipticals and spirals, 38 236 groups traced via isolated spectroscopic luminous red galaxies and 13 823 maxBCG clusters from the Sloan Digital Sky Survey covering a wide range of richness. Together these three samples allow a determination of the density profiles of dark matter halos over three orders of magnitude in mass, from 10^12M☉ to 10^15M☉. The resulting lensing signal is consistent with a Navarro–Frenk–White (NFW) or Einasto profile on scales outside the central region. In the inner regions, uncertainty in modeling of the proper identification of the halo center and inclusion of baryonic effects from the central galaxy make the comparison less reliable. We find that the NFW concentration parameter c200b decreases with halo mass, from around 10 for galactic halos to 4 for cluster halos. Assuming its dependence on halo mass in the form of c200b = c0(M/10^14h^−1 M☉)−β we find c0 = 4.6 ± 0.7 (at z = 0.22) and β = 0.13 ± 0.07, with very similar results for the Einasto profile. The slope (β) is in agreement with theoretical predictions, while the amplitude is about two standard deviations below the predictions for this mass and redshift, but we note that the published values in the literature differ at a level of 10–20% and that for a proper comparison our analysis should be repeated in simulations. We compare our results to other recent determinations, some of which find significantly higher concentrations. We discuss the implications of our results for the baryonic effects on the shear power spectrum: since these are expected to increase the halo concentration, the fact that we see no evidence of high concentrations on scales above 20% of the virial radius suggests that baryonic effects are limited to small scales, and are not a significant source of uncertainty for the current weak lensing measurements of the dark matter power spectrum.

Measurement of baryon acoustic oscillations in the Lyman-α forest fluctuations in BOSS data release 9

We use the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) to detect and measure the position of the Baryonic Acoustic Oscillation (BAO) feature in the three-dimensional correlation function in the Lyman-α flux fluctuations at a redshift zeff = 2.4. The feature is clearly detected at significance between 3 and 5 sigma (depending on the broadband model and method of error covariance matrix estimation) and is consistent with predictions of the standard ΛCDM model. We assess the biases in our method, stability of the error covariance matrix and possible systematic effects. We fit the resulting correlation function with several models that decouple the broadband and acoustic scale information. For an isotropic dilation factor, we measure 100 × (αiso − 1) = −1.6+2.0 +4.3 +7.4−2.0 −4.1 −6.8 (stat.) ±1.0 (syst.) (multiple statistical errors denote 1,2 and 3 sigma confidence limits) with respect to the acoustic scale in the fiducial cosmological model (flat ΛCDM with Ωm = 0.27, h = 0.7). When fitting separately for the radial and transversal dilation factors we find marginalised constraints 100 × (α|| − 1) = −1.3+3.5 +7.6 +12.3−3.3 −6.7 −10.2 (stat.) ±2.0 (syst.) and 100 × (α⊥ − 1) = −2.2+7.4 +17−7.1 −15 (stat.) ±3.0 (syst.). The dilation factor measurements are significantly correlated with cross-correlation coefficient of ~ −0.55. Errors become significantly non-Gaussian for deviations over 3 standard deviations from best fit value. Because of the data cuts and analysis method, these measurements give tighter constraints than a previous BAO analysis of the BOSS DR9 Lyman-α sample, providing an important consistency test of the standard cosmological model in a new redshift regime.

Extracting Primordial Non-Gaussianity without Cosmic Variance

Recent work has emphasized the possibility to probe non-Gaussianity of local type by measuring the power spectrum of highly biased tracers of large scale structure on very large scales. This method is limited by the cosmic variance, by the finite number of structures on the largest scales, and by the partial degeneracy with other cosmological parameters that can mimic the same effect. We propose an alternative method based on the fact that on large scales, halos are linearly biased, but not stochastic, tracers of dark matter: by correlating a highly biased tracer of large scale structure against an unbiased tracer, one eliminates the cosmic variance error, which can lead to a significant increase in signal to noise. For an ideal survey out to z approximately 2, the error reduction can be as large as a factor of 7, which should guarantee a detection of non-Gaussianity from an all-sky survey of this type.

How to evade the sample variance limit on measurements of redshift-space distortions

We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter β ≡ b−1f ≡ b−1dxa0lnxa0D/dxa0lnxa0a (where D is the growth factor and a the expansion factor), to, as the signal-to-noise (S/N) of a survey increases, much better precision than one could achieve with a single tracer (to arbitrary precision in the low noise limit). In combination with the power spectrum of the tracers this would allow a more precise measurement of the bias-free velocity divergence power spectrum, f2Pm, with the ultimate, zero noise limit, being that f2Pm can be measured as well as would be possible if velocity divergence was observed directly, with maximum rms improvement factor ~xa0[5.2(β2+2β+2)/β2]1/2 (e.g., 10 times better than a single tracer with β = 0.4). This would allow a determination of fD as a function of redshift with an error as low as ~ 0.1% (again, in the idealized case of the zero noise limit). The ratio b2/b1 can be determined with an even greater precision than β, potentially producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with S/N ~ 1 on scales of interest, which severely limits the usefulness of our method. Our results suggest that there are potentially large gains to be achieved from technological or theoretical developments that allow higher S/N, or, in the long term, surveys that simply observe a higher number density of galaxies.We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter beta=f/b=(dlnD/dlna)/b (where D is the growth rate and a the expansion factor), to a much better precision than one could achieve with a single tracer, to an arbitrary precision in the low noise limit. In combination with the power spectrum of the tracers this allows a much more precise measurement of the bias-free velocity divergence power spectrum, f^2 P_m - in fact, in the low noise limit f^2 P_m can be measured as well as would be possible if velocity divergence was observed directly, with rms improvement factor ~[5.2(beta^2+2 beta+2)/beta^2]^0.5 (e.g., ~10 times better than a single tracer for beta=0.4). This would allow a high precision determination of f D as a function of redshift with an error as low as 0.1%. We find up to two orders of magnitude improvement in Figure of Merit for the Dark Energy equation of state relative to Stage II, a factor of several better than other proposed Stage IV Dark Energy surveys. The ratio b_2/b_1 will be determined with an even greater precision than beta, producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with signal to noise of unity on scales of interest, and are not optimized for this technique. Our results suggest that this strategy may need to be revisited as there are large gains to be achieved from surveys with higher number densities of galaxies.

Correlation of CMB with large-scale structure. II. Weak lensing

We investigate the correlation of gravitational lensing of the cosmic microwave background (CMB) with several tracers of large-scale structure, including luminous red galaxies (LRGs), quasars, and radio Sources. The lensing field is reconstructed based on the CMB maps from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite; the LRGs and quasars are observed by the Sloan Digital Sky Survey (SDSS); and the radio sources are observed in the NRAO VLA Sky Survey (NVSS). Combining all three large-scale Structure samples, we find evidence for a positive cross correlation at the 2.5 sigma level (1.8 sigma for the SDSS samples and 2.1 sigma for NVSS); the cross correlation amplitude is 1.06 +/- 0.42 times that expected for the WMAP cosmological parameters. Our analysis extends other recent analyses in that we carefully determine bias-weighted redshift distribution of the Sources. which is needed for a meaningful cosmological interpretation of the detected signal. We investigate contamination of the signal by galactic emission, extragalactic radio and infrared sources, thermal and kinetic Sunyaev-Zeldovich effects, and the Rees-Sciama effect, and find all of them to be negligible.