Sigma | EPFL Graph Search

Sigma ('sɪgmə; uppercase Σ, lowercase σ, lowercase in word-final position ς; σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end. The Latin letter S derives from sigma while the Cyrillic letter Es derives from a lunate form of this letter. History The shape (Σς) and alphabetic position of sigma is derived from the Phoenician letter (shin). Sigma's original name may have been san, but due to the complicated early history of the Greek epichoric alphabets, san came to be identified as a separate letter in the Greek alphabet, represented as Ϻ. Herodotus reports that "san" was the name given by the Do

Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies

Richard Irving Anderson, Hsin-Yu Chen, Frédéric Courbin, Fabio Finelli, Mikhail Ivanov, Melissa Joseph, Suresh Kumar, Julien Lesgourgues, Florian Niedermann, Emre Ozulker

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

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