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1.
We optimise the parameters of the Population Monte Carlo algorithm using numerical simulations. The optimisation is based on an efficiency statistic related to the number of samples evaluated prior to convergence, and is applied to a D ‐dimensional Gaussian distribution to derive optimal scaling laws for the algorithm parameters. More complex distributions such as the banana and bimodal distributions are also studied. We apply these results to a cosmological parameter estimation problem that uses CMB anisotropy data from the WMAP nine‐year release to constrain a six parameter adiabatic model and a fifteen parameter admixture model, consisting of correlated adiabatic and isocurvature perturbations. In the case of the adiabatic model and the admixture model we find that the number of sample points increase by factors of 3 and 20, respectively, relative to the optimal Gaussian case. This is due to degeneracies in the underlying parameter space. The WMAP nine‐year data constrain the admixture model to have an isocurvature fraction of 36.3 ± 2.8 %. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

2.
Weak gravitational lensing surveys have the potential to probe mass density fluctuation in the Universe directly. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by modelling the statistics of the underlying density field in the highly non-linear regime. We propose a new method to model the complete probability distribution function of the convergence field as a function of smoothing angle and source redshift. The model relies on a hierarchical ansatz for the behaviour of higher order correlations of the density field. We compare our results with ray-tracing simulations and find very good agreement over a range of smoothing angles. Whereas the density probability distribution function is not sensitive to the cosmological model, the probability distribution function for the convergence can be used to constrain both the power spectrum and cosmological parameters.  相似文献   

3.
We study the estimators of various second-order weak lensing statistics such as the shear correlation functions  ξ±  and the aperture mass dispersion  〈 M 2ap〉  which can directly be constructed from weak lensing shear maps. We compare the efficiency with which these estimators can be used to constrain cosmological parameters. To this end we introduce the Karhunen–Loève (KL) eigenmode analysis techniques for weak lensing surveys. These tools are shown to be very effective as a diagnostics for optimizing survey strategies. The usefulness of these tools to study the effect of angular binning, the depth and width of the survey and noise contributions due to intrinsic ellipticities and number density of source galaxies on the estimation of cosmological parameters is demonstrated. Results from independent analysis of various parameters and joint estimations are compared. We also study how degeneracies among various cosmological and survey parameters affect the eigenmodes associated with these parameters.  相似文献   

4.
The real-space power spectrum of L * galaxies measured from the 2dF Galaxy Redshift Survey (2dFGRS) is presented. Markov chain Monte Carlo (MCMC) sampling was used to fit radial and angular modes resulting from a spherical harmonics decomposition of the 2dFGRS overdensity field (described in a previous paper) with 16 real-space power spectrum values and linear redshift-space distortion parameter  β( L *, 0)  . The recovered marginalized band powers are compared to previous estimates of galaxy power spectra. Additionally, we provide a simple model for the 17-dimensional likelihood hypersurface in order to allow the likelihood to be quickly estimated given a set of model band powers and β( L *, 0). The likelihood surface is not well approximated by a multivariate Gaussian distribution with model-independent covariances. Instead, a model is presented in which the distribution of each band power has a Gaussian distribution in a combination of the band power and its logarithm. The relative contribution of each component was determined by fitting the MCMC output. Using these distributions, we demonstrate how the likelihood of a given cosmological model can be quickly and accurately estimated, and we use a simple set of models to compare estimated likelihoods with likelihoods calculated using the full spherical harmonics procedure. All of the data are made publicly available (from http://www.roe.ac.uk/~wjp/ ), enabling the spherical harmonics decomposition of the 2dFGRS of Percival et al. to be easily used as a cosmological constraint.  相似文献   

5.
We present predictions for the one-point probability distribution and cumulants of the transmitted QSO flux in the high redshift Lyman- α forest. We make use of the correlation between the Lyman- α optical depth and the underlying matter density predicted by gravitational instability theory and seen in numerical hydrodynamic simulations. We have modelled the growth of matter fluctuations using the non-linear shear‐free dynamics, an approximation which reproduces well the results of perturbation theory for the cumulants in the linear and weakly non-linear clustering regime. As high matter overdensities tend to saturate in spectra, the statistics of the flux distribution are dominated by weakly non-linear overdensities. As a result, our analytic approach can produce accurate predictions, when tested against N -body simulation results, even when the underlying matter field has root-mean-square fluctuations larger than unity. Our treatment can be applied to either Gaussian or non-Gaussian initial conditions. Here we concentrate on the former case, but also include a study of a specific non-Gaussian model. We discuss how the methods and predictions we present can be used as a tool to study the generic clustering properties of the Lyman- α forest at high redshift. With such an approach, rather than concentrating on simulating specific cosmological models, we may be in a position to directly test our assumptions for the Gaussian nature of the initial conditions, and the gravitational instability origin of structure itself. In a separate paper we present results for two-point statistics.  相似文献   

6.
We present further development and the first public release of our multimodal nested sampling algorithm, called M ulti N est . This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the M ulti N est algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla Λ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The M ulti N est software, which is fully parallelized using MPI and includes an interface to C osmo MC, is available at http://www.mrao.cam.ac.uk/software/multinest/ . It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org .  相似文献   

7.
Future weak lensing surveys will directly probe the density fluctuation in the Universe. Recent studies have shown how the statistics of the weak lensing convergence field is related to the statistics of collapsed objects. Extending earlier analytical results on the probability distribution function of the convergence field, we show that the bias associated with the convergence field can be directly related to the bias associated with the statistics of underlying overdense objects. This will provide us with a direct method to study the gravity-induced bias in galaxy clustering. Based on our analytical results, which use the hierarchical Ansatz for non-linear clustering, we study how such a bias depends on the smoothing angle and the source redshift. We compare our analytical results with ray-tracing experiments through N -body simulations of four different realistic cosmological scenarios, and find a very good match. Our study shows that the bias in the convergence map strongly depends on the background geometry and hence can help us in distinguishing different cosmological models in addition to improving our understanding of the gravity-induced bias in galaxy clustering.  相似文献   

8.
We simulated both the matter and light (galaxy) distributions in a wedge of the Universe and calculated the gravitational lensing magnification caused by the mass along the line-of-sight of galaxies and galaxy groups identified in sky surveys. A large volume redshift cone containing cold dark matter particles mimics the expected cosmological matter distribution in a flat universe with low matter density and a cosmological constant. We generate a mock galaxy catalogue from the matter distribution and identify thousands of galaxy groups in the luminous sky projection. We calculate the expected magnification around galaxies and galaxy groups and then the induced quasi-stellar object (QSO)–lens angular correlation due to magnification bias. This correlation is observable and can be used both to estimate the average mass of the lens population and to make cosmological inferences. We also use analytical calculations and various analyses to compare the observational results with theoretical expectations for the cross-correlation between faint QSOs from the 2dF Survey and nearby galaxies and groups from the Automated Plate Measurement and Sloan Digital Sky Survey Early Data Release. The observed QSO–lens anticorrelations are stronger than the predictions for the cosmological model used. This suggests that there could be unknown systematic errors in the observations and data reduction, or that the model used is not adequate. If the observed signal is assumed to be solely due to gravitational lensing, then the lensing is stronger than expected, due to more massive galactic structures or more efficient lensing than simulated.  相似文献   

9.
Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Λ and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z , the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N -body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable differences.  相似文献   

10.
A comprehensive new approach is presented for deriving probability densities of physical properties characterizing the lens and source that constitute an observed galactic microlensing event. While previously encountered problems are overcome, constraints from event anomalies and model parameter uncertainties can be incorporated into the estimates. Probability densities for given events need to be carefully distinguished from the statistical distribution of the same parameters among the underlying population from which the actual lenses and sources are drawn. Using given model distributions of the mass spectrum, the mass density, and the velocity distribution of Galactic disc and bulge constituents, probability densities of lens mass, distance, and the effective lens–source velocities are derived, where the effect on the distribution that arises from additional observations of annual parallax or finite-source effects, or the absence of significant effects, is shown. The presented formalism can also be used to calculate probabilities for the lens to belong to one or another population and to estimate parameters that characterize anomalies. Finally, it is shown how detection efficiency maps for binary-lens companions in the physical parameters, such as companion mass and orbital semimajor axis, arise from values determined for the mass ratio and dimensionless projected separation parameter, including the deprojection of the orbital motion for elliptical orbits. Compared to the naive estimate based on 'typical values', the detection efficiency for low-mass companions is increased by mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller masses of the primary).  相似文献   

11.
Analytical expressions for covariances of weak lensing statistics related to the aperture mass,   M ap  , are derived for realistic survey geometries such as the Supernova Acceleration Probe (SNAP) 1 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 the finite catalogue size. 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 the survey parameters. Dependences 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 the same or different surveys. The dependence of these coefficients on various models of underlying mass correlation hierarchy is also studied. Generalizations of these coefficients at the level of three-point statistics have the potential of probing the complete shape dependence of the underlying bi-spectrum of the matter distribution. A complete error analysis incorporating all sources of errors suggests encouraging results for studies using future space-based weak lensing surveys such as SNAP.  相似文献   

12.
We present a hydrodynamical code for cosmological simulations which uses the piecewise parabolic method (PPM) to follow the dynamics of the gas component and an N -body particle–mesh algorithm for the evolution of the collisionless component. The gravitational interaction between the two components is regulated by the Poisson equation which is solved by a standard fast Fourier transform (FFT) procedure. In order to simulate cosmological flows we have introduced several modifications to the original PPM scheme which we describe in detail. Various tests of the code are presented including adiabatic expansion, single and multiple pancake formation and three-dimensional cosmological simulations with initial conditions based on the cold dark matter scenario.  相似文献   

13.
In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalizing over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article, we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors.
As an alternative we present a functional form-filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown, we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model, we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalizing over a systematic, but that in contrast the functional form-filling approach is independent of the choice of basis set.
We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of  | m ( z )| ≲ 10−3 (1 + z )0.7  is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to per cent accuracy.
A module associated with the work in this paper is available through the open source icosmo code available at http://www.icosmo.org .  相似文献   

14.
Using the ray-bundle method for calculating gravitational lens magnifications, we outline a method by which the magnification probability may be determined specifically in the weak lensing limit for cosmological models obtained from N -body simulations.
16 different models are investigated, which are variations on three broad classes of cold dark matter model: the standard model with  (Ω0, λ 0)=(1.0,0.0)  , the open model with  (Ω0, λ 0)=(0.3,0.0)  and the lambda model, which is a flat model with a cosmological constant  (Ω0, λ 0)=(0.3,0.7)  .
The effects of varying the Hubble parameter, H 0, the power spectrum shape parameter, Γ, and the cluster mass normalization, σ 8, are studied. It is shown that there is no signature of these parameters in the weak lensing magnification distributions. The magnification probability distributions are also shown to be independent of the numerical parameters such as the lens mass and simulation box size in the N -body simulations.  相似文献   

15.
There has been increasing interest by cosmologists in applying Bayesian techniques, such as Bayesian Evidence, for model selection. A typical example is in assessing whether observational data favour a cosmological constant over evolving dark energy. In this paper, the example of dark energy is used to illustrate limitations in the application of Bayesian Evidence associated with subjective judgements concerning the choice of model and priors. An analysis of recent cosmological data shows a statistically insignificant preference for a cosmological constant over simple dynamical models of dark energy. It is argued that for nested problems, as considered here, Bayesian parameter estimation can be more informative than computing Bayesian Evidence for poorly motivated physical models.  相似文献   

16.
The use of Type Ia supernovae (SNe Ia) as cosmological standard candles is a key to solving the mystery of dark energy. Improving the calibration of SNe Ia increases their power as cosmological standard candles. We find tentative evidence for a correlation between the late-time light-curve slope and the peak luminosity of SNe Ia in the B band; brighter SNe Ia seem to have shallower light-curve slopes between 100 and 150 d from maximum light. Using a Markov Chain Monte Carlo (MCMC) analysis in calibrating SNe Ia, we are able to simultaneously take into consideration the effect of dust extinction, the luminosity and light-curve width correlation (parametrized by  Δ m 15  ), and the luminosity and late-time light-curve slope correlation. For the available sample of 11 SNe Ia with well-measured late-time light curves, we find that correcting for the correlation between luminosity and late-time light-curve slope of the SNe Ia leads to an intrinsic dispersion of 0.12 mag in the Hubble diagram. Our results have significant implications for future supernova surveys aimed to illuminate the nature of dark energy.  相似文献   

17.
We present the results of weak gravitational lensing statistics in four different cosmological N -body simulations. The data have been generated using an algorithm for the three-dimensional shear, which makes use of a variable softening facility for the N -body particle masses, and enables a physical interpretation for the large-scale structure to be made. Working in three dimensions also allows the correct use of the appropriate angular diameter distances.
Our results are presented on the basis of the filled-beam approximation in view of the variable particle softening scheme in our algorithm. The importance of the smoothness of matter in the Universe for the weak lensing results is discussed in some detail.
The low-density cosmology with a cosmological constant appears to give the broadest distributions for all the statistics computed for sources at high redshifts. In particular, the range in magnification values for this cosmology has implications for the determination of the cosmological parameters from high-redshift type Ia supernovae. The possibility of determining the density parameter from the non-Gaussianity in the probability distribution for the convergence is discussed.  相似文献   

18.
Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasi-linear scales as they relied on perturbative calculations. On the other hand, observational surveys are likely to probe angular scales less than 10 arcmin, for which the relevant physical length-scales are in the non-linear regime of gravitational clustering. We use the hierarchical ansatz to compute the multipoint statistics of the weak lensing convergence for these small smoothing angles. We predict the multipoint cumulants and cumulant correlators up to fourth order and compare our results with high-resolution ray-tracing simulations. Averaging over a large number of simulation realizations for four different cosmological models, we find close agreement with the analytical calculations. In combination with our work on the probability distribution function, these results provide accurate analytical models for the full range of weak lensing statistics. The models allow for a detailed exploration of cosmological parameter space and of the dependence on angular scale and the redshift distribution of source galaxies. We compute the dependence of the higher moments of the convergence on the parameters Ω and Λ.  相似文献   

19.
Measurements of clustering in large-scale imaging surveys that make use of photometric redshifts depend on the uncertainties in the redshift determination. We have used light-cone simulations to show how the deprojection method successfully recovers the real-space correlation function when applied to mock photometric redshift surveys. We study how the errors in the redshift determination affect the quality of the recovered two-point correlation function. Considering the expected errors associated with the planned photometric redshift surveys, we conclude that this method provides information on the clustering of matter useful for the estimation of cosmological parameters that depend on the large-scale distribution of galaxies.  相似文献   

20.
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