Scale-dependent Galaxy Bias Research Articles

Optimal constraints on Primordial non-Gaussianity with the eBOSS DR16 quasars in Fourier space

We present constraints on the amplitude of local Primordial Non-Gaussianities (PNG), f NL, using the quasar sample in the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16). We analyze the power spectrum monopole, testing for the presence of scale-dependent galaxy bias induced by local PNG. Our analysis makes use of optimal redshift weights that maximize the response of the quasar sample to the possible presence of non-zero PNG. We find -4 < f NL < 27 at 68% confidence level, which is among the strongest bounds with Large Scale Structure data. The optimal analysis reduces the error bar by ~10% compared to the standard one, but this improvement is lower than the one expected from previous forecasts. In addition, the larger volume of this dataset, when compared to previous releases of the eBOSS quasar catalog, does not always correspond to a reduction of the final uncertainty on local PNG. This could suggest the presence of still unknown systematic effects in the data.If the quasars have a lower response to local PNG, our optimal constraint becomes -23 < f NL < 21 at 68%, with an improvement of 30% over standardanalyses. We alsoshow how to use the optimal weights to put data-driven priors on the sample's response tolocal PNG.

KiDS-1000: Combined halo-model cosmology constraints from galaxy abundance, galaxy clustering, and galaxy-galaxy lensing

We present constraints on the flat Λ cold dark matter cosmological model through a joint analysis of galaxy abundance, galaxy clustering, and galaxy-galaxy lensing observables with the Kilo-Degree Survey. Our theoretical model combines a flexible conditional stellar mass function, which describes the galaxy-halo connection, with a cosmological N-body simulation-calibrated halo model, which describes the non-linear matter field. Our magnitude-limited bright galaxy sample combines nine-band optical-to-near-infrared photometry with an extensive and complete spectroscopic training sample to provide accurate redshift and stellar mass estimates. Our faint galaxy sample provides a background of accurately calibrated lensing measurements. We constrain the structure growth parameter to S8 = σ8√Ωm/0.3 =√0.773−0.030+0.028 and the matter density parameter to Ωm = 0.290−0.017+0.021. The galaxy-halo connection model adopted in the work is shown to be in agreement with previous studies. Our constraints on cosmological parameters are comparable to, and consistent with, joint ‘3 × 2pt’ clustering-lensing analyses that additionally include a cosmic shear observable. This analysis therefore brings attention to the significant constraining power in the often excluded non-linear scales for galaxy clustering and galaxy-galaxy lensing observables. By adopting a theoretical model that accounts for non-linear halo bias, halo exclusion, scale-dependent galaxy bias, and the impact of baryon feedback, this work demonstrates the potential for, and a way towards, including non-linear scales in cosmological analyses. Varying the width of the satellite galaxy distribution with an additional parameter yields a strong preference for sub-Poissonian variance, improving the goodness of fit by 0.18 in terms of the reduced χ2 value (and increasing the p-value by 0.25) compared to a fixed Poisson distribution.

Bayesian field-level inference of primordial non-Gaussianity using next-generation galaxy surveys

ABSTRACT Detecting and measuring a non-Gaussian signature of primordial origin in the density field is a major science goal of next-generation galaxy surveys. The signal will permit us to determine primordial-physics processes and constrain models of cosmic inflation. While traditional approaches use a limited set of statistical summaries of the galaxy distribution to constrain primordial non-Gaussianity, we present a field-level approach by Bayesian forward modelling the entire three-dimensional galaxy survey. Since our method includes the entire cosmic field in the analysis, it can naturally and fully self-consistently exploit all available information in the large-scale structure, to extract information on the local non-Gaussianity parameter, fnl. Examples include higher order statistics through correlation functions, peculiar velocity fields through redshift-space distortions, and scale-dependent galaxy bias. To illustrate the feasibility of field-level primordial non-Gaussianity inference, we present our approach using a first-order Lagrangian perturbation theory model, approximating structure growth at sufficiently large scales. We demonstrate the performance of our approach through various tests with self-consistent mock galaxy data emulating relevant features of the SDSS-III/BOSS-like survey, and additional tests with a Stage IV mock data set. These tests reveal that the method infers unbiased values of fnl by accurately handling survey geometries, noise, and unknown galaxy biases. We demonstrate that our method can achieve constraints of $\sigma _{{f_\mathrm{nl}}} \approx 8.78$ for SDSS-III/BOSS-like data, indicating potential improvements of a factor ∼2.5 over current published constraints. We perform resolution studies on scales larger than ∼16h−1 Mpc showing the promise of significant constraints with next-generation surveys. Furthermore, the results demonstrate that our method can consistently marginalize all nuisance parameters of the data model. The method further provides an inference of the three-dimensional primordial density field, providing opportunities to explore additional signatures of primordial physics. This first demonstration of a field-level inference pipeline demonstrates a promising complementary path forward for analysing next-generation surveys.

Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements

We revisit cosmological constraints on the sum of the neutrino masses Σmν from a combination of full-shape BOSS galaxy clustering [P(k)] data and measurements of the cross-correlation between Planck Cosmic Microwave Background (CMB) lensing convergence and BOSS galaxy overdensity maps [Cℓκg], using a simple but theoretically motivated model for the scale-dependent galaxy bias in auto- and cross-correlation measurements. We improve upon earlier related work in several respects, particularly through a more accurate treatment of the correlation and covariance between P(k) and Cℓκg measurements. When combining these measurements with Planck CMB data, we find a 95% confidence level upper limit of Σmν<0.14eV, while slightly weaker limits are obtained when including small-scale ACTPol CMB data, in agreement with our expectations. We confirm earlier findings that (once combined with CMB data) the full-shape information content is comparable to the geometrical information content in the reconstructed BAO peaks given the precision of current galaxy clustering data, discuss the physical significance of our inferred bias and shot noise parameters, and perform a number of robustness tests on our underlying model. While the inclusion of Cℓκg measurements does not currently appear to lead to substantial improvements in the resulting Σmν constraints, we expect the converse to be true for near-future galaxy clustering measurements, whose shape information content will eventually supersede the geometrical one.

CFHTLenS: Galaxy bias as function of scale, stellar mass, and colour

Galaxy models predict a tight relation between the clustering of galaxies and dark matter on cosmological scales, but predictions differ notably in the details. We used this opportunity and tested two semi-analytic models by the Munich and Durham groups with data from the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). For the test we measured the scale-dependent galaxy bias factor b(k) and correlation factor r(k) from linear to non-linear scales of k ≈ 10 h Mpc−1 at two redshifts z̄ = 0.35, 0.51 for galaxies with stellar mass between 5 × 109 and 3 × 1011 h70−2 M⊙. Our improved gravitational lensing technique accounts for the intrinsic alignment of sources and the magnification of lens galaxies for better constraints for the galaxy-matter correlation r(k). Galaxy bias in CFHTLenS increases with k and stellar mass; it is colour-dependent, revealing the individual footprints of galaxy types. Despite a reasonable model agreement for the relative change with both scale and galaxy properties, there is a clear conflict for b(k) with no model preference: the model galaxies are too weakly clustered. This may flag a model problem at z ≳ 0.3 for all stellar masses. As in the models, however, there is a high correlation r(k) between matter and galaxy density on all scales, and galaxy bias is typically consistent with a deterministic bias on linear scales. Only our blue and low-mass galaxies of about 7 × 109 h70−2 M⊙ at z̄ = 0.51 show, contrary to the models, a weak tendency towards a stochastic bias on linear scales where rls = 0.75 ± 0.14 (stat.) ± 0.06 (sys.). This result is of interest for cosmological probes, such as EG, that rely on a deterministic galaxy bias. We provide Monte Carlo realisations of posterior constraints for b(k) and r(k) in CFHTLenS for every galaxy sample in this paper at the CDS.

Minimizing the impact of scale-dependent galaxy bias on the joint cosmological analysis of large-scale structures

ABSTRACT We present a mitigation strategy to reduce the impact of non-linear galaxy bias on the joint ‘3 × 2pt’ cosmological analysis of weak lensing and galaxy surveys. The Ψ-statistics that we adopt are based on Complete Orthogonal Sets of E/B Integrals. As such they are designed to minimize the contributions to the observable from the smallest physical scales where models are highly uncertain. We demonstrate that Ψ-statistics carry the same constraining power as the standard two-point galaxy clustering and galaxy–galaxy lensing statistics, but are significantly less sensitive to scale-dependent galaxy bias. Using two galaxy bias models, motivated by halo model fits to data and simulations, we quantify the error in a standard 3 × 2pt analysis where constant galaxy bias is assumed. Even when adopting conservative angular scale cuts, that degrade the overall cosmological parameter constraints, we find of order 1σ biases for Stage III surveys on the cosmological parameter S8 = σ8(Ωm/0.3)α. This arises from a leakage of the smallest physical scales to all angular scales in the standard two-point correlation functions. In contrast, when analysing Ψ-statistics under the same approximation of constant galaxy bias, we show that the bias on the recovered value for S8 can be decreased by a factor of ∼2, with less conservative scale cuts. Given the challenges in determining accurate galaxy bias models in the highly non-linear regime, we argue that 3 × 2pt analyses should move towards new statistics that are less sensitive to the smallest physical scales.

Probing correlated compensated isocurvature perturbations using scale-dependent galaxy bias

Compensated isocurvature perturbations (CIPs) are modulations of the relative baryon and dark matter density that leave the total matter density constant. The best current constraints from the primary cosmic microwave background (CMB) are consistent with CIPs some two orders of magnitude larger in amplitude than adiabatic perturbations, suggesting that there may be a huge gap in our knowledge of the early Universe. However, it was recently suggested by Barreira~et.~al. that CIPs which are correlated with the primordial curvature perturbation, as arises in some versions of the curvaton model, lead to a new observable: scale dependent galaxy bias. Combining a galaxy survey with an unbiased tracer of the density field facilitates a measurement of the amplitude of correlated CIPs that is free from cosmic variance, the main limitation on constraints from the primary CMB. Among the most promising tracers to use for this purpose is the remote dipole field, reconstructed using the technique of kinetic Sunyaev Zel'dovich (kSZ) tomography. In this paper, we evaluate the detection significance on the amplitude of correlated CIPs possible with next-generation CMB and galaxy surveys using kSZ tomography. Our analysis includes all relativistic contributions to the observed galaxy number counts and allows for both CIPs and primordial non-Gaussianity, which also gives rise to a scale dependent galaxy bias. We find that kSZ tomography can probe CIPs of comparable amplitude to the adiabatic fluctuations, representing an improvement of over two orders of magnitude upon current constraints, and an order of magnitude over what will be possible using future CMB or galaxy surveys alone.

Scale-dependent galaxy bias, CMB lensing-galaxy cross-correlation, and neutrino masses

One of the most powerful cosmological datasets when it comes to constraining neutrino masses is represented by galaxy power spectrum measurements, $P_{gg}(k)$. The constraining power of $P_{gg}(k)$ is however severely limited by uncertainties in the modeling of the scale-dependent galaxy bias $b(k)$. In this Letter we present a new method to constrain $b(k)$ by using the cross-correlation between the Cosmic Microwave Background (CMB) lensing signal and galaxy maps ($C_\ell^{\rm \kappa g}$) using a simple but theoretically well-motivated parametrization for $b(k)$. We apply the method using $C_\ell^{\rm \kappa g}$ measured by cross-correlating Planck lensing maps and the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 (DR11) CMASS galaxy sample, and $P_{gg}(k)$ measured from the BOSS DR12 CMASS sample. We detect a non-zero scale-dependence at moderate significance, which suggests that a proper modeling of $b(k)$ is necessary in order to reduce the impact of non-linearities and minimize the corresponding systematics. The accomplished increase in constraining power of $P_{gg}(k)$ is demonstrated by determining a 95% C.L. upper bound on the sum of the three active neutrino masses $M_{\nu}$ of $M_{\nu}<0.19\, {\rm eV}$. This limit represents a significant improvement over previous bounds with comparable datasets. Our method will prove especially powerful and important as future large-scale structure surveys will overlap more significantly with the CMB lensing kernel providing a large cross-correlation signal.

Scale-dependent galaxy bias from massive particles with spin during inflation

The presence of additional particles during inflation leads to non-Gaussianity in late-time correlators of primordial curvature perturbations. The shape and amplitude of this signal depend on the mass and spin of the extra particles. Constraints on this distinct form of primordial non-Gaussianity, therefore, provide a wealth of information on the particle content during inflation. We investigate the potential of upcoming galaxy surveys in constraining such a signature through its impact on the observed galaxy power spectrum. Primordial non-Gaussianity of various shapes induces a scale-dependent bias on tracers of large-scale structure, such as galaxies. Using this signature we obtain constraints on massive particles during inflation, which can have non-zero spins. In particular, we show that the prospects for constraining particles with spins 0 and 1 are promising, while constraining particles with spin 2 from power spectrum alone seems challenging. We show that the multi-tracer technique can significantly improve the constraints from the power spectrum by at least an order of magnitude. Furthermore, we analyze the effect of non-linearities due to gravitational evolution on the forecasted constraints on the masses of the extra particles and the amplitudes of the imprinted non-Gaussian signal. We find that gravitational evolution affects the constraints by less than a factor of 2.

Multipole analysis of redshift-space distortions around cosmic voids

We perform a comprehensive redshift-space distortion analysis based on cosmic voids in the large-scale distribution of galaxies observed with the Sloan Digital Sky Survey. To this end, we measure multipoles of the void-galaxy cross-correlation function and compare them with standard model predictions in cosmology. Merely considering linear-order theory allows us to accurately describe the data on the entire available range of scales and to probe void-centric distances down to about 2 h−1Mpc. Common systematics, such as the Fingers-of-God effect, scale-dependent galaxy bias, and nonlinear clustering do not seem to play a significant role in our analysis. We constrain the growth rate of structure via the redshift-space distortion parameter β at two median redshifts, β(z̄=0.32)=0.599+0.134−0.124 and β(z̄=0.54)=0.457+0.056−0.054, with a precision that is competitive with state-of-the-art galaxy-clustering results. While the high-redshift constraint perfectly agrees with model expectations, we observe a mild 2σ deviation at z̄=0.32, which increases to 3σ when the data is restricted to the lowest available redshift range of 0.15<z<0.33.

Designing an inflation galaxy survey: How to measure σ(fNL)∼1 using scale-dependent galaxy bias

The most promising method for measuring primordial non-Gaussianity in the post-Planck era is to detect large-scale, scale-dependent galaxy bias. Considering the information in the galaxy power spectrum, we here derive the properties of a galaxy clustering survey that would optimize constraints on primordial non-Gaussianity using this technique. Specifically, we ask the question what survey design is needed to reach a precision $\sigma(f_{\rm NL}^{\rm loc}) \approx 1$. To answer this question, we calculate the sensitivity to $f_{\rm NL}^{\rm loc}$ as a function of galaxy number density, redshift accuracy and sky coverage. We include the multitracer technique, which helps minimize cosmic variance noise, by considering the possibility of dividing the galaxy sample into stellar mass bins. We show that the ideal survey for $f_{\rm NL}^{\rm loc}$ looks very different than most galaxy redshift surveys scheduled for the near future. Since those are more or less optimized for measuring the BAO scale, they typically require spectroscopic redshifts. On the contrary, to optimize the $f_{\rm NL}^{\rm loc}$ measurement, a deep, wide, multi-band imaging survey is preferred. An uncertainty $\sigma(f_{\rm NL}^{\rm loc}) = 1$ can be reached with a full-sky survey that is complete to an $i$-band AB magnitude $i \approx 23$ and has a number density $\sim 8$ arcmin$^{-2}$. Requirements on the multi-band photometry are set by a modest photo-$z$ accuracy $\sigma(z)/(1+z) < 0.1$ and the ability to measure stellar mass with a precision $\sim 0.2$ dex or better (or another proxy for halo mass with equivalent scatter). While here we focus on the information in the power spectrum, even stronger constraints can potentially be obtained with the galaxy bispectrum.

Cosmological measurements with general relativistic galaxy correlations

We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the cosmological information present in the lensing convergence and in the gravitational potential terms describing the so-called ``relativistic effects'', and we find that, while smaller than the information contained in intrinsic galaxy clustering, it is not negligible. We investigate how neglecting them does bias cosmological measurements performed by future spectroscopic and photometric large-scale surveys such as SKA and Euclid. We perform a Fisher analysis using the CLASS code, modified to include scale-dependent galaxy bias and redshift-dependent magnification and evolution bias. Our results show that neglecting relativistic terms, especially lensing convergence, introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring the matter content of the Universe and primordial non-Gaussianity parameters. The analysis suggests a possible substantial systematic error in cosmological parameter constraints. Therefore, we argue that radial correlations and integrated relativistic terms need to be taken into account when forecasting the constraining power of future large-scale number counts of galaxy surveys.

Recovering dark-matter clustering from galaxies with Gaussianization

The Gaussianization transform has been proposed as a method to remove the issues of scale-dependent galaxy bias and nonlinearity from galaxy clustering statistics, but these benefits have yet to be thoroughly tested for realistic galaxy samples. In this paper, we test the effectiveness of the Gaussianization transform for different galaxy types by applying it to realistic simulated blue and red galaxy samples. We show that in real space, the shapes of the Gaussianized power spectra of both red and blue galaxies agree with that of the underlying dark matter, with the initial power spectrum, and with each other to smaller scales than do the statistics of the usual (untransformed) density field. However, we find that the agreement in the Gaussianized statistics breaks down in redshift space. We attribute this to the fact that red and blue galaxies exhibit very different fingers of god in redshift space. After applying a finger-of-god compression, the agreement on small scales between the Gaussianized power spectra is restored. We also compare the Gaussianization transform to the clipped galaxy density field and find that while both methods are effective in real space, they have more complicated behaviour in redshift space. Overall, we find that Gaussianization can be useful in recovering the shape of the underlying dark matter power spectrum to k ~ 0.5 h/Mpc and of the initial power spectrum to k ~ 0.4 h/Mpc in certain cases at z = 0.

On separate universes

The separate universe conjecture states that in General Relativity a density perturbation behaves locally (i.e. on scales much smaller than the wavelength of the mode) as a separate universe with different background density and curvature. We prove this conjecture for a spherical compensated tophat density perturbation of arbitrary amplitude and radius in ΛCDM. We then use Conformal Fermi Coordinates to generalize this result to scalar perturbations of arbitrary configuration and scale in a general cosmology with a mixture of fluids, but to linear order in perturbations. In this case, the separate universe conjecture holds for the isotropic part of the perturbations. The anisotropic part on the other hand is exactly captured by a tidal field in the Newtonian form. We show that the separate universe picture is restricted to scales larger than the sound horizons of all fluid components. We then derive an expression for the locally measured matter bispectrum induced by a long-wavelength mode of arbitrary wavelength, a new result which in standard perturbation theory is equivalent to a relativistic second-order calculation. We show that nonlinear gravitational dynamics does not generate observable contributions that scale like local-type non-Gaussianity flocNL, and hence does not contribute to a scale-dependent galaxy bias Δ b ∝ k−2 on large scales; rather, the locally measurable long-short mode coupling assumes a form essentially identical to subhorizon perturbation theory results, once the long-mode density perturbation is replaced by the synchronous-comoving gauge density perturbation. Apparent flocNL-type contributions arise through projection effects on photon propagation, which depend on the specific large-scale structure tracer and observable considered, and are in principle distinguishable from the local mode coupling induced by gravity. We conclude that any observation of flocNL beyond these projection effects signals a departure from standard single-clock inflation.

3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis

Upcoming spectroscopic galaxy surveys are extremely promising to help in addressing the major challenges of cosmology, in particular in understanding the nature of the dark universe. The strength of these surveys comes from their unprecedented depth and width. Optimal extraction of their three-dimensional information is of utmost importance to best constrain the properties of the dark universe. Although there is theoretical motivation and novel tools to explore these surveys using the 3D spherical Fourier-Bessel (SFB) power spectrum of galaxy number counts $C_\ell(k,k^\prime)$, most survey optimisations and forecasts are based on the tomographic spherical harmonics power spectrum $C^{(ij)}_\ell$. We performed a new investigation of the information that can be extracted from the tomographic and 3D SFB techniques by comparing the forecast cosmological parameter constraints obtained from a Fisher analysis in the context of planned stage IV wide-field galaxy surveys. The comparison was made possible by careful and coherent treatment of non-linear scales in the two analyses. Nuisance parameters related to a scale- and redshift-dependent galaxy bias were also included for the first time in the computation of both the 3D SFB and tomographic power spectra. Tomographic and 3D SFB methods can recover similar constraints in the absence of systematics. However, constraints from the 3D SFB analysis are less sensitive to unavoidable systematics stemming from a redshift- and scale-dependent galaxy bias. Even for surveys that are optimised with tomography in mind, a 3D SFB analysis is more powerful. In addition, for survey optimisation, the figure of merit for the 3D SFB method increases more rapidly with redshift, especially at higher redshifts, suggesting that the 3D SFB method should be preferred for designing and analysing future wide-field spectroscopic surveys.

On the baryon acoustic oscillation amplitude as a probe of radiation density

The baryon acoustic oscillation (BAO) feature in the distribution of galaxies has been widely studied as an excellent standard ruler for probing cosmic distances and expansion history, and hence dark energy. In contrast, the amplitude of the BAO feature has received relatively little study, mainly due to limited signal-to-noise, and complications due to galaxy biasing, effects of non-linear clustering and dependence on several cosmological parameters. As expected, the amplitude of the BAO feature is sensitive to the cosmic baryon fraction: for standard radiation content, the cosmic microwave background (CMB) acoustic peaks constrain this precisely and the BAO amplitude is largely a redundant cross-check. However, the CMB mainly constrains the redshift of matter-radiation equality, z_eq, and the baryon/photon ratio: if a non-standard radiation density N_eff is allowed, increasing N_eff while matching the CMB peaks leads to a reduced baryon fraction and a lower relative BAO amplitude. We construct an observable for the relative area of the BAO feature from the galaxy correlation function (Eq.~8); from linear-theory models, we find that this is mainly sensitive to N_eff and quite insensitive to other cosmological parameters. More detailed work from N-body simulations will be needed to constrain the effects of non-linearity and scale-dependent galaxy bias on this observable.

Modelling the anisotropic two-point galaxy correlation function on small scales and single-probe measurements of H(z), DA(z) and f(z) 8(z) from the Sloan Digital Sky Survey DR7 luminous red galaxies

We present a simple and efficient phenomenological model for the two-dimensional two-point galaxy correlation function that works well over a wide range of scales, from large scales down to scales as small as 25Mpc/h. Our model incorporates nonlinear effects, a scale-dependent galaxy bias on small scales, and allows the redshift-space distortions to be scale and direction dependent. We validate our model using LasDamas mock catalogs, and apply it to the Sloan Digital Sky Survey (SDSS) DR7 Luminous Red Galaxies (LRGs). Using only the monopole and quadrupole of the correlation function measured from the SDSS DR7 LRGs, we obtain improved measurements H(z)r_s(z_d)/c=0.0433\pm 0.0042, D_A(z)/r_s(z_d)=6.59\pm 0.46, and f(z)sigma_8(z)=0.429\pm 0.089 at z=0.35, using the scale range of 25<s<120Mpc/h. We expect our results and model to be useful in tightening dark energy and gravity constraints from the full analysis of current and future galaxy clustering data.

Cosmological parameter constraints from galaxy–galaxy lensing and galaxy clustering with the SDSS DR7

Recent studies have shown that the cross-correlation coefficient between galaxies and dark matter is very close to unity on scales outside a few virial radii of galaxy halos, independent of the details of how galaxies populate dark matter halos. This finding makes it possible to determine the dark matter clustering from measurements of galaxy-galaxy weak lensing and galaxy clustering. We present new cosmological parameter constraints based on large-scale measurements of spectroscopic galaxy samples from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7). We generalise the approach of Baldauf et al. (2010) to remove small scale information (below 2 and 4 Mpc/h for lensing and clustering measurements, respectively), where the cross-correlation coefficient differs from unity. We derive constraints for three galaxy samples covering 7131 sq. deg., containing 69150, 62150, and 35088 galaxies with mean redshifts of 0.11, 0.28, and 0.40. We clearly detect scale-dependent galaxy bias for the more luminous galaxy samples, at a level consistent with theoretical expectations. When we vary both \sigma_8 and \Omega_m (and marginalise over non-linear galaxy bias) in a flat LCDM model, the best-constrained quantity is \sigma_8 (\Omega_m/0.25)^{0.57}=0.80 +/- 0.05 (1-sigma, stat. + sys.), where statistical and systematic errors have comparable contributions, and we fixed n_s=0.96 and h=0.7. These strong constraints on the matter clustering suggest that this method is competitive with cosmic shear in current data, while having very complementary and in some ways less serious systematics. We therefore expect that this method will play a prominent role in future weak lensing surveys. When we combine these data with WMAP7 CMB data, constraints on \sigma_8, \Omega_m, H_0, w_{de} and \sum m_{\nu} become 30--80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.

Can we really measure ƒNL from the galaxy power spectrum?

Abstract The scale-dependent galaxy bias generated by primordial non-Gaussianity (PNG) can be used to detect and constrain deviations from standard single-field inflation. The strongest signal is expected in the local model for PNG, where the amplitude of non-Gaussianity can be expressed by a set of parameters (ƒNL, gNL, etc.). Current observational constraints from galaxy clustering on ƒNL and gNL assume that the others PNG parameters are vanishing. Using two sets of cosmological N-body simulations where both fNL and gNL are non-zero, we show that this strong assumption generally leads to biased estimates and spurious redshift dependencies of the parameters. Additionally, if the signs of ƒNL and gNL are opposite, the amplitude of the scale-dependent bias is reduced, possibly leading to a false null detection. Finally, we show that model selection techniques like the Bayesian evidence can (and should) be used to determine if more than one PNG parameter is required by the data.

Accurate predictions for the scale-dependent galaxy bias from primordial non-Gaussianity

The large-scale clustering of galaxies can serve as a probe of primordial non-Gaussianity in the Universe competitive with the anisotropies of the CMB. Here, we present improved theoretical predictions which include an important, previously overlooked correction to the bias. We demonstrate that the new predictions are able to reproduce the results of N-body simulations, explaining the significant departures seen from previous theoretical results. These refined predictions open the way to accurate constraints on primordial physics with large-scale structure surveys.