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| sigma_8 | |
|---|---|
| Name | sigma_8 |
| Type | parameter |
| Field | Cosmology |
| Related | Cosmic microwave background, Large-scale structure of the universe, Lambda-CDM model |
sigma_8 sigma_8 is a standard cosmological parameter that quantifies the amplitude of matter density fluctuations on scales of 8 h^−1 megaparsecs. It is widely used in analyses of the cosmic web, galaxy clustering, and cosmic microwave background anisotropies to compare observations with theoretical predictions from structure formation models. Measurements of sigma_8 contribute to constraints on the Lambda-CDM model, dark matter, and dark energy through their impact on growth rates and cluster abundances.
sigma_8 is defined as the root-mean-square fluctuation of the linear matter density field smoothed with a spherical top-hat window of radius 8 h^−1 Mpc, expressed in comoving coordinates. The choice of 8 h^−1 Mpc originated in early studies of galaxy clustering and Abell catalogue cluster counts and remains a conventional scale for comparing results across surveys such as Sloan Digital Sky Survey, 2dF Galaxy Redshift Survey, Dark Energy Survey, and Planck. Physically, sigma_8 encapsulates the normalization of the power spectrum P(k) and links primordial perturbations—often parameterized by inflation models like single-field inflation or slow-roll inflation—to the late-time distribution of matter influenced by processes involving Cold dark matter, baryon acoustic oscillations, and reionization.
Estimating sigma_8 uses diverse observational probes and statistical methods, including analyses of the Cosmic microwave background anisotropy spectra measured by Planck, WMAP, and COBE. Large-scale structure techniques involve two-point correlation functions and power spectrum estimation from galaxy redshift surveys such as Sloan Digital Sky Survey, 2dF Galaxy Redshift Survey, Baryon Oscillation Spectroscopic Survey, and Euclid forecasts. Weak gravitational lensing measurements from surveys like Kilo-Degree Survey, Hyper Suprime-Cam, and Dark Energy Survey extract shear auto-correlation functions and employ shear tomography and mass-mapping pipelines. Cluster abundance counts drawn from X-ray observatories such as Chandra X-ray Observatory and XMM-Newton or Sunyaev–Zel'dovich surveys by Atacama Cosmology Telescope and South Pole Telescope use mass–observable scaling relations calibrated by gravitational lensing and hydrostatic equilibrium assumptions. Cross-correlation analyses combine probes with Bayesian inference frameworks implemented in codes like CosmoMC and MontePython.
sigma_8 serves as a key normalization parameter in the Lambda-CDM model and its extensions, affecting predictions for halo mass functions such as the Press–Schechter formalism and Sheth–Tormen fits, galaxy bias models in studies using Halo occupation distribution, and nonlinear evolution characterized by N-body simulation suites like those produced by collaborations at Max Planck Institute for Astrophysics and Lawrence Berkeley National Laboratory. It enters growth-rate observables fσ8 measured in redshift-space distortion analyses from BOSS and WiggleZ, and it influences cosmological parameter degeneracies with Hubble constant estimates from Hubble Space Telescope observations and distance-ladder measurements by teams including those led by Adam Riess. sigma_8 also impacts predictions for gravitational lensing signals around galaxies and clusters studied by teams at University of Cambridge, University of Chicago, and Harvard–Smithsonian Center for Astrophysics.
CMB-based determinations from Planck typically report sigma_8 values inferred jointly with parameters like the scalar spectral index n_s and matter density Ω_m, whereas weak lensing surveys such as KiDS, DES, and HSC have reported somewhat lower favored values, leading to comparisons across datasets. Cluster abundance studies using ROSAT and SZ catalogs from Planck and South Pole Telescope yield constraints sensitive to mass calibration from weak lensing programs at institutions such as Max Planck Institute for Extraterrestrial Physics. Joint analyses combining CMB, large-scale structure, lensing, and supernova data from programs including Supernova Cosmology Project and SNe Ia compilations produce marginalized posterior distributions where sigma_8 covaries strongly with Ω_m, often summarized as constraints on the parameter combination S8 = σ8(Ωm/0.3)^0.5 used by collaborations like Dark Energy Survey.
Predictions for sigma_8 depend on the primordial power spectrum amplitude A_s, spectral index n_s, and the transfer function shaped by particle content such as Cold dark matter and massive neutrinos addressed in models by research groups at Fermilab and CERN. Extensions to Lambda-CDM model—including wCDM, modified gravity frameworks like f(R) gravity and Massive gravity, or interacting dark sector scenarios studied by teams at University of Oxford and Institut d'Astrophysique de Paris—alter linear growth and hence sigma_8. Numerical calibration using hydrodynamical simulations from collaborations such as Illustris and EAGLE refines baryonic effects on small-scale power and informs emulators used in pipeline analyses by groups at Flatiron Institute and NVIDIA-accelerated computing centers.
A noted tension exists between sigma_8 values inferred from CMB observations by Planck and lower values favored by weak lensing surveys like Kilo-Degree Survey and Dark Energy Survey, leading to active debate within collaborations including Euclid Consortium and research teams at Institute for Advanced Study. Proposed resolutions explore systematic uncertainties in lensing shape measurement pipelines, mass calibration of clusters via weak gravitational lensing and dynamical methods, or new physics such as massive neutrinos, evolving dark energy equations of state from researchers at Perimeter Institute, or modified gravity scenarios tested by experiments at Large Hadron Collider. Ongoing and upcoming surveys—LSST at Vera C. Rubin Observatory, Euclid, and Roman Space Telescope—aim to reduce statistical and systematic uncertainties to clarify whether the sigma_8 discrepancy signifies new physics or unresolved observational systematics.
Category:Cosmological parameters