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Flat $\Lambda$CDM cosmology is specified by two constant fitting parameters at the background level in the late Universe, the Hubble constant $H_0$ and matter density (today) $\Omega_m$. Mathematically, $H_0$ and $\Omega_m$ are either…

Cosmology and Nongalactic Astrophysics · Physics 2024-03-19 Eoin Ó Colgáin , M. M. Sheikh-Jabbari , Rance Solomon , Maria G. Dainotti , Dejan Stojkovic

One problem of the $\Lambda$CDM model is the tension between the $S_8$ found in Cosmic Microwave Background (CMB) experiments and the smaller one obtained from large-scale observations in the late Universe. The $\sigma_8$ quantifies the…

Cosmology and Nongalactic Astrophysics · Physics 2021-01-12 David Benisty

The parameter $S_8 \equiv \sigma_8 (\Omega_m/0.3)^{0.5}$ quantifies the amplitude of matter density fluctuations. A persistent discrepancy exists between early-universe CMB observations and late-universe probes. This review assesses the…

Cosmology and Nongalactic Astrophysics · Physics 2026-03-30 Ioannis Pantos , Leandros Perivolaropoulos

The Hubble tension between the $\Lambda$CDM-model-dependent prediction of the current expansion rate $H_0$ using Planck data and direct, model-independent measurements in the local universe from the SH0ES collaboration disagree at…

Cosmology and Nongalactic Astrophysics · Physics 2020-07-14 Kanhaiya L. Pandey , Tanvi Karwal , Subinoy Das

One of the most prominent challenges to the standard Lambda cold dark matter ($\Lambda$CDM) cosmology is the tension between the structure growth parameter $S_8$ constrained by the cosmic microwave background (CMB) data and the smaller one…

Cosmology and Nongalactic Astrophysics · Physics 2022-01-04 Lu Huang , Zhiqi Huang , Huan Zhou , Zhuoyang Li

The standard relation between the cosmological redshift and cosmic scale factor underlies cosmological inference from virtually all kinds of cosmological observations, leading to the emergence of the LambdaCDM cosmological model. This…

Cosmology and Nongalactic Astrophysics · Physics 2019-08-08 Radosław Wojtak , Francisco Prada

Within the $\Lambda$CDM model, measurements from recent Cosmic Microwave Background (CMB) and weak lensing (WL) surveys have uncovered a $\sim 3\sigma$ disagreement in the inferred value of the parameter $S_8 \equiv…

Cosmology and Nongalactic Astrophysics · Physics 2021-07-05 Rafael C. Nunes , Sunny Vagnozzi

Models of dark energy or modified gravity that tries to alleviate the tensions on the Hubble constant ($H_0$) and the matter fluctuation parameter ($\sigma_8$) are usually parameterized as function of either late or early time cosmic…

Cosmology and Nongalactic Astrophysics · Physics 2023-05-05 Ziad Sakr

The $\Lambda$CDM model successfully explains a wide range of cosmological observations; however, persistent discrepancies most notably the $H_0$ tension between early and late time measurements challenge its completeness. No proposed…

Cosmology and Nongalactic Astrophysics · Physics 2026-03-31 Upala Mukhopadhyay , Purba Mukherjee , Alexandre Tkatchenko

The excellent measurements of the cosmic microwave background (CMB) fluctuations by Planck allow us to tightly constrain the amplitude of matter fluctuations at redshift $\sim 1100$ in the $\Lambda$-cold dark matter ($\Lambda$CDM) model.…

Cosmology and Nongalactic Astrophysics · Physics 2021-12-21 Alain Blanchard , Stéphane Ilić

Recently released Planck data favor a lower value of the Hubble constant and a higher value of the fraction matter density in the standard $\Lambda$CDM model, which are discrepant with some of the low-redshift measurements. Within the…

Cosmology and Nongalactic Astrophysics · Physics 2014-07-23 Rong-Gen Cai , Zong-Kuan Guo , Bo Tang

Measurements of weak gravitational lensing at low redshifts ($z\lesssim 0.5-1$), quantified by the parameter $S_8$, favor weaker matter clustering than that expected from the standard $\Lambda$CDM cosmological model with parameters…

Cosmology and Nongalactic Astrophysics · Physics 2023-10-12 Vivian Poulin , José Luis Bernal , Ely Kovetz , Marc Kamionkowski

Weak galaxy lensing surveys have consistently reported a lower amplitude for the matter fluctuation spectrum, as measured by the $S_8$ parameter, than expected in the $\Lambda{\rm CDM}$ cosmology favoured by $Planck$. However, the expansion…

Cosmology and Nongalactic Astrophysics · Physics 2022-09-14 Alexandra Amon , George Efstathiou

The $S_8$ tension between low-redshift galaxy surveys and the primary CMB signals a possible breakdown of the $\Lambda$CDM model. Recently differing results have been obtained using low-redshift galaxy surveys and the higher redshifts…

Cosmology and Nongalactic Astrophysics · Physics 2024-03-19 Meng-Xiang Lin , Bhuvnesh Jain , Marco Raveri , Eric J. Baxter , Chihway Chang , Marco Gatti , Sujeong Lee , Jessica Muir

We use recently published redshift space distortion measurements of the cosmological growth rate, f sigma_8(z), to examine whether the linear evolution of perturbations in the R_h=ct cosmology is consistent with the observed development of…

Cosmology and Nongalactic Astrophysics · Physics 2018-09-21 Fulvio Melia

We analyze the claimed tension between redshift space distorsions measurements of $f(z)\sigma_8(z)$ and the predictions of standard $\Lambda$CDM (Planck 2015 and 2018) cosmology. We consider a dataset consisting of 17 data points extending…

Cosmology and Nongalactic Astrophysics · Physics 2020-05-20 Alba Quelle , Antonio L. Maroto

The $S_8$ parameter, which quantifies the amplitude of matter fluctuations on scales of $8h^{-1}$ Mpc, has been a source of tension between weak lensing surveys (e.g. KiDS, DES, HSC) and the Planck Cosmic Microwave Background (CMB)…

Cosmology and Nongalactic Astrophysics · Physics 2025-06-10 Stuart Marongwe , Stuart Kauffman , Moletlanyi Tshipa , Christian Corda

A major issue in contemporary cosmology is the persistent discrepancy, known as the Hubble tension, between the Hubble constant ($H_0$) estimates from local measurements and those inferred from early-Universe observations under the standard…

Cosmology and Nongalactic Astrophysics · Physics 2025-12-29 Surajit Kalita , Akhil Uniyal , Tomasz Bulik , Yosuke Mizuno

We construct an updated extended compilation of distinct (but possibly correlated) $f\sigma_8(z)$ Redshift Space Distortion (RSD) data published between 2006 and 2018. It consists of 63 datapoints and is significantly larger than previously…

Cosmology and Nongalactic Astrophysics · Physics 2018-05-09 Lavrentios Kazantzidis , Leandros Perivolaropoulos

We present constraints on the amplitude of matter fluctuations from the clustering of galaxies and their cross-correlation with the gravitational lensing convergence of the cosmic microwave background (CMB), focusing on low redshifts…

Cosmology and Nongalactic Astrophysics · Physics 2025-10-13 Andrea Rubiola , Matteo Zennaro , Carlos García-García , David Alonso
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