arXiv subjects

Tobias Baldauf

Publications and source records attributed to Tobias Baldauf.

At least 37 records · Page 2Linked to original sources

arXiv2016

Velocity bias in the distribution of dark matter halos

The standard formalism for the co-evolution of halos and dark matter predicts that any initial halo velocity bias rapidly decays to zero. We argue that, when the purpose is to compute statistics like power spectra etc., the coupling in the momentum conservation equation for the biased tracers must be modified. Our new formulation predicts the constancy in time of any statistical halo velocity bias present in the initial conditions, in agreement with peak theory. We test this prediction by studying the evolution of a conserved halo population in N-body simulations. We establish that the initial simulated halo density and velocity statistics show distinct features of the peak model and, thus, deviate from the simple local Lagrangian bias. We demonstrate, for the first time, that the time evolution of their velocity is in tension with the rapid decay expected in the standard approach.

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arXiv2015

Peak exclusion, stochasticity and convergence of perturbative bias expansions in 1+1 gravity

The Lagrangian peaks of a 1D cosmological random field representing dark matter are used as a proxy for a catalogue of biased tracers in order to investigate the small-scale exclusion in the two-halo term. The two-point correlation function of peaks of a given height is numerically estimated and analytical approximations that are valid inside the exclusion zone are derived. The resulting power spectrum of these tracers is investigated and shows clear deviations from Poisson noise at low frequencies. On large scales, the convergence of a perturbative bias expansion is discussed. Finally, we go beyond Gaussian statistics for the initial conditions and investigate the subsequent evolution of the two-point clustering of peaks through their Zel'dovich ballistic displacement, to clarify how exclusion effects mix up with scale-dependencies induced by nonlinear gravitational evolution. While the expected large-scale separation limit is recovered, significant deviations are found in the exclusion zone that tends in particular to be reduced at later times. Even though these findings apply to the clustering of one-dimensional tracers, they provide useful insights into halo exclusion and its impact on the two-halo term.

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arXiv2015

Linear response to long wavelength fluctuations using curvature simulations

We study the local response to long wavelength fluctuations in cosmological $N$-body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, most probably more precise, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naive derivation assuming a universal mass function by 18%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.

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arXiv2015

On the reach of perturbative methods for dark matter density fields

We study the mapping from Lagrangian to Eulerian space in the context of the Effective Field Theory (EFT) of Large Scale Structure. We compute Lagrangian displacements with Lagrangian Perturbation Theory (LPT) and perform the full non-perturbative transformation from displacement to density. When expanded up to a given order, this transformation reproduces the standard Eulerian Perturbation Theory (SPT) at the same order. However, the full transformation from displacement to density also includes higher order terms. These terms explicitly resum long wavelength motions, thus making the resulting density field better correlated with the true non-linear density field. As a result, the regime of validity of this approach is expected to extend that of the Eulerian EFT, and match that of the IR-resummed Eulerian EFT. This approach thus effectively enables a test of the IR-resummed EFT at the field level. We estimate the size of stochastic, non-perturbative contributions to the matter density power spectrum. We find that in our highest order calculation, at redshift z=0 the power spectrum of the density field is reproduced with an accuracy of 1 % (10 %) up to k=0.25 h/Mpc (k=0.46 h/Mpc). We believe that the dominant source of the remaining error is the stochastic contribution. Unfortunately, on these scales the stochastic term does not yet scale as $k^4$ as it does in the very low-k regime. Thus, modeling this contribution might be challenging.

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arXiv2015

On the reach of perturbative descriptions for dark matter displacement fields

We study Lagrangian Perturbation Theory (LPT) and its regularization in the Effective Field Theory (EFT) approach. We evaluate the LPT displacement with the same phases as a corresponding $N$-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra. We reliably detect a non-vanishing leading order EFT coefficient and a stochastic displacement term, uncorrelated with the LPT terms. This stochastic term is expected in the EFT framework, and, to the best of our understanding, is not an artifact of numerical errors or transients in our simulations. This term constitutes a limit to the accuracy of perturbative descriptions of the displacement field and its phases, corresponding to a $1\%$ error on the non-linear power spectrum at $k=0.2 h$/Mpc at $z=0$. Predicting the displacement power spectrum to higher accuracy or larger wavenumbers thus requires a model for the stochastic displacement.

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arXiv2015

The Bispectrum in the Effective Field Theory of Large Scale Structure

We study the bispectrum in the Effective Field Theory of Large Scale Structure, consistently accounting for the effects of short-scale dynamics. We begin by proving that, as long as the theory is perturbative, it can be formulated to arbitrary order using only operators that are local in time. We then derive all the new operators required to cancel the UV-divergences and obtain a physically meaningful prediction for the one-loop bispectrum. In addition to new, subleading stochastic noises and the viscosity term needed for the one-loop power spectrum, we find three new effective operators. The three new parameters can be constrained by comparing with N-body simulations. The best fit is precisely what is suggested by the structure of UV-divergences, hence justifying a formula for the EFTofLSS bispectrum whose only fitting parameter is already fixed by the power spectrum. This result predicts the bispectrum of N-body simulations up to $k \approx 0.22\, h\, \text{Mpc}^{-1}$ at $z=0$, an improvement by nearly a factor of two as compared to one-loop standard perturbation theory.

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arXiv2015

Near optimal bispectrum estimators for large-scale structure

Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to break the degeneracy between the linear halo bias $b_1$ and the amplitude of fluctuations $σ_8$. We propose new simple, computationally inexpensive bispectrum statistics that are near optimal for the specific applications like bias determination. Corresponding to the Legendre decomposition of nonlinear halo bias and gravitational coupling at second order, these statistics are given by the cross-spectra of the density with three quadratic fields: the squared density, a tidal term, and a shift term. For halos and galaxies the first two have associated nonlinear bias terms $b_2$ and $b_{s^2}$, respectively, while the shift term has none in the absence of velocity bias (valid in the $k \rightarrow 0$ limit). Thus the linear bias $b_1$ is best determined by the shift cross-spectrum, while the squared density and tidal cross-spectra mostly tighten constraints on $b_2$ and $b_{s^2}$ once $b_1$ is known. Since the form of the cross-spectra is derived from optimal maximum-likelihood estimation, they contain the full bispectrum information on bias parameters. Perturbative analytical predictions for their expectation values and covariances agree with simulations on large scales, $k\lesssim 0.09h/\mathrm{Mpc}$ at $z=0.55$ with Gaussian $R=20h^{-1}\mathrm{Mpc}$ smoothing, for matter-matter-matter, and matter-matter-halo combinations. For halo-halo-halo cross-spectra the model also needs to include corrections to the Poisson stochasticity.

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arXiv2014

Understanding higher-order nonlocal halo bias at large scales by combining the power spectrum with the bispectrum

Understanding the relation between underlying matter distribution and biased tracers such as galaxy or dark matter halo is essential to extract cosmological information from ongoing or future galaxy redshift surveys. At sufficiently large scales such as the BAO scale, a standard approach for the bias problem on the basis of the perturbation theory (PT) is to assume the `local bias' model in which the density field of biased tracers is deterministically expanded in terms of matter density field at the same position. The higher-order bias parameters are then determined by combining the power spectrum with higher-order statistics such as the bispectrum. As is pointed out by recent studies, however, nonlinear gravitational evolution naturally induces nonlocal bias terms even if initially starting only with purely local bias. As a matter of fact, previous works showed that the second-order nonlocal bias term, which corresponds to the gravitational tidal field, is important to explain the characteristic scale-dependence of the bispectrum. In this paper we extend the nonlocal bias term up to third order, and investigate whether the PT-based model including nonlocal bias terms can simultaneously explain the power spectrum and the bispectrum of simulated halos in $N$-body simulations. We show that the power spectrum, including density and momentum, and the bispectrum between halo and matter in $N$-body simulations can be simultaneously well explained by the model including up to third-order nonlocal bias terms up to k~0.1h/Mpc. Also, the results seem in a good agreement with theoretical predictions of a simple coevolution picture, although the agreement is not perfect. These demonstration clearly shows a failure of the local bias model even at such large scales, and we conclude that nonlocal bias terms should be consistently included in order to model statistics of halos. [abridged]

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arXiv2014

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality

The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude $f_{\rm NL}^{\rm loc}$ ($f_{\rm NL}^{\rm eq}$), natural target levels of sensitivity are $Δf_{\rm NL}^{\rm loc, eq.} \simeq 1$. We highlight that such levels are within reach of future surveys by measuring 2-, 3- and 4-point statistics of the galaxy spatial distribution. This paper summarizes a workshop held at CITA (University of Toronto) on October 23-24, 2014.

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arXiv2014

Lagrangian perturbation theory at one loop order: successes, failures, and improvements

We apply the convolved Lagrangian perturbation theory (CLPT) formalism, in which one can express the matter density power spectrum in terms of integrals over a function of cumulants of the displacement field, allowing for a resummation of the terms, to evaluate the full one loop power spectrum. We keep the cumulants up to third order, extending the Zel'dovich approximation and providing the power spectrum analogous to the calculations recently performed for the correlation function. We compare the results to the N-body simulations and to the Lagrangian perturbation simulations up to the second order. We find that the analytic calculations are in a good agreement with the LPT simulations, but when compared to full N-body simulations, we find that while one loop calculations improve upon the Zel'dovich approximation in the power spectrum, they still significantly lack power. As found previously in the correlation function one loop CLPT improves slightly against Zel'dovich above 30Mpc/h, but is actually worse than Zel'dovich below that. We investigate the deficiencies of the CLPT approach and argue that main problem of CLPT is its inability to trap particles inside dark matter halos, which leads to an overestimate of the small scale power of the displacement field and to an underestimate of the small scale power from one halo term effects. We model this using the displacement field damped at a nonlinear scale (CLPTs). To explore this in more detail we decompose the power spectrum and correlation function into three additive components: Zel'dovich, residual BAO wiggle, and residual broad band. One loop CLPT predicts small modifications to BAO wiggles that are enhanced in CLPTs, with up to 5\% corrections to correlation function around BAO scale.

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arXiv2013

Halo Stochasticity from Exclusion and non-linear Clustering

The clustering of galaxies in ongoing and upcoming galaxy surveys contains a wealth of cosmological information, but extracting this information is a non-trivial task since galaxies and their host haloes are stochastic tracers of the matter density field. This stochasticity is usually modeled as Poisson shot noise, which is constant as a function of wavenumber with amplitude given by 1/n, where n is the number density of galaxies. Here we use dark matter haloes in N-body simulations to show evidence for deviations from this simple behaviour and develop models that explain the behaviour of the large scale stochasticity. First, haloes are extended, non-overlapping objects, i.e., their correlation function needs to go to -1 on small scales. This leads to a negative correction to the stochasticity relative to the Poisson value at low wavenumber k, decreasing to zero for wavenumbers large compared to the inverse exclusion scale. Second, haloes show a non-linear enhancement of clustering outside the exclusion scale, leading to a positive stochasticity correction. Both of these effects go to zero for high-k, making the stochasticity scale dependent even for k<0.1 h/Mpc. We show that the corrections in the low-k regime are the same in Eulerian and Lagrangian space, but that the transition scale is pushed to smaller scales for haloes observed at present time, relative to the initial conditions. These corrections vary with halo mass and redshift. We also discuss simple applications of these effects to the galaxy samples with non-vanishing satellite fraction, where the stochasticity can again deviate strongly from the fiducial Poisson expectation. Overall these effects affect the clustering of galaxies at a level of a few percent even on very large scales and need to be modelled properly if we want to extract high precision cosmological information from the upcoming galaxy surveys.

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arXiv2013

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 σ_8 and Ω_m (and marginalise over non-linear galaxy bias) in a flat LCDM model, the best-constrained quantity is σ_8 (Ω_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 σ_8, Ω_m, H_0, w_{de} and \sum m_ν become 30--80 per cent tighter than with CMB data alone, since our data break several parameter degeneracies.

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arXiv2012

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 μ, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of μand 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.

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arXiv2012

Cluster Density Profiles as a Test of Modified Gravity

We present a new test of gravitational interactions at the r\sim(0.2-20)Mpc scale, around the virial radius of dark matter halos measured through cluster-galaxy lensing of maxBCG clusters from the Sloan Digital Sky Survey (SDSS). We employ predictions from self-consistent simulations of f(R) gravity to find an upper bound on the background field amplitude of f_R0<3.5x10^-3 at the 1D-marginalized 95% confidence level. As a model-independent assessment of the constraining power of cluster profiles measured through weak gravitational lensing, we also constrain the amplitude F_0 of a phenomenological modification based on the profile enhancement induced by f(R) gravity when not including effects from the increased cluster abundance in f(R). In both scenarios, dark-matter-only simulations of the concordance model corresponding to f_R0=0 and F_0=0 are consistent with the lensing measurements, i.e., at the 68% and 95% confidence level, respectively.

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arXiv2012

Evidence for Quadratic Tidal Tensor Bias from the Halo Bispectrum

The relation between the clustering properties of luminous matter in the form of galaxies and the underlying dark matter distribution is of fundamental importance for the interpretation of ongoing and upcoming galaxy surveys. The so called local bias model, where galaxy density is a function of local matter density, is frequently discussed as a means to infer the matter power spectrum or correlation function from the measured galaxy correlation. However, gravitational evolution generates a term quadratic in the tidal tensor and thus non-local in the density field, even if this term is absent in the initial conditions (Lagrangian space). Because the term is quadratic, it contributes as a loop correction to the power spectrum, so the standard linear bias picture still applies on large scales, however, it contributes at leading order to the bispectrum for which it is significant on all scales. Such a term could also be present in Lagrangian space if halo formation were influenced by the tidal field. We measure the corresponding coupling strengths from the matter-matter-halo bispectrum in numerical simulations and find a non-vanishing coefficient for the tidal tensor term. We find no scale dependence of the bias parameters up to k=0.1 h/Mpc and that the tidal effect is increasing with halo mass. While the Lagrangian bias picture is a better description of our results than the Eulerian bias picture, our results suggest that there might be a tidal tensor bias already in the initial conditions. We also find that the coefficients of the quadratic density term deviate quite strongly from the theoretical predictions based on the spherical collapse model and a universal mass function. Both quadratic density and tidal tensor bias terms must be included in the modeling of galaxy clustering of current and future surveys if one wants to achieve the high precision cosmology promise of these datasets.

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arXiv2011

Galaxy Bias and non-Linear Structure Formation in General Relativity

Length scales probed by large scale structure surveys are becoming closer to the horizon scale. Further, it has been recently understood that non-Gaussianity in the initial conditions could show up in a scale dependence of the bias of galaxies at the largest distances. It is therefore important to include General Relativistic effects. Here we provide a General Relativistic generalization of the bias, valid both for Gaussian and non-Gaussian initial conditions. The collapse of objects happens on very small scales, while long-wavelength modes are always in the quasi linear regime. Around every collapsing region, it is therefore possible to find a reference frame that is valid for all times and where the space time is almost flat: the Fermi frame. Here the Newtonian approximation is applicable and the equations of motion are the ones of the N-body codes. The effects of long-wavelength modes are encoded in the mapping from the cosmological frame to the local frame. For the linear bias, the effect of the long-wavelength modes on the dynamics is encoded in the local curvature of the Universe, which allows us to define a General Relativistic generalization of the bias in the standard Newtonian setting. We show that the bias due to this effect goes to zero as the squared ratio of the physical wavenumber with the Hubble scale for modes longer than the horizon, as modes longer than the horizon have no dynamical effects. However, the bias due to non-Gaussianities does not need to vanish for modes longer than the Hubble scale, and for non-Gaussianities of the local kind it goes to a constant. As a further application, we show that it is not necessary to perform large N-body simulations to extract information on long-wavelength modes: N-body simulations can be done on small scales and long-wavelength modes are encoded simply by adding curvature to the simulation and rescaling the coordinates.

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arXiv2011

Primordial non-Gaussianity in the Bispectrum of the Halo Density Field

The bispectrum vanishes for linear Gaussian fields and is thus a sensitive probe of non-linearities and non-Gaussianities in the cosmic density field. Hence, a detection of the bispectrum in the halo density field would enable tight constraints on non-Gaussian processes in the early Universe and allow inference of the dynamics driving inflation. We present a tree level derivation of the halo bispectrum arising from non-linear clustering, non-linear biasing and primordial non-Gaussianity. A diagrammatic description is developed to provide an intuitive understanding of the contributing terms and their dependence on scale, shape and the non-Gaussianity parameter fNL. We compute the terms based on a multivariate bias expansion and the peak-background split method and show that non-Gaussian modifications to the bias parameters lead to amplifications of the tree level bispectrum that were ignored in previous studies. Our results are in a good agreement with published simulation measurements of the halo bispectrum. Finally, we estimate the expected signal to noise on fNL and show that the constraint obtainable from the bispectrum analysis significantly exceeds the one obtainable from the power spectrum analysis.

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arXiv2010

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 $C_{ij}\equiv<(δ_i -b_iδ_m)(δ_j-b_jδ_m)>$, where $δ_m$ is the dark matter overdensity in Fourier space, $δ_i$ 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.

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