Halo Bias Research Articles

Scale-dependent bias from the primordial non-Gaussianity with a Gaussian-squared field

We investigate the halo bias in the casewhere the primordial curvature fluctuations, Φ, are sourced from both a Gaussian random field and a Gaussian-squared field, asΦ(x) = ϕ(x)+ψ(x)2−⟨ψ(x)2ångle,so-called ``ungaussiton model''.We employ the peak-background split formulaand find a new scale-dependence in the halo bias inducedfrom the Gaussian-squared field.

Local stochastic non-Gaussianity and N-body simulations

Large-scale clustering of highly biased tracers of large-scale structure has emerged as one of the best observational probes of primordial non-Gaussianity of the local type (i.e. fNLlocal).This type of non-Gaussianity can be generated in multifield models of inflation such as the curvaton model.Recently, Tseliakhovich, Hirata, and Slosar showed that the clustering statistics depend qualitatively onthe ratio of inflaton to curvaton power ξ after reheating, a free parameter of the model.If ξ is significantly different from zero, so that the inflaton makes a non-negligible contribution tothe primordial adiabatic curvature, then the peak-background split ansatz predicts that the halo biaswill be stochastic on large scales.In this paper, we test this prediction in N-body simulations.We find that large-scale stochasticity is generated, in qualitative agreement with the prediction, butthat the level of stochasticity is overpredicted by ≈ 30%.Other predictions, such as ξ independence of the halo bias, are confirmed by the simulations.Surprisingly, even in the Gaussian case we do not find that halo model predictions for stochasticity agree consistently with simulations, suggesting that semi-analytic modeling of stochasticity is generallymore difficult than modeling halo bias.

Oscillating bispectra and galaxy clustering: A novel probe of inflationary physics with large-scale structure

Many models of inflation predict oscillatory features in the bispectrum of primordial fluctuations. Since it has been shown that primordial non-Gaussianity can lead to a scale-dependent halo bias, we investigate the effect of oscillations in the three-point function on the clustering of dark-matter halos. Interestingly, we find that features in the inflaton potential such as oscillations or sharp steps get imprinted in the mass dependence of the non-Gaussian halo bias. In this paper, we focus on models displaying a sharp feature in the inflaton potential as well as resonant non-Gaussianity. In both cases, we find a strong scale dependence for the non-Gaussian halo bias with a slope similar to that of the local model. In the resonant case, we find that the non-Gaussian bias oscillates with halo mass, a novel feature that is unique to this type of models. In the case of a sharp feature in the inflaton potential, we find that the clustering of halos is enhanced at the mass scale corresponding to the Fourier mode that exited the horizon when the inflaton was crossing the feature in the potential. Both of these are new effects that open the possibility of characterizing the inflationary potential with large-scale-structure surveys. We briefly discuss the prospects for detecting these non-Gaussian effects.

Scale-dependent bias from primordial non-Gaussianity with trispectrum

Abstract We study the scale-dependent bias of the halo power spectrum arising from primordial non-Gaussianity. We present an analytic result of the halo bias including up to the trispectrum contributions. We find that the scale-dependent bias opens a new possibility of probing the relation between the non-linearity parameters fNL and τNL.

Halo bias in the excursion set approach with correlated steps

In the Excursion Set approach, halo abundances and clustering are closely related. This relation is exploited in many modern methods which seek to constrain cosmological parameters on the basis of the observed spatial distribution of clusters. However, to obtain analytic expressions for these quantities, most Excursion Set based predictions ignore the fact that, although different k-modes in the initial Gaussian field are uncorrelated, this is not true in real space: the values of the density field at a given spatial position, when smoothed on different real-space scales, are correlated in a nontrivial way. We show that when the excursion set approach is extended to include such correlations, then one must be careful to account for the fact that the associated prediction for halo bias is explicitly a real-space quantity. Therefore, care must be taken when comparing the predictions of this approach with measurements in simulations, which are typically made in Fourier-space. We show how to correct for this effect, and demonstrate that ignorance of this effect in recent analyses of halo bias has led to incorrect conclusions and biased constraints.

Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding

Recent results of N-body simulations have shown that current theoretical models are not able to correctly predict the amplitude of the scale-dependent halo bias induced by primordial non-Gaussianity, for models going beyond the simplest, local quadratic case. Motivated by these discrepancies, we carefully examine three theoretical approaches based on (1) the statistics of thresholded regions, (2) a peak-background split method based on separation of scales, and (3) a peak-background split method using the conditional mass function. We first demonstrate that the statistics of thresholded regions, which is shown to be equivalent at leading order to a local bias expansion, cannot explain the mass-dependent deviation between theory and N-body simulations. In the two formulations of the peak-background split on the other hand, we identify an important, but previously overlooked, correction to the non-Gaussian bias that strongly depends on halo mass. This new term is in general significant for any primordial non-Gaussianity going beyond the simplest local fNL model. In a separate paper, we compare these new theoretical predictions with N-body simulations, showing good agreement for all simulated types of non-Gaussianity.

The dark matter haloes and host galaxies of Mg ii absorbers at z∼ 1

Strong foreground absorption features from singly-ionized Magnesium (Mg II) are commonly observed in the spectra of quasars and are presumed to probe a wide range of galactic environments. To date, measurements of the average dark matter halo masses of intervening Mg II absorbers by way of large-scale cross-correlations with luminous galaxies have been limited to z<0.7. In this work we cross-correlate 21 strong (W{\lambda}2796>0.6 {\deg}A) Mg II absorption systems detected in quasar spectra from the Sloan Digital Sky Survey Data Release 7 with ~32,000 spectroscopically confirmed galaxies at 0.7<z<1.45 from the DEEP2 galaxy redshift survey. We measure dark matter (DM) halo biases of b_G=1.44\pm0.02 and b_A=1.49\pm0.45 for the DEEP2 galaxies and Mg II absorbers, respectively, indicating that their clustering amplitudes are roughly consistent. Haloes with the bias we measure for the Mg II absorbers have a corresponding mass of 1.8(+4.2/-1.6) \times 10^12h-1M_sun, although the actual mean absorber halo mass will depend on the precise distribution of absorbers within DM haloes. This mass estimate is consistent with observations at z=0.6, suggesting that the halo masses of typical Mg II absorbers do not significantly evolve from z~1. We additionally measure the average W{\lambda}2796>0.6 \AA gas covering fraction to be f =0.5 within 60 h-1kpc around the DEEP2 galaxies, and we find an absence of coincident strong Mg II absorption beyond a projected separation of ~40 h-1kpc. Although the star-forming z>1 DEEP2 galaxies are known to exhibit ubiquitous blueshifted Mg II absorption, we find no direct evidence in our small sample linking W{\lambda}2796>0.6 \AA absorbers to galaxies with ongoing star formation.

Testing the warm dark matter paradigm with large-scale structures

We explore the impact of a LWDM cosmological scenario on the clustering properties of large-scale structure in the Universe. We do this by extending the halo model. The new development is that we consider two components to the mass density: one arising from mass in collapsed haloes, and the second from a smooth component of uncollapsed mass. Assuming that the nonlinear clustering of dark matter haloes can be understood, then from conservation arguments one can precisely calculate the clustering properties of the smooth component and its cross-correlation with haloes. We then explore how the three main ingredients of the halo calculations, the mass function, bias and density profiles are affected by WDM. We show that, relative to CDM: the mass function is suppressed by ~50%, for masses ~100 times the free-streaming mass-scale; the bias of low mass haloes can be boosted by up to 20%; core densities of haloes can be suppressed. We also examine the impact of relic thermal velocities on the density profiles, and find that these effects are constrained to scales r<1 kpc/h, and hence of little importance for dark matter tests, owing to uncertainties in the baryonic physics. We use our modified halo model to calculate the non-linear matter power spectrum, and find significant small-scale power in the model. However, relative to the CDM case, the power is suppressed. We then calculate the expected signal and noise that our set of LWDM models would give for a future weak lensing mission. We show that the models should in principle be separable at high significance. Finally, using the Fisher matrix formalism we forecast the limit on the WDM particle mass for a future full-sky weak lensing mission like Euclid or LSST. With Planck priors and using multipoles l<5000, we find that a lower limit of 2.6 keV should be easily achievable.

Nonlinear biasing and redshift-space distortions in Lagrangian resummation theory andN-body simulations

Understanding a behavior of galaxy biasing is crucial for future galaxy redshift surveys. One aim is to measure the baryon acoustic oscillations (BAOs) within the precision of a few percent level. Using 30 large cosmological N-body simulations for a standard LCDM cosmology, we study the halo biasing over a wide redshift range. We compare the simulation results with theoretical predictions proposed by Matsubara (2008) which naturally incorporate the halo bias and redshift-space distortions into their formalism of perturbation theory with a resummation technique via the Lagrangian picture. The power spectrum and correlation function of halos obtained from Lagrangian resummation theory (LRT) well agree with N-body simulation results on scales of BAOs. Especially nonlinear effects on the baryon acoustic peak of the halo correlation function are accurately explained both in real and redshift space. We find that nonlinearity and scale dependence of bias are fairly well reproduced by 1-loop LRT up to k=0.35hMpc^{-1} (z=2 and 3) within a few percent level in real space and up to k=0.1hMpc^{-1} (z=2) and 0.15hMpc^{-1} (z=3) in redshift space. Thus, the LRT is very powerful for accurately extracting cosmological information in upcoming high redshift BAO surveys.

Constraints on primordial non-Gaussianity from large scale structure probes

In this paper we measure the angular power spectra Cℓ of three high-redshift large-scale structure probes: the radio sources from the NRAO VLA Sky Survey (NVSS), the quasar catalogue of Sloan Digital Sky Survey Release Six (SDSS DR6 QSOs) and the MegaZ-LRG (DR7), the final SDSS II Luminous Red Galaxy (LRG) photometric redshift survey. We perform a global analysis of the constraints on the amplitude of primordial non-Gaussianity from these angular power spectra, as well as from their cross-correlation power spectra with the cosmic microwave background (CMB) temperature map. In particular, we include non-Gaussianity of the type arising from single-field slow roll, multifields, curvaton (local type), and those which effects on the halo clustering can be described by the equilateral template (related to higher-order derivative type non-Gaussianity) and by the enfolded template (related to modified initial state or higher-derivative interactions). When combining all data sets, we obtain limits of fNL = 48±20, fNL = 50±265 and fNL = 183±95 at 68% confidence level for local, equilateral and enfolded templates, respectively. Furthermore, we explore the constraint on the cubic correction gNLϕ3 on the bias of dark matter haloes and obtain a limit of −1.2 × 105 < gNL < 11.3 × 105 at 95% confidence level.

The non-Gaussian halo mass function with fNL, gNL and τNL

Primordial non-Gaussianity has emerged as one of the most promising probes of the inflationary epoch. While the cosmic microwave background and large-scale halo bias currently provide the most stringent constraints on the non-Gaussian parameter fNL, the abundance of dark matter halos is a complementary probe which may allow tests of Gaussianity which are independent of the precise form of non-Gaussian initial conditions. We study the halo mass function in N-body simulations with a range of non-Gaussian initial conditions. In addition to the usual fNL model, we consider gNLΦ3-type non-Gaussianity and models where the 4-point amplitude τNL is an independent parameter. We introduce a new analytic form for the halo mass function in the presence of primordial non-Gaussianity, the ``log-Edgeworth'' mass function, and find good agreement with the N-body simulations. The log-Edgeworth mass function introduces no free parameters and can be constructed from first principles for any model of primordial non-Gaussianity.

Excursion set halo mass function and bias in a stochastic barrier model of ellipsoidal collapse

We use the excursion set formalism to compute the properties of the halo mass distribution for a stochastic barrier model which encapsulates the main features of the ellipsoidal collapse of dark matter halos. Non-Markovian corrections due to the sharp filtering of the linear density field in real space are computed with the path-integral technique introduced by Maggiore and Riotto [M. Maggiore and A. Riotto, Astrophys. J. 711, 907 (2010).]. Here, we provide a detailed derivation of the results presented in [P. S. Corasaniti and I. Achitouv, Phys. Rev. Lett. 106, 241302 (2011).] and extend the mass function analysis to higher redshift. We also derive an analytical expression for the linear halo bias. We find a remarkable agreement with $N$-body simulation data from Tinker et al. [J. L. Tinker et al., Astrophys. J. 688, 709 (2008).] with differences $\ensuremath{\lesssim}5%$ over the range of mass probed by simulations. The excursion set solution from Monte Carlo generated random walks shows the same level of agreement, thus confirming the validity of the path-integral approach for the barrier model considered here. Similarly, the analysis of the linear halo bias shows deviations no greater than 20%. Overall these results indicate that the excursion set formalism in combination with a realistic modeling of the conditions of halo collapse can provide an accurate description of the halo mass distribution.

Probability of the most massive cluster under non-Gaussian initial conditions

Very massive high redshift clusters can be used to constrain and test the Lambda CDM model. Taking into account the observational constraints of Jee et al. (2009) we have calculated the probability for the most massive cluster to be found in the range (5.2-7.6)e14 M_sun, between redshifts 1.4-2.2, with a sky area of 11 sqdeg and under non-Gaussian initial conditions. Clusters constrain the non-Gaussianity on smaller scales than current cosmic microwave background or halo bias data and so can be used to test for running of the non-Gaussianity parameter f_NL.

Implications of multiple high-redshift galaxy clusters

To date, 14 high-redshift ($z&gt;1.0$) galaxy clusters with mass measurements have been observed, spectroscopically confirmed, and are reported in the literature. These objects should be exceedingly rare in the standard $\ensuremath{\Lambda}$ cold dark matter ($\ensuremath{\Lambda}\mathrm{CDM}$) model. We conservatively approximate the selection functions of these clusters' parent surveys and quantify the tension between the abundances of massive clusters as predicted by the standard $\ensuremath{\Lambda}\mathrm{CDM}$ model and the observed ones. We alleviate the tension, considering non-Gaussian primordial perturbations of the local type, characterized by the parameter ${f}_{\mathrm{NL}}$, and derive constraints on ${f}_{\mathrm{NL}}$ arising from the mere existence of these clusters. At the $95%$ confidence level, ${f}_{\mathrm{NL}}&gt;467$, with cosmological parameters fixed to their most likely WMAP5 values, or ${f}_{\mathrm{NL}}\ensuremath{\gtrsim}123$ (at $95%$ confidence) if we marginalize over prior WMAP5 parameters. In combination with ${f}_{\mathrm{NL}}$ constraints from cosmic microwave background and halo bias, this determination implies a scale dependence of ${f}_{\mathrm{NL}}$ at $\ensuremath{\simeq}3\ensuremath{\sigma}$. Given the assumptions made in the analysis, we expect any future improvements to the modeling of the non-Gaussian mass function, survey volumes, or selection functions to increase the significance of ${f}_{\mathrm{NL}}&gt;0$ found here. In order to reconcile these massive, high-$z$ clusters with ${f}_{\mathrm{NL}}=0$, their masses would need to be systematically lowered by $1.5\ensuremath{\sigma}$, or the ${\ensuremath{\sigma}}_{8}$ parameter should be $\ensuremath{\sim}3\ensuremath{\sigma}$ higher than cosmic microwave background (and large-scale structure) constraints. The existence of these objects is a puzzle: it either represents a challenge to the $\ensuremath{\Lambda}\mathrm{CDM}$ paradigm or it is an indication that the mass estimates of clusters are dramatically more uncertain than we think.

THE NONLINEAR BIASING OF THE zCOSMOS GALAXIES UP TOz∼ 1 FROM THE 10k SAMPLE

We use the overdensity field reconstructed in the volume of the COSMOS area to study the nonlinear biasing of the zCOSMOS galaxies. The galaxy overdensity field is reconstructed using the current sample of ~8500 accurate zCOSMOS redshifts at I(AB)<22.5 out to z~1 on scales R from 8 to 12 Mpc/h. By comparing the probability distribution function (PDF) of galaxy density contrast delta_g to the lognormal approximation of the PDF of the mass density contrast delta, we obtain the mean biasing function b(delta,z,R) between the galaxy and matter overdensity field and its second moments b(hat) and b(tilde) up to z~1. Over the redshift interval 0.4<z<1 the conditional mean function <delta_g|delta> = b(delta,z,R) delta is of the following characteristic shape. The function vanishes in the most underdense regions and then sharply rises in a nonlinear way towards the mean densities. <delta_g|delta> is almost a linear tracer of the matter in the overdense regions, up to the most overdense regions in which it is nonlinear again and the local effective slope of <delta_g|delta> vs. delta is smaller than unity. The <delta_g|delta> function is evolving only slightly over the redshift interval 0.4<z<1. The linear biasing parameter increases from b(hat)=1.24+/-0.11 at z=0.4 to b(hat)=1.64+/-0.15 at z=1 for the M_B<-20-z sample of galaxies. b(hat) does not show any dependence on the smoothing scale from 8 to 12 Mpc/h, but increases with luminosity. The measured nonlinearity parameter b(tilde)/b(hat) is of the order of a few percent (but it can be consistent with 0) and it does not change with redshift, the smoothing scale or the luminosity. By matching the linear bias of galaxies to the halo bias, we infer that the M_B<-20-z galaxies reside in dark matter haloes with a characteristic mass of about 3-6 x 10^12 Msol, depending on the halo bias fit.

Most massive haloes with Gumbel statistics

We present an analytical calculation of the extreme value statistics for dark matter halos - that is, the probability distribution of the most massive halo within some region of the universe of specified shape and size. Our calculation makes use of the counts-in-cells formalism for the correlation functions, and the halo bias derived from the Sheth-Tormen mass function. We demonstrate the power of the method on spherical regions, comparing the results to measurements in a large cosmological dark matter simulation and achieving good agreement. Particularly good fits are obtained for the most likely value of the maximum mass and for the high-mass tail of the distribution, relevant in constraining cosmologies by observations of most massive clusters.

Publisher’s Note: Nonlinear clustering in models with primordial non-Gaussianity: The halo model approach [Phys. Rev. D83, 043526 (2011)

We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts. The primordial non-Gaussianity is modeled as a quadratic correction to the local Gaussian potential, and is characterized by the parameter f_NL. In our formulation of the halo model we pay special attention to the effect of halo exclusion, and show that this can potentially solve the long standing problem of excess power on large scales in this model. The model depends on the mass function, clustering and density profiles of halos. We test these ingredients using a large ensemble of high-resolution Gaussian and non-Gaussian numerical simulations. In particular, we provide a first exploration of how density profiles change in the presence of primordial non-Gaussianities. We find that for f_NL positive/negative high mass halos have an increased/decreased core density, so being more/less concentrated than in the Gaussian case. We also examine the halo bias and show that, if the halo model is correct, then there is a small asymmetry in the scale-dependence of the bias on very large scales, which arises because the Gaussian bias must be renormalized. We show that the matter power spectrum is modified by ~2.5% and ~3.5% on scales k~1.0 h/Mpc at z=0 and z=1, respectively. Our halo model calculation reproduces the absolute amplitude to within 10% and the ratio of non-Gaussian to Gaussian spectra to within 1%. We also measure the matter correlation functions and find similarly good agreement between the model and the data. We anticipate that this modeling will be useful for constraining f_NL from measurements of the shear correlation function in future weak lensing surveys such as Euclid.

Scale-dependent halo bias from scale-dependent growth

We derive a general expression for the large-scale halo bias, in theories with a scale-dependent linear growth, using the excursion set formalism. Such theories include modified gravity models, and models in which the dark energy clustering is non-negligible. A scale dependence is imprinted in both the formation and evolved biases by the scale-dependent growth. Mergers are accounted for in our derivation, which thus extends earlier work which focused on passive evolution. There is a simple analytic form for the bias for those theories in which the nonlinear collapse of perturbations is approximately the same as in general relativity. As an illustration, we apply our results to a simple Yukawa modification of gravity, and use SDSS measurements of the clustering of luminous red galaxies to constrain the theory's parameters.

A generalized local ansatz and its effect on halo bias

Motivated by the properties of early universe scenarios that produce observationally large local non-Gaussianity, we perform N-body simulations with non-Gaussian initial conditions from a generalized local ansatz. The bispectra are schematically of the local shape, but with scale-dependent amplitude. We find that in such cases the size of the non-Gaussian correction to the bias of small and large mass objects depends on the amplitude of non-Gaussianity roughly on the scale of the object. In addition, some forms of the generalized bispectrum alter the scale dependence of the non-Gaussian term in the bias by a fractional power of k. These features may allow significant observational constraints on the particle physics origin of any observed local non-Gaussianity, distinguishing between scenarios where a single field or multiple fields contribute to the curvature fluctuations. While analytic predictions for the non-Gaussian bias agree qualitatively with the simulations, we find numerically a stronger observational signal than expected. This suggests that a more precise understanding of halo formation is needed to fully explain the consequences of primordial non-Gaussianity.

Nonlinear clustering in models with primordial non-Gaussianity: The halo model approach

We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts in the context of primordial non-Gaussianity that is a quadratic correction to the local Gaussian potential, characterized by the parameter ${f}_{\mathrm{NL}}$. In our formulation of the halo model we pay special attention to the effect of halo exclusion and show that this can potentially solve the long-standing problem of excess power on large scales in this model. The halo model depends on the mass function, clustering of halo centers, and the density profiles. We test these ingredients using a large ensemble of high-resolution Gaussian and non-Gaussian numerical simulations, covering ${f}_{\mathrm{NL}}={0,+100,\ensuremath{-}100}$. In particular, we provide a first exploration of how halo density profiles change in the presence of primordial non-Gaussianity. We find that for ${f}_{\mathrm{NL}}$ positive (negative) high-mass haloes have an increased (decreased) core density, so being more (less) concentrated than in the Gaussian case. We also examine the halo bias and show that, if the halo model is correct, then there is a small asymmetry in the scale dependence of the bias on very large scales, which arises because the Gaussian bias must be renormalized. We show that the matter power spectrum is modified by $\ensuremath{\sim}2.5%$ and $\ensuremath{\sim}3.5%$ on scales $k\ensuremath{\sim}1.0\text{ }h\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$ at $z=0$ and $z=1$, respectively. Our halo model calculation reproduces the absolute amplitude to within $\ensuremath{\lesssim}10%$ and the ratio of non-Gaussian to Gaussian spectra to within $\ensuremath{\lesssim}1%$. We also measure the matter correlation function and find similarly good levels of agreement between the halo model and the data. We anticipate that this modeling will be useful for constraining ${f}_{\mathrm{NL}}$ from measurements of the shear correlation function in future weak lensing surveys such as Euclid.