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Concept# Lambda-CDM model

Summary

The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda (Greek Λ) associated with dark energy; second, the postulated cold dark matter (abbreviated CDM); and third, ordinary matter. It is frequently referred to as the standard model of Big Bang cosmology because it is the simplest model that provides a reasonably good account of the following properties of the cosmos:

- the existence and structure of the cosmic microwave background
- the large-scale structure in the distribution of galaxies
- the observed abundances of hydrogen (including deuterium), helium, and lithium
- the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

Official source

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Cosmology is the study of the structure and evolution of the universe as a whole. This course describes the principal themes of cosmology, as seen
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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.

Benjamin Audren, Julien Lesgourgues

We address the issue of computing the non-linear matter power spectrum on mildly non-linear scales with efficient semi-analytic methods. We implemented M. Pietroni's Time Renormalization Group (TRG) method and its Dynamical 1-Loop (D1L) limit in a numerical module for the new Boltzmann code CLASS. Our publicly released module is valid for Lambda CDM models, and optimized in such away to run in less than a minute for D1L, or in one hour (divided by number of nodes) for TRG. A careful comparison of the D1L, TRG and Standard 1-Loop approaches reveals that results depend crucially on the assumed initial bispectrum at high redshift. When starting from a common assumption, the three methods give roughly the same results, showing that the partial resumation of diagrams beyond one loop in the TRG method improves one-loop results by a negligible amount. A comparison with highly accurate simulations by M. Sato & T. Matsubara shows that all three methods tend to over-predict non-linear corrections by the same amount on small wavelengths. Percent precision is achieved until k similar to 0.2 hMpc(-)1 for z >= 2, or until k similar to 0.14 hMpc(-1) at z = 1.

2011Since the public release of Planck data, several attempts have been made to explain the observed small tensions with other data sets, most of them involving an extension of the Lambda cold dark matter (Lambda CDM) model. We try here an alternative approach to the data analysis, based on separating the constraints coming from the different epochs in cosmology, in order to assess which part of the standard model generates the tension with the data. To this end, we perform a particular analysis of Planck data probing only the early cosmological evolution, until the time of photon decoupling. Then, we utilize this result to see if the Lambda CDM model can fit all observational constraints probing only the late cosmological background evolution, discarding any information concerning the late perturbation evolution. We find that all tensions between the data sets are removed, suggesting that our standard assumptions on the perturbed late-time history, as well as on reionization, could sufficiently bias our parameter extraction and be the source of the alleged tensions.

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