arXiv subjects

Roman Scoccimarro

Publications and source records attributed to Roman Scoccimarro.

87 records · Page 5Linked to original sources

arXiv2000

Linear and nonlinear contributions to pairwise peculiar velocities

We write the correlation function of dark matter particles, xi(r), as the sum of two terms - one which accounts for nonlinear evolution, and dominates on small scales, and another which is essentially the term from linear theory, and dominates on large scales. We use models of the number and spatial distribution of haloes and halo density profiles to describe the nonlinear term and its evolution. The result provides a good description of the evolution of xi(r) in simulations. We then use this decomposition to provide simple and accurate models of how the single particle velocity dispersion evolves with time, and how the first and second moments of the pairwise velocity distribution depend on scale. The key idea is to use the simple physics of linear theory on large scales, the simple physics of the virial theorem on small scales, and our model for the correlation function to tell us how to weight the two types of contributions (linear and nonlinear) to the pairwise velocity statistics. When incorporated into the streaming model, our results will allow a simple accurate description of redshift-space distortions over the entire range of linear to highly nonlinear regimes.

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arXiv2000

A New Angle on Gravitational Clustering

We describe a new approach to gravitational instability in large-scale structure, where the equations of motion are written and solved as in field theory in terms of Feynman diagrams. The basic objects of interest are the propagator (which propagates solutions forward in time), the vertex (which describes non-linear interactions between waves) and a source with prescribed statistics which describes the effect of initial conditions. We show that loop corrections renormalize these quantities, and discuss applications of this formalism to a better understanding of gravitational instability and to improving non-linear perturbation theory in the transition to the non-linear regime. We also consider the role of vorticity creation due to shell-crossing and show using N-body simulations that at small (virialized) scales the velocity field reaches equipartition, i.e. the vorticity power spectrum is about twice the divergence power spectrum.

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arXiv2000

The Bispectrum: From Theory to Observations

The bispectrum is the lowest-order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the evolution of the bispectrum is well understood theoretically from non-linear perturbation theory and numerical simulations, applications to galaxy surveys require a number of issues to be addressed. In this paper we consider the effect on the bispectrum of stochastic non-linear biasing, radial redshift distortions, non-Gaussian initial conditions, survey geometry and sampling. We find that: 1) bias stochasticity does not affect the use of the bispectrum to recover the mean biasing relation between galaxies and mass, at least for models in which the scatter is uncorrelated at large scales. 2) radial redshift distortions do not change significantly the monopole power spectrum and bispectrum compared to their plane-parallel values. 3) survey geometry leads to finite volume effects which must be taken into account in current surveys before comparison with theoretical predictions can be made. 4) sparse sampling and survey geometry correlate different triangles leading to a breakdown of the Gaussian likelihood approximation. We develop a likelihood analysis using bispectrum eigenmodes, calculated by Monte Carlo realizations of mock surveys generated with second-order Lagrangian perturbation theory and checked against N-body simulations. In a companion paper we apply these results to the analysis of the bispectrum of IRAS galaxies.

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arXiv2000

How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering

We study galaxy clustering using halo models, where gravitational clustering is described in terms of dark matter halos. At small scales, clustering statistics are dominated by halo density profiles, whereas at large scales, correlations are the result of combining non-linear perturbation theory with halo biasing. Galaxies are assumed to follow the dark matter profiles, and galaxy formation efficiency is given by the number of galaxies as a function of halo mass. This approach leads to generic predictions: the galaxy power spectrum shows a power-law behavior even though the dark matter does not, and the galaxy higher-order correlations show smaller amplitudes at small scales than their dark matter counterparts, as observed in galaxy catalogs. We find that requiring to fit both the second and third order moments of the APM galaxies provides a strong constraint on galaxy formation models. The data at large scales require that galaxy formation be relatively efficient at small masses, m =10^10 Msun/h, whereas data at smaller scales require that the number of galaxies in a halo scale as the mass to the 0.8th power in the high-mass limit. These constraints are independent of those derived from the luminosity function or Tully-Fisher relation. We also predict the power spectrum, bispectrum, and higher-order moments of the mass density field. Although halo models agree well with measurements of the mass power spectrum and the higher order Sp parameters in N-body simulations, the model assumption that halos are spherical leads to disagreement in the configuration dependence of the bispectrum at small scales. We stress the importance of finite volume effects in higher-order statistics and show how they can be estimated in this approach.

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arXiv1999

Power Spectrum Correlations Induced by Non-Linear Clustering

Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to non-trivial cross-correlations between different band-powers. We calculate the power-spectrum covariance matrix in non-linear perturbation theory (weakly non-linear regime), in the hierarchical model (strongly non-linear regime), and from numerical simulations in real and redshift space. We discuss the impact of these results on parameter estimation from power spectrum measurements and their dependence on the size of the survey and the choice of band-powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the non-linear scale, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z=1, the non-Gaussian contribution rises significantly around l=1000, and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the 3D field falls faster than 1/k^2.

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arXiv1999

Hyperextended Cosmological Perturbation Theory: Predicting Non-linear Clustering Amplitudes

We consider the long-standing problem of predicting the hierarchical clustering amplitudes $S_p$ in the strongly non-linear regime of gravitational evolution. N-body results for the non-linear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated ansatz that yields the strongly non-linear behavior of the skewness, $S_3$, starting from leading-order perturbation theory. When generalized to higher-order ($p>3$) polyspectra or correlation functions, this ansatz leads to a good description of non-linear amplitudes in the strongly non-linear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the non-linear evolution of the bispectrum that interpolates between the weakly and strongly non-linear regimes, analogous to previous expressions for the power spectrum.

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arXiv1998

The Bispectrum as a Signature of Gravitational Instability in Redshift-Space

The bispectrum provides a characteristic signature of gravitational instability that can be used to probe the Gaussianity of the initial conditions and the bias of the galaxy distribution. We study how this signature is affected by redshift distortions using perturbation theory and high-resolution numerical simulations. We obtain perturbative results for the multipole expansion of the redshift-space bispectrum which provide a natural way to break the degeneracy between bias and $Ω$ present in measurements of the redshift-space power spectrum. We propose a phenomenological model that incorporates the perturbative results and also describes the bispectrum in the transition to the non-linear regime. We stress the importance of non-linear effects and show that inaccurate treatment of these can lead to significant discrepancies in the determination of bias from galaxy redshift surveys. At small scales we find that the bispectrum monopole exhibits a strong configuration dependence that reflects the velocity dispersion of clusters. Therefore, the hierarchical model for the three-point function does not hold in redshift-space.

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arXiv1998

Redshift Distortions: Perturbative and N-body Results

I discuss the evolution of the redshift-space bispectrum via perturbation theory (PT) and large high-resolution numerical simulations. At large scales, we give the multipole expansion of the bispectrum in PT, which provides a natural way to break the degeneracy between bias and $Ω$ present in measurements of the power spectrum distortions. At intermediate scales, we propose a simple phenomenological model to take into account non-linear effects. N-body results show that at small scales the perturbative shape of the bispectrum monopole in redshift-space is preserved, breaking the hierarchical form valid in the absence of distortions.

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arXiv1998

The Impact of Inhomogeneous Reionization on Cosmic Microwave Background Anisotropy

Hydrogen atoms in the Universe that initially formed at redshift z = 1100 were reionized at 5 < z < 60. It is likely that this transition proceeded through a mixed phase of partial ionization. We develop an analytic approach to calculating the effect on the cosmic microwave background (CMB) of Thomson scattering off this inhomogeneous distribution of free electrons. We study two models of the reionization process, one of which associates ionized patches with overdense regions of the smoothed density field. We find the generated anisotropy to have a power spectrum which peaks at angular scales corresponding to the extent of the ionized regions, and has a width that reflects the correlations between them. There is considerable uncertainty in the amplitude, which depends on how efficiently collapsed objects can reionize the surrounding medium. We calculate the effect of neglecting inhomogeneous reionization in the determination of cosmological parameters from high resolution CMB maps and find that it may be a significant source of systematic error.

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arXiv1997

Transients from Initial Conditions: A Perturbative Analysis

The standard procedure to generate initial conditions (IC) in numerical simulations is to use the Zel'dovich approximation (ZA). Although the ZA correctly reproduces the linear growing modes of density and velocity perturbations, non-linear growth is inaccurately represented because of the ZA failure to conserve momentum. This implies that it takes time for the actual dynamics to establish the correct statistical properties of density and velocity fields. We extend perturbation theory (PT) to include transients as non-linear excitations of decaying modes caused by the IC. We focus on higher-order statistics of the density contrast and velocity divergence, characterized by the S_p and T_p parameters. We find that the time-scale of transients is determined, at a given order p, by the spectral index n. The skewness factor S_3 (T_3) attains 10% accuracy only after a=6 (a=15) for n=0, whereas higher (lower) n demands more (less) expansion away from the IC. These requirements become much more stringent as p increases. An Omega=0.3 model requires a factor of two larger expansion than an Omega=1 model to reduce transients by the same amount. The predicted transients in S_p are in good agreement with numerical simulations. More accurate IC can be achieved by using 2nd order Lagrangian PT (2LPT), which reproduces growing modes up to 2nd order and thus eliminates transients in the skewness. We show that for p>3 this reduces the required expansion by more than an order of magnitude compared to the ZA. Setting up 2LPT IC only requires minimal, inexpensive changes to ZA codes. We suggest simple steps for its implementation.

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arXiv1997

Non-Linear Evolution of the Bispectrum of Cosmological Perturbations

The bispectrum, the three-point function of density fluctuations in Fourier space, is the lowest order statistic that carries information about the spatial coherence of large-scale structures. For Gaussian initial conditions, when the density fluctuation amplitude is small, tree-level (leading order) perturbation theory predicts a characteristic dependence of the bispectrum on the shape of the triangle formed by the three wave vectors. This configuration dependence provides a signature of gravitational instability, and departures from it in galaxy catalogs can be interpreted as due to bias, that is, non-gravitational effects. On the other hand, N-body simulations indicate that the reduced three-point function becomes relatively shape-independent in the strongly non-linear regime. In order to understand this non-linear transition and assess the domain of reliability of shape-dependence as a probe of bias, we calculate the one-loop (next-to-leading order) corrections to the bispectrum in perturbation theory. We compare these results with measurements in numerical simulations with scale-free and CDM initial power spectra. We find that the one-loop corrections account very well for the departures from the tree-level results measured in numerical simulations on weakly non-linear scales. In this regime, the reduced bispectrum qualitatively retains its tree-level shape, but the amplitude can change significantly. At smaller scales, the reduced bispectrum in the simulations starts to flatten, an effect which can be partially understood from the one-loop results. In the strong clustering regime, where perturbation theory breaks down entirely, the simulation results confirm that the reduced bispectrum has almost no dependence on triangle shape, in rough agreement with the hierarchical ansatz.

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arXiv1997

Understanding Gravitational Clustering with Non-Linear Perturbation Theory

I discuss new results concerning the evolution of the bispectrum due to gravitational instability from gaussian initial conditions using one-loop perturbation theory (PT). Particular attention is paid to the transition from weakly non-linear scales to the non-linear regime at small scales. Comparison with numerical simulations is made to assess the regime of validity of the perturbative approach.

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arXiv1996

Cosmological Perturbations: Entering the Non-Linear Regime

We consider one-loop corrections to the bispectrum and skewness of cosmological density fluctuations induced by gravitational evolution. As has been established by comparison with numerical simulations, tree-level perturbation theory (PT) describes these quantities at the largest scales. One-loop PT provides a tool to probe the transition to the non-linear regime on smaller scales. In this work, we find that, as a function of spectral index n, the one-loop bispectrum follows a pattern analogous to that of the one-loop power spectrum, which shows a change in behavior at a critical index n_c = -1.4, where non-linear corrections vanish. For the bispectrum, for n less than n_c, one-loop corrections increase the configuration dependence of the leading order contribution; for n greater than n_c, one-loop corrections tend to cancel the configuration dependence of the tree-level bispectrum, in agreement with known results from n=-1 numerical simulations. A similar situation is shown to hold for the Zel'dovich approximation (ZA), where n_c = -1.75. Using dimensional regularization, we obtain explicit analytic expressions for the one-loop bispectrum for n=-2 initial power spectra, for both the exact dynamics of gravitational instability and the ZA. We also compute the skewness factor, including local averaging of the density field, for n=-2: S_3(R) = 4.02 + 3.83 sigma^2(R) for gaussian smoothing and S_3(R) = 3.86 + 3.18 sigma^2(R) for top-hat smoothing, where sigma^2(R) is the variance of the density field fluctuations smoothed over a window of radius R. Comparison with fully non-linear numerical simulations implies that, for n < -1, one-loop PT can extend our understanding of nonlinear clustering down to scales where the transition to the stable clustering regime begins.

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arXiv1996

Loop Corrections in Non-Linear Cosmological Perturbation Theory II. Two-point Statistics and Self-Similarity

We calculate the lowest-order non-linear contributions to the power spectrum, two-point correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scale-free initial power spectra, $P(k) \sim k^n$. These results extend and in some cases correct previous work in the literature on cosmological perturbation theory. Comparing with the scaling behavior observed in N-body simulations, we find that the validity of non-linear perturbation theory depends strongly on the spectral index $n$. For $n<-1$, we find excellent agreement over scales where the variance $σ^2(R) \la 10$; however, for $n \geq -1$, perturbation theory predicts deviations from self-similar scaling (which increase with $n$) not seen in numerical simulations. This anomalous scaling suggests that the principal assumption underlying cosmological perturbation theory, that large-scale fields can be described perturbatively even when fluctuations are highly non-linear on small scales, breaks down beyond leading order for spectral indices $n \geq -1$. For $n < -1$, the power spectrum, variance, and correlation function in the scaling regime can be calculated using dimensional regularization.

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arXiv1995

Loop Corrections in Non-Linear Cosmological Perturbation Theory

Using a diagrammatic approach to Eulerian perturbation theory, we analytically calculate the variance and skewness of the density and velocity divergence induced by gravitational evolution from Gaussian initial conditions, including corrections *beyond* leading order. Except for the power spectrum, previous calculations in cosmological perturbation theory have been confined to leading order (tree level)-we extend these to include loop corrections. For scale-free initial power spectra, the one-loop variance σ^2 = σ^2_l + 1.82 σ^4_l and the skewness S_3 = 34/7 + 9.8 σ^2_l, where σ_l is the rms fluctuation of the linear density field. We also compute loop corrections to the variance, skewness, and kurtosis for several non-linear approximation schemes, where the calculation can be easily generalized to 1-point cumulants of higher order and arbitrary number of loops. We find that the Zel'dovich approximation gives the best approximation to the loop corrections of exact perturbation theory, followed by the Linear Potential approximation (LPA) and the Frozen Flow approximation (FFA), in qualitative agreement with the relative behavior of tree-level results. In LPA and FFA, loop corrections are infrared divergent for spectral indices n < 0; this is related to the breaking of Galilean invariance in these schemes.

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