Matter Density Fluctuations Research Articles

Growth of matter fluctuations in [formula omitted] gravity

In this work, I present for the first time the analysis concerning the growth of matter fluctuations in the framework of f(R,T) modified gravity where I presume f(R,T)=R+λT, where R denote the Ricci scalar, T the trace of energy momentum tensor and λ a constant. I first solve the Friedman equations assuming a dust universe (ω=0) for the Hubble parameter H(z) and then employ it in the equation of matter density fluctuations δ(z) to solve for δ(z) and the growth rate f(z). Next, I proceed to show the behavior of f(z) and δ(z) with redshift for some values of λ with observational constraints. Finally, following the prescription of [31], I present an analytical expression for the growth index γ which is redshift dependent and the expression reduces to 3/5 for λ=0, which is the growth index for a dust universe.

Local Primordial Non-Gaussianities and super-sample variance

Fluctuations with wavelengths larger than the volume of a galaxy survey affect the measurement of the galaxy power spectrum within the survey itself. In the presence of local Primordial Non-Gaussianities (PNG), in addition to super-sample matter density and tidal fluctuations, the large-scale gravitational potential also induces a modulation of the observed power spectrum. In this work we investigate this modulation by computing for the first time the response of the redshift-space galaxy power spectrum to the presence of a long wavelength gravitational potential, fully accounting for the stochastic contributions. For biased tracers new response functions arise due to couplings between the small-scale fluctuations in the density, velocity and gravitational fields, the latter through scale dependent bias operators, and the large-scale gravitational potential. We study the impact of the super-sample modes on the measurement of the amplitude of the primordial bispectrum of the local-shape, fNLloc, accounting for modulations of both the signal and the covariance of the galaxy power spectrum by the long modes. Considering DESI-like survey specifications, we show that in most cases super-sample modes cause little or no degradation of the constraints, and could actually reduce the errorbars on fNLloc by (10–30)%, if external information on the bias parameters is available.

A tomographic map of the large-scale matter distribution using the eBOSS—Stripe 82 Lyα forest

The Lyman-α (hereafter Lyα) forest is a probe of large-scale matter density fluctuations at high redshift, z > 2.1. It consists of H I absorption spectra along individual lines-of-sight. If the line-of-sight density is large enough, 3D maps of H I absorption can be inferred by tomographic reconstruction. In this article, we investigate the Lyα forest available in the Stripe 82 field (220 deg2), based on the quasar spectra from SDSS Data Release DR16. The density of observed quasar spectra is 37 deg−2 with a mean pixel signal-to-noise ratio of two per angstrom. This study provides an intermediate case between the average SDSS density and that of the much denser but smaller CLAMATO survey. We derive a 3D map of large-scale matter fluctuations from these data, using a Wiener filter technique. The total volume of the map is 0.94 h−3 Gpc3. Its resolution is 13 h−1 Mpc, which is related to the mean transverse distance between nearest lines-of-sight. From this map, we provide a catalog of voids and protocluster candidates in the cosmic web. The map-making and void catalog are compared to simulated eBOSS Stripe 82 observations. A stack over quasar positions provides a visualization of the Lyα forest-quasar cross-correlation. This tomographic reconstruction constitutes the largest-volume high-redshift 3D map of matter fluctuations.

The 21-cm signals from ultracompact minihaloes as a probe of primordial small-scale fluctuations

ABSTRACT Ultracompact minihaloes (UCMHs) can form after the epoch of matter–radiation equality, if the density fluctuations of dark matter have significantly large amplitude on small scales. The constraint on the UCMH abundance allows us to access such small-scale fluctuations. In this paper, we present that, through the measurement of 21-cm fluctuations before the epoch of reionization, we can obtain a constraint on the UCMH abundance. We calculate the 21-cm signal from UCMHs and show that UCMHs provide the enhancement of the 21-cm fluctuations. We also investigate the constraint on the UCMH abundance and small-scale curvature perturbations. Our results indicate that the upcoming 21-cm observation, the Square Kilometre Array (SKA), provides the constraint on amplitude of primordial curvature power spectrum, ${\cal A}_{\zeta } \lesssim 10^{-6}$ on 100 ≲ k ≲ 1000 Mpc−1. Although it is not stronger than the one from the non-detection of gamma-rays induced by dark matter annihilation in UCMHs, the constraint by the SKA will be important because this constraint is independent of the dark matter particle model.

Relativistic effects in the large-scale structure with effective dark energy fluids

We study the imprints of an effective dark energy fluid in the large scale structure of the universe through the observed angular power spectrum of galaxies in the relativistic regime. We adopt the phenomenological approach that introduces two parameters {Q,η} at the level of linear perturbations and allow to take into account the modified clustering (or effective gravitational constant) and anisotropic stress appearing in models beyond ΛCDM . We characterize the effective dark energy fluid by an equation of state parameter w=−0.95 and various sound speed cases in the range 10−6⩽ cs2⩽ 1, thus covering K-essence and quintessence cosmologies. We calculate the angular power spectra of standard and relativistic effects for these scenarios under the {Q,η} parametrization, and we compare these relative to a fiducial ΛCDM cosmology. We find that, overall, deviations relative to ΛCDM are stronger at low redshift since the behavior of the dark energy fluid can mimic the cosmological constant during matter domination era but departs during dark energy domination. In particular, at z=0.1 the matter density fluctuations are suppressed by up to ∼3% for the quintessence-like case, while redshift-space distortions and Doppler effect can be enhanced by ∼15% at large scales for the lowest sound speed scenario. On the other hand, at z=2 we find deviations of up to ∼5% in gravitational lensing, whereas the Integrated Sachs-Wolfe effect can deviate up to ∼17%. Furthermore, when considering an imperfect dark energy fluid scenario, we find that all effects are insensitive to the presence of anisotropic stress at low redshift, and only the Integrated Sachs-Wolfe effect can detect this feature at z=2 and very large scales.

Consistency of the local Hubble constant with the cosmic microwave background

A significant tension has become manifest between the current expansion rate of our Universe measured from the cosmic microwave background by the Planck satellite and from local distance probes, which has prompted for interpretations of that as evidence of new physics. Within conventional cosmology a likely source of this discrepancy is identified here as a matter density fluctuation around the cosmic average of the 40 Mpc environment in which the calibration of Supernovae Type Ia separations with Cepheids and nearby absolute distance anchors is performed. Inhomogeneities on this scale easily reach 40% and more. In that context, the discrepant expansion rates serve as evidence of residing in an underdense region of δenv≈−0.5±0.1. The probability for finding this local expansion rate given the Planck data lies at the 95% confidence level. Likewise, a hypothetical equivalent local data set with mean expansion rate equal to that of Planck, while statistically favoured, would not gain strong preference over the actual data in the respective Bayes factor. These results therefore suggest borderline consistency between the local and Planck measurements of the Hubble constant. Generally accounting for the environmental uncertainty, the local measurement may be reinterpreted as a constraint on the cosmological Hubble constant of H0=74.7−4.2+5.8 km/s/Mpc. The current simplified analysis may be augmented with the employment of the full available data sets, an impact study for the immediate ≲10 Mpc environment of the distance anchors, more prone to inhomogeneities, as well as expansion rates measured by quasar lensing, gravitational waves, currently limited to the same 40 Mpc region, and local galaxy distributions.

New constraints on the mass bias of galaxy clusters from the power spectra of the thermal Sunyaev–Zeldovich effect and cosmic shear

Abstract The thermal Sunyaev–Zeldovich (tSZ) power spectrum is a powerful probe of the present-day amplitude of matter density fluctuations, and has been measured up to $\ell \approx 10^3$ from the Planck data. The largest systematic uncertainty in the interpretation of this data is the so-called “mass bias” parameter B, which relates the true halo mass to the mass proxy used by the Planck team as $M\,_{\rm 500c}^{\rm Planck}=M\,_{\rm 500c}^{\rm true}/B$. Since the power spectrum of the cosmic weak lensing shear is also sensitive to the amplitude of matter density fluctuations via $S_8\equiv \sigma _8 \Omega _{\rm m}^{\alpha }$ with $\alpha \sim 0.5$, we can break the degeneracy between the mass bias and the cosmological parameters by combining the tSZ and cosmic shear power spectra. In this paper, we perform a joint likelihood analysis of the tSZ power spectrum from Planck and the cosmic shear power spectrum from Subaru Hyper Suprime-Cam. Our analysis does not use the primordial cosmic microwave background (CMB) information. We obtain a new constraint on the mass bias as $B = 1.37 ^{+0.15}_{-0.23}$ or $(1-b) = B^{-1}=0.73^{+0.08}_{-0.13}$ ($68\%$ confidence limit), for $\sigma _8 < 0.9$. This value of B is lower than that needed to reconcile the tSZ data with the primordial CMB and CMB lensing data, i.e., $B = 1.64 \pm 0.19$, but is consistent with the mass bias expected from hydrodynamical simulations, $B = 1.28 \pm 0.20$. Thus our results indicate that the mass bias is consistent with the non-thermal pressure support from mass accretion of galaxy clusters via the cosmic structure formation, and that the cosmologies inferred from the tSZ and the cosmic shear are consistent with each other.

Absorption in the 21-cm Line in Primordial Matter Density Fluctuations at the Stage of Their Nonlinear Compression

The mechanisms of absorption formation in the cosmic microwave background (CMB) spectrum at the frequency of the 21-cm line of the transition between the ground-state hyperfine sublevels of the hydrogen atom are analyzed. We show that a strong nonlinearity at the compression stage of primordial matter density fluctuations can give rise to a significant (in depth) absorption even before the explosions of the first stars. In this case, the main effect is due to the heating of matter in a certain narrow range of temperatures under cloud compression. We consider a steady-state radiative transfer in the 21-cm line in a medium that represents a contracting primordial matter density fluctuation at a given redshift z modeled by a homogeneous spherically symmetric cloud in the state of collapse with an adiabatic change in the gas temperature. For a sequence of cloud states with different degrees of compression we have calculated the frequency profiles of the line in the flux of radiation emerging from the cloud. In the initial state we specify the cloud radius r0, while the gas density is assumed to be equal to the mean cosmological density for a given redshift. We show that for a separate cloud at z = 20, r0 = 1 kpc, and a degree of radius compression of 1.9 the absorption depth in the line center can reach 0.9 K. When averaged over an ensemble of clouds, the central frequency of the line and its width are determined by the details of the fluctuation evolution dynamics.

The effective field theory of large scale structure at three loops

We study the power spectrum of dark matter density fluctuations in the framework of the Effective Field Theory of Large Scale Structures (EFTofLSS) up to three loop orders. We show that the extra coefficients in the EFT are sufficient to match numerical simulations with percent accuracy when a generic renormalization prescription is implemented (allowing for running of the individual counter-terms). We show that the level of accuracy increases with respect to the two loop results, up to k ≃ 0.4 h Mpc−1 at redshift z=0, although the overall improvement is somewhat marginal. At the same time, we argue there is evidence that the behavior of the loop expansion in the EFTofLSS is typical of an asymptotic series, already on the brink of its maximum predictive power (at z=0). Hence, the inclusion of higher orders will likely deteriorate the matching to data, even at moderate values of k. Part of the reason for this behavior is due to large contributions to the (renormalized) power spectrum at three loop order from mildly non-linear scales, even after the UV counter-terms are included. In conclusion, the EFTofLSS to three loop orders provides the best approximation to the (deterministic part of the) power spectrum in the weakly non-linear regime at z=0, and higher loops are not expected to improve our level of accuracy.

Cosmology with dropout selection: straw-man surveys & CMB lensing

We seek to prove the means, motive and opportunity of 'dropout' selected 2 ⩽ z ⩽ 5 galaxies for large-scale structure. Together with acquired low-z tracers, these samples would map practically every linear mode and facilitate a tomographic decomposition of the Cosmic Microwave Background (CMB) lensing kernel over an unprecedented volume. With this, one may infer (the time evolution of) matter density fluctuations and perform compelling tests of horizon-scale General Relativity, neutrino masses and Inflation—viz., curvature, running of the spectral index and a scale-dependent halo bias induced by (local) primordial non-Gaussianity. This is facilitated by the order-of-magnitude increase in sensitivity achieved by planned CMB, optical-to-near-infrared imaging and spectroscopy. Focusing on traditional color-color—rather than photometric redshift—selection, we estimate the expected completeness, contamination, and spectroscopic survey speed of tailored Lyman-break galaxy (LBG) samples. With these in hand, we forecast the potential of CMB lensing cross-correlation, `clustering redshifts' and Redshift-Space Distortions (RSD) analyses. In particular, we estimate: the depth dependence of interlopers based on CFHTLS-Archive-Research Survey (CARS) data and propagate this to biases in cosmology; a simple relation for the dependence of the linear galaxy bias on redshift and depth; new inferences of non-linear halo bias at these redshifts using legacy data; detailed forecasts of LBG spectra as would be observed by the Dark Energy Spectroscopic Instrument, Prime Focus Spectrograph, and their successors. We further assess the relative competitiveness of these spectroscopic facilities based on an intuitive figure-of-merit and define modern equivalents to traditional color selection criteria for the Large Synoptic Survey Telescope, where necessary. We confirm these science cases to be compelling for achievable facilities in the next decade by defining a LBG sample of increasing Lyman-α equivalent width with redshift, which delivers both percent-level RSD constraints on the growth rate at high-z and measurements of CMB lensing cross-correlation at z=3 and 4 with a significance measured in the hundreds, given sufficient area overlap. Finally, we discuss the limitations of this initial exploration and provide avenues for future investigation.

Constraining neutrino mass and dark energy with peculiar velocities and lensing dispersions of Type Ia supernovae

We show that peculiar velocities of Type Ia supernovae can be used to derive constraints on the sum of neutrino masses, $\Sigma m_{\nu}$, and dark energy equation of state, $w = w_0+w_a(1-a)$, from measurements of the magnitude-redshift relation, complementary to galaxy redshift and weak lensing surveys. Light from a supernova propagates through a perturbed Universe so the luminosity distance is modified from its homogeneous prediction. This modification is proportional to the matter density fluctuation and its time derivative due to gravitational lensing and peculiar velocity respectively. At low redshifts, the peculiar velocity signal dominates while at high redshifts lensing does. We show that using lensing and peculiar velocity of supernovae from the upcoming surveys WFIRST and ZTF, without other observations, we can constrain $\Sigma m_{\nu} \lesssim 0.31$ eV, $\sigma(w_0) \lesssim 0.02$, and ${\sigma(w_a)} \lesssim 0.18$ ($1-\sigma$ CL) in the $\Sigma m_{\nu}$-$w_0$-$w_a$ parameter space, where all the other cosmological parameters are fixed. We find that adding peculiar velocity information from low redshifts shrinks the volume of the parameter ellipsoid in this space by $\sim 33$%. We also allow $\Omega_{\text{CDM}}$ to vary as well as $\Sigma m_{\nu}$, $w_0$ and $w_a$, and demonstrate how these constraints degrade as a consequence.

Cosmological evolutions in Tsujikawa model of f(R) Gravity

We concentrate on the cosmological properties in the Tsujikawa model (TM) of viable $f(R)$ gravity with the dynamical background evolution and linear perturbation theory by using the CosmoMC package. We study the constraints of the cosmological variables along with the model parameter from the current observational data. In particular, we show that the matter density fluctuation is suppressed and the constraint of the neutrino mass sum is relaxed in the TM, which are similar to other viable $f(R)$ models. In addition, we discuss the parameters of the deceleration and equation of state for dark energy in the TM and compare them with those in the $\Lambda$CDM model.

Revisiting Ryskin’s model of cosmic acceleration

Cosmic backreaction as an additional source of the expansion of the universe has been a debate topic since the discovery of cosmic acceleration. The major concern is whether the self interaction of small-scale nonlinear structures would source gravity on very large scales. Gregory Ryskin argued against the additional inclusion of gravitational interaction energy of astronomical objects, whose masses are mostly inferred from gravitational effects and hence should already contain all sources with long-range gravity forces. Ryskin proposed that the backreaction contribution to the energy momentum tensor comes instead from the rest of the universe beyond the observable patch. Ryskin’s model solves the fine-tuning problem and is in good agreement with the Hubble diagram of Type Ia supernovae. In this article we revisit Ryskin’s model and show that it is inconsistent with at least one of the following statements: (i) the universe is matter-dominated at low redshift (z ≲ 2); (ii) the universe is radiation-dominated at sufficiently high redshift; (iii) matter density fluctuations are tiny (≲10−4) at the recombination epoch.

Constraining degenerate higher-order scalar-tensor theories with linear growth of matter density fluctuations

We investigate the potential of cosmological observations, such as galaxy surveys, for constraining degenerate higher-order scalar-tensor (DHOST) theories, focusing in particular on the linear growth of the matter density fluctuations. We develop a formalism to describe the evolution of the matter density fluctuations during the matter dominated era and in the early stage of the dark energy dominated era in DHOST theories, and give an approximate expression for the gravitational growth index in terms of several parameters characterizing the theory and the background solution under consideration. By employing the current observational constraints on the growth index, we obtain a new constraint on a parameter space of DHOST theories. Combining our result with other constraints obtained from the Newtonian stellar structure, we show that the degeneracy between the effective parameters of DHOST theories can be broken without using the Hulse-Taylor pulsar constraint.

Matter power spectra in viable f(R) gravity models with dynamical background

We study the matter power spectra in the viable f(R) gravity models with the dynamical background evolution and linear perturbation theory by using the CosmoMC package. We show that these viable f(R) models generally shorten the age of the universe and suppress the matter density fluctuation. We examine the allowed ranges of the model parameters and the constraints of the cosmological variables from the current observational data, and find that the dynamical evolution of rho _{DE}(z) plays an important role to constrain the neutrino masses.

Breaking degeneracies in modified gravity with higher (than 2nd) order weak-lensing statistics

General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is cosmological, scales. Many extensions to GR have been studied that are not yet ruled out by the data, including by that of the recent direct gravitational wave detections. Degeneracies among the standard model (ΛCDM) and modified gravity (MG) models, as well as among different MG parameters, must be addressed in order to best exploit information from current and future surveys and to unveil the nature of dark energy. We propose various higher-order statistics in the weak-lensing signal as a new set of observables able to break degeneracies between massive neutrinos and MG parameters. We have tested our methodology on so-called f(R) models, which constitute a class of viable models that can explain the accelerated universal expansion by a modification of the fundamental gravitational interaction. We have explored a range of these models that still fit current observations at the background and linear level, and we show using numerical simulations that certain models which include massive neutrinos are able to mimic ΛCDM in terms of the 3D power spectrum of matter density fluctuations. We find that depending on the redshift and angular scale of observation, non-Gaussian information accessed by higher-order weak-lensing statistics can be used to break the degeneracy between f(R) models and ΛCDM. In particular, peak counts computed in aperture mass maps outperform third- and fourth-order moments.

Density split statistics: Cosmological constraints from counts and lensing in cells in DES Y1 and SDSS data

We derive cosmological constraints from the probability distribution function (PDF) of evolved large-scale matter density fluctuations. We do this by splitting lines of sight by density based on their count of tracer galaxies, and by measuring both gravitational shear around and counts-in-cells in overdense and underdense lines of sight, in Dark Energy Survey (DES) First Year and Sloan Digital Sky Survey (SDSS) data. Our analysis uses a perturbation theory model (see companion paper Friedrich at al.) and is validated using N-body simulation realizations and log-normal mocks. It allows us to constrain cosmology, bias and stochasticity of galaxies w.r.t. matter density and, in addition, the skewness of the matter density field. From a Bayesian model comparison, we find that the data weakly prefer a connection of galaxies and matter that is stochastic beyond Poisson fluctuations on <=20 arcmin angular smoothing scale. The two stochasticity models we fit yield DES constraints on the matter density $\Omega_m=0.26^{+0.04}_{-0.03}$ and $\Omega_m=0.28^{+0.05}_{-0.04}$ that are consistent with each other. These values also agree with the DES analysis of galaxy and shear two-point functions (3x2pt) that only uses second moments of the PDF. Constraints on $\sigma_8$ are model dependent ($\sigma_8=0.97^{+0.07}_{-0.06}$ and $0.80^{+0.06}_{-0.07}$ for the two stochasticity models), but consistent with each other and with the 3x2pt results if stochasticity is at the low end of the posterior range. As an additional test of gravity, counts and lensing in cells allow to compare the skewness $S_3$ of the matter density PDF to its LCDM prediction. We find no evidence of excess skewness in any model or data set, with better than 25 per cent relative precision in the skewness estimate from DES alone.

Impact of a primordial magnetic field on cosmic microwave background B modes with weak lensing

We discuss the manner in which the primordial magnetic field (PMF) suppresses the cosmic microwave background (CMB) $B$ mode due to the weak-lensing (WL) effect. The WL effect depends on the lensing potential (LP) caused by matter perturbations, the distribution of which at cosmological scales is given by the matter power spectrum (MPS). Therefore, the WL effect on the CMB $B$ mode is affected by the MPS. Considering the effect of the ensemble average energy density of the PMF, which we call "the background PMF," on the MPS, the amplitude of MPS is suppressed in the wave number range of $k>0.01~h$ Mpc$^{-1}$.The MPS affects the LP and the WL effect in the CMB $B$ mode; however, the PMF can damp this effect. Previous studies of the CMB $B$ mode with the PMF have only considered the vector and tensor modes. These modes boost the CMB $B$ mode in the multipole range of $\ell > 1000$, whereas the background PMF damps the CMB $B$ mode owing to the WL effect in the entire multipole range. The matter density in the Universe controls the WL effect. Therefore, when we constrain the PMF and the matter density parameters from cosmological observational data sets, including the CMB $B$ mode, we expect degeneracy between these parameters. The CMB $B$ mode also provides important information on the background gravitational waves, inflation theory, matter density fluctuations, and the structure formations at the cosmological scale through the cosmological parameter search. If we study these topics and correctly constrain the cosmological parameters from cosmological observations including the CMB $B$ mode, we need to correctly consider the background PMF.

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: structure growth rate measurement from the anisotropic quasar power spectrum in the redshift range 0.8 &lt; z &lt; 2.2

We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample (DR14Q). We measure the redshift space distortions using the power spectrum monopole, quadrupole and hexadecapole inferred from 148,659 quasars between redshifts 0.8 and 2.2 covering a total sky footprint of 2112.9 deg$^2$. We constrain the logarithmic growth of structure times the amplitude of dark matter density fluctuations, $f\sigma_8$, and the Alcock-Paczynski dilation scales which allow constraints to be placed on the angular diameter distance $D_A(z)$ and the Hubble $H(z)$ parameter. At the effective redshift of $z_{\rm eff}=1.52$, $f\sigma_8(z_{\rm eff})=0.420\pm0.076$, $H(z_{\rm eff})=[162\pm 12]\, (r_s^{\rm fid}/r_s)\,{\rm km\, s}^{-1}{\rm Mpc}^{-1}$, and $D_A(z_{\rm eff})=[1.85\pm 0.11]\times10^3\,(r_s/r_s^{\rm fid})\,{\rm Mpc}$, where $r_s$ is the comoving sound horizon at the baryon drag epoch and the superscript `fid' stands for its fiducial value. The errors take into account the full error budget, including systematics and statistical contributions. These results are in full agreement with the current $\Lambda$-Cold Dark Matter ($\Lambda$CDM) cosmological model inferred from Planck measurements. Finally, we compare our measurements with other eBOSS companion papers and find excellent agreement, demonstrating the consistency and complementarity of the different methods used for analysing the data.

Testing the consistency of three-point halo clustering in Fourier and configuration space

We compare reduced three-point correlations $Q$ of matter, haloes (as proxies for galaxies) and their cross correlations, measured in a total simulated volume of $\sim100 \ (h^{-1} \text{Gpc})^{3}$, to predictions from leading order perturbation theory on a large range of scales in configuration space. Predictions for haloes are based on the non-local bias model, employing linear ($b_1$) and non-linear ($c_2$, $g_2$) bias parameters, which have been constrained previously from the bispectrum in Fourier space. We also study predictions from two other bias models, one local ($g_2=0$) and one in which $c_2$ and $g_2$ are determined by $b_1$ via an approximately universal relation. Overall, measurements and predictions agree when $Q$ is derived for triangles with $(r_1r_2r_3)^{1/3} \gtrsim 60 h^{-1}\text{Mpc}$, where $r_{1-3}$ are the sizes of the triangle legs. Predictions for $Q_{matter}$, based on the linear power spectrum, show significant deviations from the measurements at the BAO scale (given our small measurement errors), which strongly decrease when adding a damping term or using the non-linear power spectrum, as expected. Predictions for $Q_{halo}$ agree best with measurements at large scales when considering non-local contributions. The universal bias model works well for haloes and might therefore be also useful for tightening constraints on $b_1$ from $Q$ in galaxy surveys. Such constraints are independent of the amplitude of matter density fluctuation ($\sigma_8$) and hence break the degeneracy between $b_1$ and $\sigma_8$, present in galaxy two-point correlations.