arXiv subjects

Patrick Valageas

Publications and source records attributed to Patrick Valageas.

90 records · Page 5Linked to original sources

arXiv2008

Propagators in Lagrangian space

It has been found recently that propagators, e.g. the cross-correlation spectra of the cosmic fields with the initial density field, decay exponentially at large-k in an Eulerian description of the dynamics. We explore here similar quantities defined for a Lagrangian space description. We find that propagators in Lagrangian space do not exhibit the same properties: they are found not to be monotonic functions of time, and to track back the linear growth rate at late time (but with a renormalized amplitude). These results have been obtained with a novel method which we describe alongside. It allows the formal resummation of the same set of diagrams as those that led to the known results in Eulerian space. We provide a tentative explanation for the marked differences seen between the Eulerian and the Lagrangian cases, and we point out the role played by the vorticity degrees of freedom that are specific to the Lagrangian formalism. This provides us with new insights into the late-time behavior of the propagators.

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arXiv2007

Using the Zeldovich dynamics to test expansion schemes

We apply various expansion schemes that may be used to study gravitational clustering to the simple case of the Zeldovich dynamics. Using the well-known exact solution of the Zeldovich dynamics we can compare the predictions of these various perturbative methods with the exact nonlinear result and study their convergence properties. We find that most systematic expansions fail to recover the decay of the response function in the highly nonlinear regime. ``Linear methods'' lead to increasingly fast growth in the nonlinear regime for higher orders, except for Pade approximants that give a bounded response at any order. ``Nonlinear methods'' manage to obtain some damping at one-loop order but they fail at higher orders. Although it recovers the exact Gaussian damping, a resummation in the high-k limit is not justified very well as the generation of nonlinear power does not originate from a finite range of wavenumbers (hence there is no simple separation of scales). No method is able to recover the relaxation of the matter power spectrum on highly nonlinear scales. It is possible to impose a Gaussian cutoff in a somewhat ad-hoc fashion to reproduce the behavior of the exact two-point functions for two different times. However, this cutoff is not directly related to the clustering of matter and disappears in exact equal-time statistics such as the matter power spectrum. On a quantitative level, the usual perturbation theory, and the nonlinear scheme to which one adds an ansatz for the response function with such a Gaussian cutoff, are the two most efficient methods. These results should hold for the gravitational dynamics as well (this has been checked at one-loop order), since the structure of the equations of motion is identical for both dynamics.

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arXiv2007

Large-N expansions applied to gravitational clustering

We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical properties of the density and velocity fields for Gaussian initial conditions. Then, we present large-N expansions (associated with a generalization to N fields or with a semi-classical expansion) of the path-integral defined by this action. This provides a systematic expansion for two-point functions such as the response function and the usual two-point correlation. We present the results of two such expansions (and related variants) at one-loop order for a SCDM and a LCDM cosmology. We find that the response function exhibits fast oscillations in the non-linear regime with an amplitude which either follows the linear prediction (for the direct steepest-descent scheme) or decays (for the 2PI effective action scheme). On the other hand, the correlation function agrees with the standard one-loop result in the quasi-linear regime and remains well-behaved in the highly non-linear regime. This suggests that these large-N expansions could provide a good framework to study the dynamics of gravitational clustering in the non-linear regime. Moreover, the use of various expansion schemes allows one to estimate their range of validity without the need of N-body simulations and could provide a better accuracy in the weakly non-linear regime.

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arXiv2006

Relaxation of a 1-D gravitational system

We study the relaxation towards thermodynamical equilibrium of a 1-D gravitational system. This OSC model shows a series of critical energies $E_{cn}$ where new equilibria appear and we focus on the homogeneous ($n=0$), one-peak ($n=\pm 1$) and two-peak ($n=2$) states. Using numerical simulations we investigate the relaxation to the stable equilibrium $n=\pm 1$ of this $N-$body system starting from initial conditions defined by equilibria $n=0$ and $n=2$. We find that in a fashion similar to other long-range systems the relaxation involves a fast violent relaxation phase followed by a slow collisional phase as the system goes through a series of quasi-stationary states. Moreover, in cases where this slow second stage leads to a dynamically unstable configuration (two peaks with a high mass ratio) it is followed by a new sequence ``violent relaxation/slow collisional relaxation''. We obtain an analytical estimate of the relaxation time $t_{2\to \pm 1}$ through the mean escape time of a particle from its potential well in a bistable system. We find that the diffusion and dissipation coefficients satisfy Einstein's relation and that the relaxation time scales as $N e^{1/T}$ at low temperature, in agreement with numerical simulations.

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arXiv2006

Thermodynamics and dynamics of a 1-D gravitational system

We describe a one-dimensional self-gravitating system derived from the problem of large-scale structure formation in cosmology. Considering small times so that the expansion can be neglected we present a thermodynamical analysis of this system. We find a second-order phase transition at $T_{c1}$ from an homogeneous equilibrium at high temperature to a clustered phase (with a density peak at one of the boundaries of the system) at low temperature. There also exists an infinite series of unstable equilibria which appear at lower temperatures $T_{cn}$, reflecting the scale-free nature of the gravitational interaction and the usual Jeans instability. We find that, as for the similar HMF (Hamiltonian mean field) model, all three micro-canonical, canonical and grand-canonical ensembles agree with each other, as well as with the stability properties associated with a hydrodynamical approach. On the other hand, the collisionless dynamics governed by the Vlasov equation yields the same results except that at low $T$ the equilibrium associated with two density peaks (one at each boundary) becomes stable.

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arXiv2006

How many SNeIa do we need to detect the effect of weak lensing ?

We show that as many as 4000 SNeIa may be required to detect the effect of weak lensing on their flux distribution with a high level of significance. However, if the intrinsic SNeIa magnitude dispersion is unknown one needs an even higher number of SNeIa (an order of magnitude more) to reach a similar level of statistical significance. Moreover, the ability to separate the lensing contribution from the intrinsic scatter depends sensitively on the amplitude of the latter. Using a Kolmogorov - Smirnov (K-S) test we check how the required number of SNeIa changes with level of significance. Our model incorporates a completely analytical description of weak lensing which has been tested extensively against numerical simulations. Thus, future missions such as SNAP may be able to detect non-Gaussianity at a lower significance level of 10% (through the K-S test) only if the intrinsic scatter is known from external data (e.g. from low redshift observations) whereas ALPACA with 100,000 SNe will definitely detect non-Gaussianity with a very high confidence even if the intrinsic magnitude dispersion is not known a priori.

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arXiv2005

Do measurements of the one-point distribution of aperture-mass improve constraints on cosmology ?

We study the possibility of using the entire probability distribution function (PDF) of the aperture mass Map and its related cumulative probability distribution function (CPDF) to obtain meaningful constraints on cosmological parameters. Deriving completely analytic expressions for the associated covariance matrices, we construct the Fisher matrix and use it to estimate the accuracy with which various cosmological parameters can be recovered from future surveys using such statistics. This formalism also includes the effect of various noises such as intrinsic ellipticity distribution of galaxies and finite survey size. The estimation errors are then compared with the ones derived from low order moments of the PDF (variance and skewness) to check how efficiently the high Map tail can be used to constrain cosmological parameters such as Omega_m, sigma_8 and dark energy equation of state w_de. We find that for future surveys such as JDEM the full PDF does not bring significant tightening of constraints on cosmology beyond what is already achievable by the joint use of second and third order moments.

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arXiv2005

Cosmological Constraints from Weak Lensing Surveys

Focusing on the well motivated aperture mass statistics $\Map$, we study the possibility of constraining cosmological parameters using future space based SNAP class weak lensing missions. Using completely analytical results we construct the covariance matrix for estimators based on two-point and three-point statistics. Our approach incorporates an accurate modelling of higher-order statistics to describe cosmic variance as well as various sources of discrete noise at small angular scales. These results are then fed into a Fisher matrix based analysis to study cosmological parameter degeneracies. Joint and independent analysis, with or without redshift binning, for various parameter combinations are presented. An analytical modelling of the covariance matrix opens up the possibility of testing various approximations which are often used in derivations of semi-analytical results. These include how inclusion of full non-Gaussian terms in covariance matrix affects parameter estimation. Inclusion of three-point information and how such information can enhance the accuracy with which certain parameters can be estimated is also studied in detail. It is shown that broad correlation structure among various angular scales in such circumstances implies reduction in number of available angular scales which carry completely independent information. On the other hand, the effect of theoretical inaccuracies, in modelling either the power-spectrum or bi-spectrum evolution, onto the measure of cosmological parameters from weak lensing surveys is also considered. Several cosmological parameters, $\Om$, $σ_8$, spectral index $n_s$, running of spectral index $α_s$ and equation of state of the dark energy $\wde$ are included in the analysis.

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arXiv2005

Cosmology with Weak Lensing Surveys

Weak gravitational lensing surveys measure the distortion of the image of distant sources due to the deflections of light rays by the fluctuations of the gravitational potential along the line of sight. Since they probe the non-linear matter power spectrum itself at medium redshift such surveys are complimentary to both galaxy surveys (which follow stellar light) and cosmic microwave background observations (which probe the linear regime at high redshift). Ongoing CMB experiments such as WMAP and the future Planck satellite mission will measure the standard cosmological parameters with unprecedented accuracy. The focus of attention will then shift to understanding the nature of dark matter and vacuum energy: several recent studies suggest that lensing is the best method for constraining the dark energy equation of state. During the next 5 year period ongoing and future weak lensing surveys such as the Joint Dark Energy Mission (JDEM, e.g. SNAP) or the Large-aperture Synoptic Survey Telescope (LSST) will play a major role in advancing our understanding of the universe in this direction. In this review article we describe various aspects of weak lensing surveys and how they can help us in understanding our universe.

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arXiv2005

On the estimation of gravity-induced non-Gaussianities from weak lensing surveys

We study various measures of weak lensing distortions in future surveys, taking into account the noise arising from the finite survey size and the intrinsic ellipticity of galaxies. We also consider a realistic redshift distribution of the sources, as expected for the SNAP mission. We focus on the low order moments and the full distribution function (pdf) of the aperture-mass $\Map$ and of the smoothed shear component $\gammais$. We also propose new unbiased estimators for low-order cumulants which have less scatter than the usual estimators of non-Gaussianity based on the moments themselves. Then, using an analytical model which has already been seen to provide a good description of weak gravitational lensing through comparison against numerical simulations, we study the statistical measures which can be extracted from future surveys like the SNAP experiment. We recover the fact that at small angular scales ($1'<θ_s<10'$) the variance can be extracted with a few percent level accuracy. Non-Gaussianity can also be measured from the skewness of the aperture-mass (at a 10% level) while the shear kurtosis is more noisy and cannot be easily measured beyond 6'. On the other hand, we find that the pdf of the estimator associated with the aperture-mass can be distinguished both from the Gaussian and the Edgeworth expansion and could provide useful constraints, while this appears to be difficult to realize with the shear component. Finally, we investigate various survey strategies and the possibility to perform a redshift binning of the sample.

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arXiv2004

Evolution of the Cosmological Density Distribution Function: A New Analytical Model

The one-point probability distribution function (pdf) of the large-scale density field is an important tool to follow the evolution of cosmological structures. In this paper we present a new model for this pdf for all regimes and all densities, that is from linear to highly non-linear scales and from rare voids up to rare high densities. This is probably the simplest model one can build which is consistent with normalization constraints and known rigorous results (the quasi-linear regime and the rare void limit). It is fully parameterized by the non-linear variance and skewness. We obtain a good agreement with N-body data from realistic cosmological simulations of the VIRGO consortium and we find that it works significantly better than previous models such as the lognormal model or the Extended Perturbation Theory (EPT). We explain this success as a result of the tight constraints onto the pdf provided by these consistency conditions. We also point out that while the Lagrangian dynamics of typical fluctuations is quite complex the statistical outcome seems rather simple. This simple model should be useful for studies which require a realistic and convenient description of this pdf.

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arXiv2004

Covariance of Weak Lensing Observables

Analytical expressions for covariances of weak lensing statistics related to the aperture mass $\Map$ are derived for realistic survey geometries such as SNAP for a range of smoothing angles and redshift bins. We incorporate the contributions to the noise due to the intrinsic ellipticity distribution and the effects of finite size of the catalogue. Extending previous results to the most general case where the overlap of source populations is included in a complete analysis of error estimates, we study how various angular scales in various redshifts are correlated and how the estimation scatter changes with survey parameters. Dependence on cosmological parameters and source redshift distributions are studied in detail. Numerical simulations are used to test the validity of various ingredients to our calculations. Correlation coefficients are defined in a way that makes them practically independent of cosmology. They can provide important tools to cross-correlate one or more different surveys, as well as various redshift bins within the same survey or various angular scales from same or different surveys. Dependence of these coefficients on various models of underlying mass correlation hierarchy is also studied. Generalisations of these coefficients at the level of three-point statistics have the potential to probe the complete shape dependence of the underlying bi-spectrum of the matter distribution. A complete error analysis incorporating all sources of errors suggest encouraging results for studies using future space based weak lensing surveys such as SNAP.

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arXiv2004

On Cross-correlating Weak Lensing Surveys

The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal to noise ratio, such as SNAP. However, removal of any systematics or noise will remain a major cause of concern for any weak lensing survey. One of the best ways of spotting any undetected source of systematic noise is to compare surveys which probe the same part of the sky. In this paper we study various measures which are useful in cross correlating weak lensing surveys with diverse survey strategies. Using two different statistics - the shear components and the aperture mass - we construct a class of estimators which encode such cross-correlations. These techniques will also be useful in studies where the entire source population from a specific survey can be divided into various redshift bins to study cross correlations among them. We perform a detailed study of the angular size dependence and redshift dependence of these observables and of their sensitivity to the background cosmology. We find that one-point and two-point statistics provide complementary tools which allow one to constrain cosmological parameters and to obtain a simple estimate of the noise of the survey.

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arXiv2004

Weak lensing shear and aperture-mass from linear to non-linear scales

In this paper we describe the predictions for the smoothed weak lensing shear and aperture-mass of two simple analytical models of the density field: the minimal tree-model and the stellar model. Both models give identical results for the statistics of the 3-d density contrast smoothed over spherical cells and only differ by the detailed angular dependence of the many-body density correlations. We have shown in previous work that they also yield almost identical results for the pdf of the smoothed convergence, $κ_s$. We find that both models give rather close results for both the shear and the positive tail of the aperture-mass. However, we note that at small angular scales ($θ_s \la 2'$) the tail of the pdf $\cP(\Map)$ for negative $\Map$ shows a strong variation between the two models and the stellar model actually breaks down for $θ_s \la 0.4'$ and $\Map<0$. This shows that the statistics of the aperture-mass provides a very precise probe of the detailed structure of the density field, as it is sensitive to both the amplitude and the detailed angular behaviour of the many-body correlations. On the other hand, the minimal tree-model shows good agreement with numerical simulations over all scales and redshifts of interest, while both models provide a good description of the pdf $\cP(γ_{is})$ of the smoothed shear components. Therefore, the shear and the aperture-mass provide robust and complimentary tools to measure the cosmological parameters as well as the detailed statistical properties of the density field.

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arXiv2004

From linear to non-linear scales: analytical and numerical predictions for the weak lensing convergence

Weak lensing convergence can be used directly to map and probe the dark mass distribution in the universe. Building on earlier studies, we recall how the statistics of the convergence field are related to the statistics of the underlying mass distribution, in particular to the many-body density correlations. We describe two model-independent approximations which provide two simple methods to compute the probability distribution function, pdf, of the convergence. We apply one of these to the case where the density field can be described by a log-normal pdf. Next, we discuss two hierarchical models for the high-order correlations which allow one to perform exact calculations and evaluate the previous approximations in such specific cases. Finally, we apply these methods to a very simple model for the evolution of the density field from linear to highly non-linear scales. Comparisons with the results obtained from numerical simulations, obtained from a number of different realizations, show excellent agreement with our theoretical predictions. We have probed various angular scales in the numerical work and considered sources at 14 different redshifts in each of two different cosmological scenarios, an open cosmology and a flat cosmology with non-zero cosmological constant. Our simulation technique employs computations of the full 3-d shear matrices along the line of sight from the source redshift to the observer and is complementary to more popular ray-tracing algorithms. Our results therefore provide a valuable cross-check for such complementary simulation techniques, as well as for our simple analytical model, from the linear to the highly non-linear regime.

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arXiv2003

Analytical Predictions for Statistics of Cosmic Shear: Tests Against Simulations

Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of the convergence field on small angular scales by suitably modeling the statistics of the underlying density field in the highly non-linear regime. We extend such methods to model the complete probability distribution function, PDF, of the shear as a function of smoothing angle. Our model relies on a simple hierarchical Ansatz for the behaviour of the higher-order correlations in the density field. We compare our predictions with the results of numerical simulations and find excellent agreement for different cosmological scenarios. Our method provides a new way to study the evolution of non-Gaussianity in gravitational clustering and should help to break the degeneracies in parameter estimation based on analysis of the power spectrum alone.

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arXiv1998

The Mass and Luminosity Functions of Galaxies and their Evolution

We set up a model for the evolution of the galaxy luminosity function, taking advantage of recent work that brought in some better understanding of the mass function for gravitationally condensed objects. The physics of cooling of the baryonic component allows us to distinguish halos that become groups or clusters from those that eventually form galaxies (possibly within the former objects). With our new mass function and our new application of the cooling criteria - which motivated this paper - we get a satisfactory and natural cutoff at the bright end of the luminosity function, the needed flat slope for faint magnitudes and the correct trend in colors (brighter galaxies are redder ) within the framework of the hierarchical clustering picture. This infirms earlier claims that the latter was inadequate to reproduce the former observations. We find the velocity dispersion to be a much better parameter than mass or radius to characterize galaxies. We find that bright galaxies form at z~2 from mergers with a rather quiet evolution afterwards, whereas small galaxies are the result of a continuous merging process active up to the present epoch. The transition is found to occur at the observed transition between bright spirals and small dwarf ellipticals or irregulars. The quasar multiplicity as a function of redshift is also discussed.

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arXiv1997

The Multiplicity Function of Galaxies, Clusters and Voids

We calculate the multiplicity function of matter condensations by directly considering the actual, deeply non-linear density field, which we compare to the popular Press-Schechter approximation. We show the mass function is a function of a unique parameter that contains all the dependence on the mass and radius of the object. It enables us to derive the mass function of general astrophysical objects (in addition to just-virialized halos) which may be defined by any density threshold, that may even vary with the mass of the object. This is beyond the reach of usual formulations based on the initial gaussian field and gives a clear illustration of the advantages of our approach. We explain why numerical tests seem to favor both Press-Schechter and non-linear prescriptions even though the two approximations differ by their scaling as a function of mass as well as a function of redshift. The difference between the two is due to the fact that the Press-Schechter prescription assumes that present-day mass fluctuations can be recognized in the early linear universe, and that their number is conserved, while the non-linear approach takes into account their evolution which leads to an increase of the number of highly non-linear objects (very large or small masses). This difference is seen to be of the same magnitude as the difference obtained by varying the initial spectrum of density fluctuations. Earlier conclusions drawn about the relevance of the latter using analytical approximations to the mass function must thus be reexamined.

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