CMB Anisotropies, Cosmological Parameters and Fundamental Physics: Current Status & Perspectives

I describe briefly the Cosmic Microwave Background (hereafter CMB) physics which explains why high accuracy observations of its spatial structure are a unique observational tool both for the determination of the global cosmological parameters and to constrain observationally the physics of the early universe. I also briefly survey the many experiments which have measured the anisotropies of the CMB and led to crucial advances in observational Cosmology. The somewhat frantic series of new results has recently culminated with the outcome of the WMAP satellite which confirmed earlier results, set new standards of accuracy, and suggested that the Universe may have reionised earlier than anticipated. Many more CMB experiments are currently taking data or being planned, with the Planck satellite on the 2007 Horizon poised to extract all the cosmological information in the temperature anisotropies, and foray deeply into polarisation.Comment: To appear in the proceedings of "Where Cosmology and Fundamental Physics Meet", 23-26 June, 2003, Marseille, Franc

The Planck mission

These lecture from the 100th Les Houches summer school on "Post-planck cosmology" of July 2013 discuss some aspects of the Planck mission, whose prime objective was a very accurate measurement of the temperature anisotropies of the Cosmic Microwave Background (CMB). We announced our findings a few months ago, on March 21$^{st}$, 2013. I describe some of the relevant steps we took to obtain these results, sketching the measurement process, how we processed the data to obtain full sky maps at 9 different frequencies, and how we extracted the CMB temperature anisotropies map and angular power spectrum. I conclude by describing some of the main cosmological implications of the statistical characteristics of the CMB we found. Of course, this is a very much shortened and somewhat biased view of the \Planck\ 2013 results, written with the hope that it may lead some of the students to consult the original papers.Comment: 53 p.-34 fig; for spacetime consideration, the file here is not paying justice to the actual thing; a closer approximation of it can be found at https://www.researchgate.net/profile/Francois_Bouchet/publication/262004262_The_Planck_Mission/file/e0b495363b042e81dd.pd

Kurtosis in Large-Scale Structure as a Constraint on Non-Gaussian Initial Conditions

We calculate the kurtosis of a large-scale density field which has undergone weakly non-linear gravitational evolution from arbitrary non-Gaussian initial conditions. It is well known that the weakly evolved {\twelveit skewness} is equal to its initial value plus the term induced by gravity, which scales with the rms density fluctuation in precisely the same way as for Gaussian initial conditions. As in the case of skewness, the evolved {\twelveit kurtosis} is equal to its initial value plus the contribution induced by gravity. The scaling of this induced contribution, however, turns out to be qualitatively different for Gaussian versus non-Gaussian initial conditions. Therefore, measurements of the kurtosis can serve as a powerful discriminating test between the hypotheses of Gaussian and non-Gaussian nature of primordial density fluctuations.Comment: uuencoded compressed tar file including postscript text (17 pages) and 2 postscript figures, submitted to MNRA

Error estimation for the MAP experiment

We report here the first full sky component separation and CMB power spectrum estimation using a Wiener filtering technique on simulated data from the upcoming MAP experiment, set to launch in early 2001. The simulations included contributions from the three dominant astrophysical components expected in the five MAP spectral bands, namely CMB radiation, Galactic dust, and synchrotron emission. We assumed a simple homogeneous and isotropic white noise model and performed our analysis up to a spherical harmonic multipole lmax=512 on the fraction of the sky defined by b>20 degrees. We find that the reconstruction errors are reasonably well fitted by a Gaussian with an rms of 24 $\mu$K, but with significant deviations in the tails. Our results further support the predictions on the resulting CMB power spectrum of a previous estimate by Bouchet and Gispert (1999), which entailed a number of assumptions this work removes.Comment: 5 pages, 3 color figures, version accepted in A&A Letter

Three-Point Statistics from a New Perspective

Multipole expansion of spatial three-point statistics is introduced as a tool for investigating and displaying configuration dependence. The novel parametrization renders the relation between bi-spectrum and three-point correlation function especially transparent as a set of two-dimensional Hankel transforms. It is expected on theoretical grounds, that three-point statistics can be described accurately with only a few multipoles. In particular, we show that in the weakly non-linear regime, the multipoles of the reduced bispectrum, $Q_l$, are significant only up to quadrupole. Moreover, the non-linear bias in the weakly non-linear regime only affects the monopole order of these statistics. As a consequence, a simple, novel set of estimators can be constructed to constrain galaxy bias. In addition, the quadrupole to dipole ratio is independent of the bias, thus it becomes a novel diagnostic of the underlying theoretical assumptions: weakly non-linear gravity and perturbative local bias. To illustrate the use of our approach, we present predictions based on both power law, and CDM models. We show that the presently favoured SDSS-WMAP concordance model displays strong ``baryon bumps'' in the $Q_l$'s. Finally, we sketch out three practical techniques estimate these novel quantities: they amount to new, and for the first time edge corrected, estimators for the bispectrum.Comment: 5 pages 6 figures, ApL accepte

Simulations of the Microwave Sky and of its ``Observations''

Here follows a preliminary report on the construction of fake millimeter and sub-millimeter skies, as observed by virtual instruments, e.g. the COBRA/SAMBA mission, using theoretical modeling and data extrapolations. Our goal is to create maps as realistic as possible of the relevant physical contributions which may contribute to the detected signals. This astrophysical modeling is followed by simulations of the measurement process itself by a given instrumental configuration. This will enable a precise determination of what can and cannot be achieved with a particular experimental configuration, and provide a feedback on how to improve the overall design. It is a key step on the way to define procedures for the separation of the different physical processes in the future observed maps. Note that this tool will also prove useful in preparing and analyzing current (\eg\ balloon borne) Microwave Background experiments. Keywords: Cosmology -- Microwave Background Anisotropies.Comment: 6 pages of uuencoded compressed postscript (1.2 Mb uncompressed), to appear in the proceedings of the meeting "Far Infrared and Sub-millimeter Space Missions in the Next Decade'', Paris, France, Eds. M. Sauvage, Space Science Revie

Self-similarity and scaling behavior of scale-free gravitational clustering

We measure the scaling properties of the probability distribution of the smoothed density field in $N$-body simulations of expanding universes with scale-free initial power-spectra, with particular attention to the predictions of the stable clustering hypothesis. We concentrate our analysis on the ratios $S_Q(\ell)\equiv {\bar \xi}_Q/{\bar \xi}_2^{Q-1}$, $Q \leq 5$, where ${\bar \xi}_Q$ is the averaged $Q$-body correlation function over a cell of radius $\ell$. The behavior of the higher order correlations is studied through that of the void probability distribution function. As functions of ${\bar \xi}_2$, the quantities $S_Q$, $3 \leq Q \leq 5$, exhibit two plateaus separated by a smooth transition around ${\bar \xi}_2 \sim 1$. In the weakly nonlinear regime, {\bar \xi}_2 \la 1, the results are in reasonable agreement with the predictions of perturbation theory. In the nonlinear regime, ${\bar \xi}_2 > 1$, the function $S_Q({\bar \xi}_2)$ is larger than in the weakly nonlinear regime, and increasingly so with $-n$. It is well-fitted by the expression $S_Q= ({\bar \xi}_2/100)^{0.045(Q-2)}\ {\widetilde S}_Q$for all$n. This weak dependence on scale proves {\em a small, but significant departure from the stable clustering predictions} at least for n=0$and$n=+1$. The analysis of$P_0$confirms that the expected scale-invariance of the functions$S_Q$is not exactly attained in the part of the nonlinear regime we probe, except possibly for$n=-2$and marginally for$n=-1$. In these two cases, our measurements are not accurate enough to be discriminant.Comment: 31 pages, postscript file, figure 1 missing. Postscript file including figure 1 available at ftp://ftp-astro-theory.fnal.gov:/pub/Publications/Pub-95-256-

Omega from the skewness of the cosmic velocity divergence

We propose a method for measuring the cosmological density parameter $\Omega$ from the statistics of the divergence field, $\theta \equiv H^{-1} \div v$, the divergence of peculiar velocity, expressed in units of the Hubble constant, $H \equiv 100 h km/s/Mpc$. The velocity field is spatially smoothed over $\sim 10 h^{-1} Mpc$ to remove strongly nonlinear effects. Assuming weakly-nonlinear gravitational evolution from Gaussian initial fluctuations, and using second-order perturbative analysis, we show that \propto -\Omega^{-0.6} ^2. The constant of proportionality depends on the smoothing window. For a top-hat of radius R and volume-weighted smoothing, this constant is $26/7-\gamma$, where $\gamma=-d\log / d\log R$. If the power spectrum is a power law, $P(k)\propto k^n$, then $\gamma=3+n$. A Gaussian window yields similar results. The resulting method for measuring $\Omega$ is independent of any assumed biasing relation between galaxies and mass. The method has been successfully tested with numerical simulations. A preliminary application to real data, provided by the POTENT recovery procedure from observed velocities favors $\Omega \sim 1$. However, because of an uncertain sampling error, this result should be treated as an assessment of the feasibility of our method rather than a definitive measurement of $\Omega$.Comment: 16 pages + 2 figures, uuencoded postscript file, also available by anonymous ftp from ftp.cita.utoronto.ca in directory /cita/francis/div_skewness, CITA 94-1