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)

Does the speed of light depend upon the vacuum ?

We propose a quantum model for the vacuum filled of virtual particle pairs. The main originality of this model is to define a density and a life-time of the virtual particles. Compared to the usual QED $(p,E)$ framework, we add here the $(x,t)$ space time parameters. We show how $\epsilon_0$ and $\mu_0$ originate from the polarization and the magnetization of these virtual pairs when the vacuum is stressed by an electrostatic or magnetostatic field respectively. We obtain numerical values very close to the measured values. The exact equalities constraint the free parameters of our vacuum model. Then we show that if we simply model the propagation of a photon in vacuum as a succession of transient captures with virtual pairs, we can derive a finite velocity of the photon with a magnitude close to the measured speed of light $c$. Again this is the occasion to adjust better our vacuum model. Since the transit time of a photon is a statistical process we expect it to be fluctuating and this translates into a fluctuation of $c$ which, if measured, would bring another piece of information on the vacuum. When submitted to a stress the vacuum may change and this will induce a variation in the electromagnetic constants. We show this to be the case around a gravitational mass. It gives a physical interpretation of a varying vacuum refractive index equivalent to the curved space-time in General Relativity. The known measurements of the deflection of light by a mass, the Shapiro delay and the gravitational redshift do bring constraints on the way inertial masses should depend upon the vacuum. At last some experimental predictions are proposed.Comment: 25 page

Almost clean rings and arithmetical rings

It is shown that a commutative B\'ezout ring $R$ with compact minimal prime spectrum is an elementary divisor ring if and only if so is $R/L$ for each minimal prime ideal $L$. This result is obtained by using the quotient space $\mathrm{pSpec} R$ of the prime spectrum of the ring $R$ modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if $R$ is arithmetical, $\mathrm{pSpec} R$ is Hausdorff and there is a bijection between this quotient space and the minimal prime spectrum $\mathrm{Min} R$, which is a homeomorphism if and only if $\mathrm{Min} R$ is compact. If $x$ is a closed point of $\mathrm{pSpec} R$, there is a pure ideal $A(x)$ such that $x=V(A(x))$. If $R$ is almost clean, i.e. each element is the sum of a regular element with an idempotent, it is shown that $\mathrm{pSpec} R$ is totally disconnected and, $\forall x\in\mathrm{pSpec} R$, $R/A(x)$ is almost clean; the converse holds if every principal ideal is finitely presented. Some questions posed by Facchini and Faith at the second International Fez Conference on Commutative Ring Theory in 1995, are also investigated. If $R$ is a commutative ring for which the ring $Q(R/A)$ of quotients of $R/A$ is an IF-ring for each proper ideal $A$, it is proved that $R_P$ is a strongly discrete valuation ring for each maximal ideal $P$ and $R/A$ is semicoherent for each proper ideal $A$

A mechanism giving a finite value to the speed of light, and some experimental consequences

We admit that the vacuum is not empty but is filled with continuously appearing and disappearing virtual fermion pairs. We show that if we simply model the propagation of the photon in vacuum as a series of transient captures within the virtual pairs, we can derive the finite light velocity $c$ as the average delay on the photon propagation. We then show that the vacuum permittivity $\epsilon_0$ and permeability $\mu_0$ originate from the polarization and the magnetization of the virtual fermions pairs. Since the transit time of a photon is a statistical process within this model, we expect it to be fluctuating. We discuss experimental tests of this prediction. We also study vacuum saturation effects under high photon density conditions.Comment: Submitted to International Journal of Modern Physics A. arXiv admin note: substantial text overlap with arXiv:1106.399

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&

About the connection between the CℓC_{\ell} power spectrum of the Cosmic Microwave Background and the Γm\Gamma_{m} Fourier spectrum of rings on the sky

In this article we present and study a scaling law of the $m\Gamma_m$ CMB Fourier spectrum on rings which allows us (i) to combine spectra corresponding to different colatitude angles (e.g. several detectors at the focal plane of a telescope), and (ii) to recover the $C_l$ power spectrum once the $\Gamma_m$ coefficients have been measured. This recovery is performed numerically below the 1% level for colatitudes $\Theta> 80^\circ$ degrees. In addition, taking advantage of the smoothness of the $C_l$ and of the $\Gamma_m$, we provide analytical expressions which allow to recover one of the spectrum at the 1% level, the other one being known.Comment: 8 pages, 8 figure

On the Link Between Strongly Connected Iteration Graphs and Chaotic Boolean Discrete-Time Dynamical Systems

Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a continuous function, whose discrete-time iterations are chaotic if and only if the iteration graph of the Boolean network is strongly connected. Then, sufficient conditions for this strong connectivity are expressed on the interaction graph of this network, leading to a constructive method of chaotic function computation. The whole approach is evaluated in the chaos-based pseudo-random number generation context

HFI L2 DPC destripping and mapmaking modules

PoS(CMB2006)049International audienceThe data processing of the data from the High Frequency Instrument (HFI) of the Planck mission will use several modules. Destriping is expected to play a central role in the mapmaking stage. This paper outlines two existing HFI l2 DPC destriping modules together with estimations of their performances. MOKAPIX is a temperature data destriping tool based on scanning redundancies on the sky. We have developped another modules, BOGOPIX , based on the same philosophy, to perform simultaneously destriping and relative intercalibration

Destriping of Polarized Data in a CMB Mission with a Circular Scanning Strategy

A major problem in Cosmic Microwave Background (CMB) anisotropy mapping, especially in a total-power mode, is the presence of low-frequency noise in the data streams. If unproperly processed, such low-frequency noise leads to striping in the maps. To deal with this problem, solutions have already been found for mapping the CMB temperature fluctuations but no solution has yet been proposed for the measurement of CMB polarization. Complications arise due to the scan-dependent orientation of the measured polarization. In this paper, we investigate a method for building temperature and polarization maps free of striping effects in the case of a circular scanning strategy mission such as that of the Planck satellite