Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure

One of the main signatures of primordial non-Gaussianity of the local type is a scale-dependent correction to the bias of large-scale structure tracers such as galaxies or clusters, whose amplitude depends on the bias of the tracers itself. The dominant source of noise in the power spectrum of the tracers is caused by sampling variance on large scales (where the non-Gaussian signal is strongest) and shot noise arising from their discrete nature. Recent work has argued that one can avoid sampling variance by comparing multiple tracers of different bias, and suppress shot noise by optimally weighting halos of different mass. Here we combine these ideas and investigate how well the signatures of non-Gaussian fluctuations in the primordial potential can be extracted from the two-point correlations of halos and dark matter. On the basis of large $N$-body simulations with local non-Gaussian initial conditions and their halo catalogs we perform a Fisher matrix analysis of the two-point statistics. Compared to the standard analysis, optimal weighting- and multiple-tracer techniques applied to halos can yield up to one order of magnitude improvements in \fnl-constraints, even if the underlying dark matter density field is not known. We compare our numerical results to the halo model and find satisfactory agreement. Forecasting the optimal \fnl-constraints that can be achieved with our methods when applied to existing and future survey data, we find that a survey of $50h^{-1}\mathrm{Gpc}^3$ volume resolving all halos down to 10^{11}\hMsun at $z=1$ will be able to obtain \sigma_{\fnl}\sim1 (68% cl), a factor of $\sim20$ improvement over the current limits. Decreasing the minimum mass of resolved halos, increasing the survey volume or obtaining the dark matter maps can further improve these limits, potentially reaching the level of \sigma_{\fnl}\sim0.1. (abridged)Comment: V1: 23 pages, 12 figures, submitted to PRD. V2: 24 pages, added appendix and citations, matched to PRD published versio

Constraints on the Abundance of Highly Ionized Proto-Cluster Regions from the Absence of Large Voids in the Lyman Alpha Forest

Energetic feedback processes during the formation of galaxy clusters may have heated and ionized a large fraction of the intergalactic gas in proto-cluster regions. When such a highly ionized hot ``super-bubble'' falls along the sightline to a background quasar, it would be seen as a large void, with little or no absorption, in the Lyman alpha forest. We examine the spectra of 137 quasars in the Sloan Digital Sky Survey, to search for such voids, and find no clear evidence of their existence. The size distribution of voids in the range 5-70 Angstrom (corresponding to physical sizes of approximately 3-35 comoving Mpc/h) is consistent with the standard model for the Lyman alpha forest without additional hot bubbles. We adapt a physical model for HII bubble growth during cosmological reionization (Furlanetto, Zaldarriaga and Hernquist 2004), to describe the expected size-distribution of hot super-bubbles at redshift around z = 3. This model incorporates the conjoining of bubbles around individual neighboring galaxies. Using the non-detection of voids, we find that models in which the volume filling factor of hot bubbles exceeds approximately 20 percent at z=3 can be ruled out, primarily because they overproduce the number of large (40-50 Angstrom) voids. We conclude that any pre-heating mechanism that explains galaxy cluster observations must avoid heating the low-density gas in the proto-cluster regions, either by operating relatively recently (z<3) or by depositing entropy in the high-density regions.Comment: submitted to ApJ, 9 emulateapj pages with 3 figure

How to suppress the shot noise in galaxy surveys

Galaxy surveys are one of the most powerful means to extract the cosmological information and for a given volume the attainable precision is determined by the galaxy shot noise sigma_n^2 relative to the power spectrum P. It is generally assumed that shot noise is white and given by the inverse of the number density n. In this paper we argue one may be able to considerably improve upon this: in the halo picture of cosmological structure all of the dark matter is in halos of varying mass and galaxies are formed inside these halos, but for the dark matter mass and momentum conservation guarantee that nonlinear effects cannot develop a white noise in the dark matter power spectrum on large scales. This suggests that with a suitable weighting a similar effect may be achieved for galaxies, suppressing their shot noise. We explore this idea with N-body simulations by weighting central halo galaxies by halo mass and find that the resulting shot noise can be reduced dramatically relative to expectations, with a 10-30 suppression at the highest number density of n=4*10^-3 (Mpc/h)^3 resolved in our simulations. For specific applications other weighting schemes may achieve even better results and for n=3*10^-4(Mpc/h)^3 we can reduce sigma_n^2/P by up to a factor of 10 relative to uniform weighting. These results open up new opportunities to extract cosmological information in galaxy surveys, such as the recently proposed multi-tracer approach to cancel sampling variance, and may have important consequences for the planning of future redshift surveys. Taking full advantage of these findings may require better understanding of galaxy formation process to develop accurate tracers of the halo mass.Comment: 4 pages, 3 figure

Minimizing the stochasticity of halos in large-scale structure surveys

In recent work (Seljak, Hamaus and Desjacques 2009) it was found that weighting central halo galaxies by halo mass can significantly suppress their stochasticity relative to the dark matter, well below the Poisson model expectation. In this paper we extend this study with the goal of finding the optimal mass-dependent halo weighting and use $N$-body simulations to perform a general analysis of halo stochasticity and its dependence on halo mass. We investigate the stochasticity matrix, defined as $C_{ij}\equiv<(\delta_i -b_i\delta_m)(\delta_j-b_j\delta_m)>$, where $\delta_m$ is the dark matter overdensity in Fourier space, $\delta_i$ the halo overdensity of the $i$-th halo mass bin and $b_i$ the halo bias. In contrast to the Poisson model predictions we detect nonvanishing correlations between different mass bins. We also find the diagonal terms to be sub-Poissonian for the highest-mass halos. The diagonalization of this matrix results in one large and one low eigenvalue, with the remaining eigenvalues close to the Poisson prediction $1/\bar{n}$, where $\bar{n}$ is the mean halo number density. The eigenmode with the lowest eigenvalue contains most of the information and the corresponding eigenvector provides an optimal weighting function to minimize the stochasticity between halos and dark matter. We find this optimal weighting function to match linear mass weighting at high masses, while at the low-mass end the weights approach a constant whose value depends on the low-mass cut in the halo mass function. Finally, we employ the halo model to derive the stochasticity matrix and the scale-dependent bias from an analytical perspective. It is remarkably successful in reproducing our numerical results and predicts that the stochasticity between halos and the dark matter can be reduced further when going to halo masses lower than we can resolve in current simulations.Comment: 17 pages, 14 figures, matched the published version in Phys. Rev. D including one new figur

Optimal dataset combining in f_nl constraints from large scale structure in an idealised case

We consider the problem of optimal weighting of tracers of structure for the purpose of constraining the non-Gaussianity parameter f_NL. We work within the Fisher matrix formalism expanded around fiducial model with f_NL=0 and make several simplifying assumptions. By slicing a general sample into infinitely many samples with different biases, we derive the analytic expression for the relevant Fisher matrix element. We next consider weighting schemes that construct two effective samples from a single sample of tracers with a continuously varying bias. We show that a particularly simple ansatz for weighting functions can recover all information about f_NL in the initial sample that is recoverable using a given bias observable and that simple division into two equal samples is considerably suboptimal when sampling of modes is good, but only marginally suboptimal in the limit where Poisson errors dominate.Comment: 6 pages, 5 figures; v2: comment on weighting for PS determination, fixed a couple of typos; v3: revised, matches version accepted by JCA

Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of \mu, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of \mu and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion.Comment: 37 pages, 13 figures, published in JCA

The distribution of ejected subhalos and its implication for halo assembly bias

Using a high-resolution cosmological $N$-body simulation, we identify the ejected population of subhalos, which are halos at redshift $z=0$ but were once contained in more massive `host' halos at high redshifts. The fraction of the ejected subhalos in the total halo population of the same mass ranges from 9% to 4% for halo masses from $\sim 10^{11}$ to \sim 10^{12}\msun. Most of the ejected subhalos are distributed within 4 times the virial radius of their hosts. These ejected subhalos have distinct velocity distribution around their hosts in comparison to normal halos. The number of subhalos ejected from a host of given mass increases with the assembly redshift of the host. Ejected subhalos in general reside in high-density regions, and have a much higher bias parameter than normal halos of the same mass. They also have earlier assembly times, so that they contribute to the assembly bias of dark matter halos seen in cosmological simulations. However, the assembly bias is {\it not} dominated by the ejected population, indicating that large-scale environmental effects on normal halos are the main source for the assembly bias.Comment: revised version, submitted to MNRA

Large non-Gaussian Halo Bias from Single Field Inflation

We calculate Large Scale Structure observables for non-Gaussianity arising from non-Bunch-Davies initial states in single field inflation. These scenarios can have substantial primordial non-Gaussianity from squeezed (but observable) momentum configurations. They generate a term in the halo bias that may be more strongly scale-dependent than the contribution from the local ansatz. We also discuss theoretical considerations required to generate an observable signature.Comment: 30 pages, 14 figures, typos corrected and minor changes to match published version JCAP09(2012)00

Effect of Background Evolution on the Curvaton Non-Gaussianity

We investigate how the background evolution affects the curvature perturbations generated by the curvaton, assuming a curvaton potential that may deviate slightly from the quadratic one, and parameterizing the background fluid density as \rho\propto a^{-\alpha}, where a is the scale factor, and \alpha depends on the background fluid. It turns out that the more there is deviation from the quadratic case, the more pronounced is the dependence of the curvature perturbation on \alpha. We also show that the background can have a significant effect on the nonlinearity parameters f_NL and g_NL. As an example, if at the onset of the curvaton oscillation there is a dimension 6 contribution to the potential at 5 % level and the energy fraction of the curvaton to the total one at the time of its decay is at 1 %, we find variations \Delta f_NL \sim \mathcal{O}(10) and \Delta g_NL \sim \mathcal{O}(10^4) between matter and radiation dominated backgrounds. Moreover, we demonstrate that there is a relation between f_NL and g_NL that can be used to probe the form of the curvaton potential and the equation of state of the background fluid.Comment: 14 pages, 8 figure