Generic description of CMB power spectra

Taking advantage of the smoothness of CMB Cl power spectra, we derive a simple and model-independent parameterization of their measurement. It allows to describe completely the spectrum, ie. provide an estimate of the value and the error for any real l point at the percent level, down to low l multipole. We provide this parameterization for WMAP first year data and show that the spectrum is consistent with the smoothness hypothesis. We also show how such a parameterization allows to retrieve the Cl spectra from the measurement of Fourier rings on the sky (Gamma(m)) or from the angular correlation function (c(theta)

Overall determination of the CKM matrix

We discuss the problem of theoretical uncertainties in the combination of observables related to the CKM matrix elements and propose a statistically sensible method for combining them. The overall fit is performed on present data, and constraints on the matrix elements are presented as well as on fB*sqrt(Bb). We then explore the implications of recent measurements and developments: jpsi-KS CP asymmetry, epsilon_prime/epsilon and B -> K pi branching fractions. Finally, we extract from the overall fit the Standard Model expectations for the rare kaon decays K -> pi nu anti-nu.Comment: Talk given at Heavy Flavours 8, Southampton, UK, 199

Angpow: a software for the fast computation of accurate tomographic power spectra

The statistical distribution of galaxies is a powerful probe to constrain cosmological models and gravity. In particular the matter power spectrum $P(k)$ brings information about the cosmological distance evolution and the galaxy clustering together. However the building of $P(k)$ from galaxy catalogues needs a cosmological model to convert angles on the sky and redshifts into distances, which leads to difficulties when comparing data with predicted $P(k)$ from other cosmological models, and for photometric surveys like LSST. The angular power spectrum $C_\ell(z_1,z_2)$ between two bins located at redshift $z_1$ and $z_2$ contains the same information than the matter power spectrum, is free from any cosmological assumption, but the prediction of $C_\ell(z_1,z_2)$ from $P(k)$ is a costly computation when performed exactly. The Angpow software aims at computing quickly and accurately the auto ($z_1=z_2$) and cross ($z_1 \neq z_2$) angular power spectra between redshift bins. We describe the developed algorithm, based on developments on the Chebyshev polynomial basis and on the Clenshaw-Curtis quadrature method. We validate the results with other codes, and benchmark the performance. Angpow is flexible and can handle any user defined power spectra, transfer functions, and redshift selection windows. The code is fast enough to be embedded inside programs exploring large cosmological parameter spaces through the $C_\ell(z_1,z_2)$ comparison with data. We emphasize that the Limber's approximation, often used to fasten the computation, gives wrong $C_\ell$ values for cross-correlations.Comment: Published in Astronomy & Astrophysic

A direct method to compute the galaxy count angular correlation function including redshift-space distortions

In the near future, cosmology will enter the wide and deep galaxy survey area allowing high-precision studies of the large scale structure of the universe in three dimensions. To test cosmological models and determine their parameters accurately, it is natural to confront data with exact theoretical expectations expressed in the observational parameter space (angles and redshift). The data-driven galaxy number count fluctuations on redshift shells, can be used to build correlation functions $C(\theta; z_1, z_2)$ on and between shells which can probe the baryonic acoustic oscillations, the distance-redshift distortions as well as gravitational lensing and other relativistic effects. Transforming the model to the data space usually requires the computation of the angular power spectrum $C_\ell(z_1, z_2)$ but this appears as an artificial and inefficient step plagued by apodization issues. In this article we show that it is not necessary and present a compact expression for $C(\theta; z_1, z_2)$ that includes directly the leading density and redshift space distortions terms from the full linear theory. It can be evaluated using a fast integration method based on Clenshaw-Curtis quadrature and Chebyshev polynomial series. This new method to compute the correlation functions without any Limber approximation, allows us to produce and discuss maps of the correlation function directly in the observable space and is a significant step towards disentangling the data from the tested models

A novel estimator of the polarization amplitude from normally distributed Stokes parameters

We propose a novel estimator of the polarization amplitude from a single measurement of its normally distributed $(Q,U)$ Stokes components. Based on the properties of the Rice distribution and dubbed 'MAS' (Modified ASymptotic), it meets several desirable criteria:(i) its values lie in the whole positive region; (ii) its distribution is continuous; (iii) it transforms smoothly with the signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one; (iv) it is unbiased and reaches its components' variance as soon as the SNR exceeds 2; (v) it is analytic and can therefore be used on large data-sets. We also revisit the construction of its associated confidence intervals and show how the Feldman-Cousins prescription efficiently solves the issue of classical intervals lying entirely in the unphysical negative domain. Such intervals can be used to identify statistically significant polarized regions and conversely build masks for polarization data. We then consider the case of a general $[Q,U]$ covariance matrix and perform a generalization of the estimator that preserves its asymptotic properties. We show that its bias does not depend on the true polarization angle, and provide an analytic estimate of its variance. The estimator value, together with its variance, provide a powerful point-estimate of the true polarization amplitude that follows an unbiased Gaussian distribution for a SNR as low as 2. These results can be applied to the much more general case of transforming any normally distributed random variable from Cartesian to polar coordinates.Comment: Accepted by MNRA

CP violation with BaBar

The BABAR experiment is a new generation detector located at the SLAC B factory PEP-II ring which should start taking data at the end of 1999. Its main goal is the study of CP violation in the B0-B0b system. After explaining the nature of this CP violation, I review the scientific program for achieving this study in many different modes, in the light of the recent developments obtained both on the experimental and theoretical side. Implications for the Standard Model are then discussed.Comment: 17 pages, 8 postscript figures (using epsfig.sty

Agnostic cosmology in the CAMEL framework

Cosmological parameter estimation is traditionally performed in the Bayesian context. By adopting an "agnostic" statistical point of view, we show the interest of confronting the Bayesian results to a frequentist approach based on profile-likelihoods. To this purpose, we have developed the Cosmological Analysis with a Minuit Exploration of the Likelihood ("CAMEL") software. Written from scratch in pure C++, emphasis was put in building a clean and carefully-designed project where new data and/or cosmological computations can be easily included. CAMEL incorporates the latest cosmological likelihoods and gives access from the very same input file to several estimation methods: (i) A high quality Maximum Likelihood Estimate (a.k.a "best fit") using MINUIT ; (ii) profile likelihoods, (iii) a new implementation of an Adaptive Metropolis MCMC algorithm that relieves the burden of reconstructing the proposal distribution. We present here those various statistical techniques and roll out a full use-case that can then used as a tutorial. We revisit the $\Lambda$CDM parameters determination with the latest Planck data and give results with both methodologies. Furthermore, by comparing the Bayesian and frequentist approaches, we discuss a "likelihood volume effect" that affects the optical reionization depth when analyzing the high multipoles part of the Planck data. The software, used in several Planck data analyzes, is available from http://camel.in2p3.fr. Using it does not require advanced C++ skills.Comment: Typeset in Authorea. Online version available at: https://www.authorea.com/users/90225/articles/104431/_show_articl

Reconstruction of the cosmic microwave background lensing for Planck

Aims. We prepare real-life cosmic microwave background (CMB) lensing extraction with the forthcoming Planck satellite data by studying two systematic effects related to the foreground contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and the impact of removing a large contaminated region of the sky. Methods. We first use the generalized morphological component analysis (GMCA) method to perform a component separation within a simplified framework, which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then restore them with a recently developed inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. Results. We find that the foreground residuals from the GMCA method does not significantly alter the lensed signal, which is also true for the mask corrected with the inpainting method, even in the presence of point source residuals

Relieving tensions related to the lensing of CMB temperature power spectra

The angular power spectra of the cosmic microwave background (CMB) temperature anisotropies reconstructed from Planck data seem to present too much gravitational lensing distortion. This is quantified by the control parameter $A_L$ that should be compatible with unity for a standard cosmology. With the Class Boltzmann solver and the profile-likelihood method, for this parameter we measure a 2.6$\sigma$ shift from 1 using the Planck public likelihoods. We show that, owing to strong correlations with the reionization optical depth $\tau$ and the primordial perturbation amplitude $A_s$, a $\sim2\sigma$ tension on $\tau$ also appears between the results obtained with the low ($\ell\leq 30$) and high ($30<\ell\lesssim 2500$) multipoles likelihoods. With Hillipop, another high-$\ell$ likelihood built from Planck data, this difference is lowered to $1.3\sigma$. In this case, the $A_L$ value is still in disagreement with unity by $2.2\sigma$, suggesting a non-trivial effect of the correlations between cosmological and nuisance parameters. To better constrain the nuisance foregrounds parameters, we include the very high $\ell$ measurements of the Atacama Cosmology Telescope (ACT) and South Pole Telescope (SPT) experiments and obtain $A_L = 1.03 \pm 0.08$. The Hillipop+ACT+SPT likelihood estimate of the optical depth is $\tau=0.052\pm{0.035,}$ which is now fully compatible with the low $\ell$ likelihood determination. After showing the robustness of our results with various combinations, we investigate the reasons for this improvement that results from a better determination of the whole set of foregrounds parameters. We finally provide estimates of the $\Lambda$CDM parameters with our combined CMB data likelihood.Comment: accepted by A&