Probing The Gravity Induced Bias with Weak Lensing: Test of Analytical results Against Simulations

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 directly be related to the bias associated with the statistics of underlying over-dense objects. This will provide us a direct method to study the gravity induced bias in galaxy clustering. Based on our analytical results which use the hierarchical {\em ansatz} for non-linear clustering, we study how such a bias depends on the smoothing angle and the source red-shift. We compare our analytical results against ray tracing experiments through N-body simulations of four different realistic cosmological scenarios and found 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.Comment: 17 pages including 8 figures and 1 table, MNRAS, submitte

Error Estimates for Measurements of Cosmic Shear

In the very near future, weak lensing surveys will map the projected density of the universe in an unbiased way over large regions of the sky. In order to interpret the results of studies it is helpful to develop an understanding of the errors associated with quantities extracted from the observations. In a generalization of one of our earlier works, we present estimators of the cumulants and cumulant correlators of the weak lensing convergence field, and compute the variance associated with these estimators. By restricting ourselves to so-called compensated filters we are able to derive quite simple expressions for the errors on these estimates. We also separate contributions from cosmic variance, shot noise and intrinsic ellipticity of the source galaxies.Comment: 12 pages, including 5 figures, uses mn.sty. Substantially revised version accepted by MNRA

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.Comment: 20 pages, final version published in MNRA

Planck 2013 results. XXII. Constraints on inflation

We analyse the implications of the Planck data for cosmic inflation. The Planck nominal mission temperature anisotropy measurements, combined with the WMAP large-angle polarization, constrain the scalar spectral index to be ns = 0:9603 _ 0:0073, ruling out exact scale invariance at over 5_: Planck establishes an upper bound on the tensor-to-scalar ratio of r < 0:11 (95% CL). The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V00 < 0. Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n _ 2 do not provide a good fit to the data. Planck does not find statistically significant running of the scalar spectral index, obtaining dns=dln k = 0:0134 _ 0:0090. We verify these conclusions through a numerical analysis, which makes no slowroll approximation, and carry out a Bayesian parameter estimation and model-selection analysis for a number of inflationary models including monomial, natural, and hilltop potentials. For each model, we present the Planck constraints on the parameters of the potential and explore several possibilities for the post-inflationary entropy generation epoch, thus obtaining nontrivial data-driven constraints. We also present a direct reconstruction of the observable range of the inflaton potential. Unless a quartic term is allowed in the potential, we find results consistent with second-order slow-roll predictions. We also investigate whether the primordial power spectrum contains any features. We find that models with a parameterized oscillatory feature improve the fit by __2 e_ _ 10; however, Bayesian evidence does not prefer these models. We constrain several single-field inflation models with generalized Lagrangians by combining power spectrum data with Planck bounds on fNL. Planck constrains with unprecedented accuracy the amplitude and possible correlation (with the adiabatic mode) of non-decaying isocurvature fluctuations. The fractional primordial contributions of cold dark matter (CDM) isocurvature modes of the types expected in the curvaton and axion scenarios have upper bounds of 0.25% and 3.9% (95% CL), respectively. In models with arbitrarily correlated CDM or neutrino isocurvature modes, an anticorrelated isocurvature component can improve the _2 e_ by approximately 4 as a result of slightly lowering the theoretical prediction for the ` <_ 40 multipoles relative to the higher multipoles. Nonetheless, the data are consistent with adiabatic initial conditions

Scaling in Gravitational Clustering, 2D and 3D Dynamics

Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been made for the moments and the shape of the one-point probability distribution function (PDF) of the top-hat smoothed density. In this paper we perform a series of systematic checks of these predictions against N-body computations both in 2D and 3D with a wide range of featureless power spectra. In agreement with previous studies, we found that the reconstructed PDF-s work remarkably well down to very low probabilities, even when the variance approaches unity. Our results for 2D reproduce the features for the 3D dynamics. In particular we found that the PT predictions are more accurate for spectra with less power on small scales. The nonlinear regime has been explored with various tools, PDF-s, moments and Void Probability Function (VPF). These studies have been done with unprecedented dynamical range, especially for the 2D case, allowing in particular more robust determinations of the asymptotic behaviour of the VPF. We have also introduced a new method to determine the moments based on the factorial moments. Results using this method and taking into account the finite volume effects are presented.Comment: 13 pages, Latex file, 9 Postscript Figure

Remote-scope Promotion: Clarified, Rectified, and Verified

Modern accelerator programming frameworks, such as OpenCL, organise threads into work-groups. Remote-scope promotion (RSP) is a language extension recently proposed by AMD researchers that is designed to enable applications, for the first time, both to optimise for the common case of intra-work-group communication (using memory scopes to provide consistency only within a work-group) and to allow occasional inter-work-group communication (as required, for instance, to support the popular load-balancing idiom of work stealing). We present the first formal, axiomatic memory model of OpenCL extended with RSP. We have extended the Herd memory model simulator with support for OpenCL kernels that exploit RSP, and used it to discover bugs in several litmus tests and a work-stealing queue, that have been used previously in the study of RSP. We have also formalised the proposed GPU implementation of RSP. The formalisation process allowed us to identify bugs in the description of RSP that could result in well-synchronised programs experiencing memory inconsistencies. We present and prove sound a new implementation of RSP that incorporates bug fixes and requires less non-standard hardware than the original implementation. This work, a collaboration between academia and industry, clearly demonstrates how, when designing hardware support for a new concurrent language feature, the early application of formal tools and techniques can help to prevent errors, such as those we have found, from making it into silicon