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Concept

Sigma

Résumé

Sigma (capitale Σ, minuscule σ, ς en fin de mot ; en grec σίγμα) est la lettre de l'alphabet grec, précédée par rhô et suivie par tau. Dérivée de la lettre shin x12px|shin de l'alphabet phénicien, elle est l'ancêtre de la lettre S de l'alphabet latin et de la lettre С de l'alphabet cyrillique. Caractéristiques Usage En grec moderne comme en grec ancien, la lettre sigma représente la consonne fricative alvéolaire sourde (). Ce son est voisé en devant ou . Dans le système de numération grecque, sigma vaut 200 ; par exemple représente le nombre 200. Comme la plupart des autres lettres grecques, le sigma est parfois utilisé en dehors de son contexte alphabétique grec dans les sciences. σ sert par exemple en physique à noter la conductivité électrique, en mathématiques à noter le rayon dans les coordonnées sphériques ou l'écart-type d'une série statistique ou encore en mécanique pour noter une contrainte. Σ, quant à lui, est utilisé dans l'écriture de la sommat

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https://fr.wikipedia.org/wiki/Sigma

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, , , , , , , , ,

The standard Lambda Cold Dark Matter (Lambda CDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant H-0, the sigma(8)-S-8 tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the 5.0 sigma tension between the Planck CMB estimate of the Hubble constant H-0 and the SH0ES collaboration measurements. After showing the H-0 evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density Omega(m), and the amplitude or rate of the growth of structure (sigma(8), f sigma(8)). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the H-0-S-8 tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questions. (C) 2022 The Author(s). Published by Elsevier B.V.

ELSEVIER2022

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Cosmological implications of the full shape of anisotropic clustering measurements in BOSS and eBOSS

Cheng Zhao

We present the analysis of the full shape of anisotropic clustering measurement from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) quasar sample together with the combined galaxy sample from the Baryon Oscillation Spectroscopic Survey (BOSS), re-analysed using an updated recipe for the non-linear matter power spectrum and the non-local bias parameters. We obtain constraints for flat Lambda cold dark matter cosmologies, focusing on the cosmological parameters that are independent of the Hubble parameter h. Our recovered value for the Root Mean Square (RMS) linear perturbation theory variance as measured on the scale of 12 Mpc is sigma(12) = 0.805 +/- 0.049, while using the traditional reference scale of 8 h(-1) Mpc gives sigma(8) = 0.815 +/- 0.044. We quantify the agreement between our measurements and the latest cosmic microwave background data from Planck using the suspiciousness metric, and find them to be consistent within 0.64 +/- 0.03 sigma. Combining our clustering constraints with the 3 x 2pt data sample from the Dark Energy Survey Year 1 release slightly degrades this agreement to the level of 1.54 +/- 0.08 sigma, while still showing an overall consistency with Planck. We furthermore study the effect of imposing a Planck - like prior on the parameters that define the shape of the linear matter power spectrum, and find significantly tighter constraints on the parameters that control the evolution of density fluctuations. In particular, the combination of low-redshift data sets prefers a value of the physical dark energy density omega(DE) = 0.335 +/- 0.011, which is 1.7 sigma higher than the one preferred by Planck.

OXFORD UNIV PRESS2022

Chargement

Cosmological constraints from weak lensing peak statistics with Canada-France-Hawaii Telescope Stripe 82 Survey

Jean-Paul Richard Kneib, Huanyuan Shan, Qiao Wang

We derived constraints on cosmological parameters using weak lensing peak statistics measured on the similar to aEuro parts per thousand 130 deg(2) of the Canada-France-Hawaii Telescope Stripe 82 Survey. This analysis demonstrates the feasibility of using peak statistics in cosmological studies. For our measurements, we considered peaks with signal-to-noise ratio in the range of nu = [3, 6]. For a flat I > cold dark matter model with only (Omega(m), sigma(8)) as free parameters, we constrained the parameters of the following relation I (8) pound = sigma(8)(Omega(m)/0.27)(alpha) to be I (8) pound = 0.82 +/- 0.03 and alpha = 0.43 +/- 0.02. The alpha value found is considerably smaller than the one measured in two-point and three-point cosmic shear correlation analyses, showing a significant complement of peak statistics to standard weak lensing cosmological studies. The derived constraints on (Omega(m), sigma(8)) are fully consistent with the ones from either WMAP9 or Planck. From the weak lensing peak abundances alone, we obtained marginalized mean values of tex-math id="TM0002" notation="LaTeX"

\Omega _{\rm m}=0.38{+0.27}_{-0.24}

/tex-math and sigma(8) = 0.81 +/- 0.26. Finally, we also explored the potential of using weak lensing peak statistics to constrain the mass-concentration relation of dark matter haloes simultaneously with cosmological parameters.

Oxford University Press2015

Chargement

Cosmological constraints from weak lensing peak statistics with Canada-France-Hawaii Telescope Stripe 82 Survey

Jean-Paul Richard Kneib, Huanyuan Shan, Qiao Wang

\Omega _{\rm m}=0.38{+0.27}_{-0.24}

Oxford University Press2015

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ELSEVIER2022