CMBFAST

CMBFAST
Name	CMBFAST
Author	Uros Seljak and Matias Zaldarriaga
Released	1996
Latest release	4.0 (1999)
Programming language	Fortran
Operating system	Unix-like, Microsoft Windows
Genre	Cosmology software, numerical simulation

CMBFAST is a numerical code for computing anisotropy and polarization power spectra of the cosmic microwave background based on linear perturbation theory. The program accelerated precision calculations used by teams working with data from experiments such as COBE, WMAP, and Planck, and influenced analysis pipelines at institutions like NASA, ESA, and major university observatories. Developed in the late 1990s, it combined physical models associated with Big Bang cosmology, perturbation theory used in General Relativity, and numerical methods established in computational physics.

Overview

CMBFAST computes temperature and polarization angular power spectra for scalar, vector, and tensor perturbations in Friedmann–Lemaître–Robertson–Walker cosmologies, supporting models with baryons, cold dark matter, hot dark matter, and a cosmological constant. The code implements the line-of-sight integration approach to solve the Boltzmann equation for photons coupled to baryons and neutrinos, interfacing with parameter estimation frameworks used by collaborations such as SDSS, BOSS, ACT, and SPT. Users supply cosmological parameters like the Hubble constant (H0), baryon density, dark matter density, and reionization history; outputs feed likelihood analyses performed with tools developed by groups at Princeton University, Harvard University, Caltech, and University of Cambridge.

History and Development

CMBFAST was authored by Uros Seljak and Matias Zaldarriaga and released publicly after demonstrating large speed gains over earlier Boltzmann solvers used by teams at University of Chicago, University of California, Berkeley, and Max Planck Institute for Astrophysics. Its 1996 publication followed milestones in observational cosmology including the COBE Differential Microwave Radiometer detection of anisotropy and theoretical advances from researchers at Institute for Advanced Study, Cambridge University, and Princeton Plasma Physics Laboratory. Subsequent versions integrated feedback from groups at Stanford University, University of Oxford, and Columbia University, and the code was widely cited in analyses supporting results from WMAP and later Planck mission papers authored by teams at Jet Propulsion Laboratory and European Space Agency.

Methodology and Algorithms

The core algorithm applies the line-of-sight integration formalism to reduce the dimensionality of the Boltzmann hierarchy, employing spherical Bessel transforms and source function evaluation for recombination and reionization epochs modeled after calculations by Peebles and Zel'dovich-era recombination theory. It solves coupled differential equations for photon, baryon, neutrino, and dark matter perturbations within a Lambda-CDM framework, using numerical ODE integrators and fast evaluation of Legendre series similar to methods developed at Los Alamos National Laboratory and in numerical libraries from Netlib. The code handles polarization via tensor harmonics introduced in works by Seljak and Zaldarriaga and uses approximations to truncate multipole expansions while controlling numeric error, an approach examined at CERN and by researchers at Lawrence Berkeley National Laboratory.

Features and Capabilities

CMBFAST supports computation of temperature (TT), polarization (EE), and cross-correlation (TE) power spectra, and can include tensor-mode (gravitational-wave) contributions relevant to proposals from BICEP and Keck Array. It allows variations in primordial power spectrum parameters inspired by inflationary models from Alan Guth, Andrei Linde, and Alexei Starobinsky, and can incorporate massive neutrino species consistent with results from Super-Kamiokande and Sudbury Neutrino Observatory. The package includes options for varying recombination histories, optical depth to reionization as constrained by Planck Collaboration, and nonstandard components such as early dark energy tested by teams at Perimeter Institute and Kavli Institute.

Performance and Validation

CMBFAST achieved orders-of-magnitude speedups over earlier line-by-line hierarchy integrators used in analyses at Princeton University and Harvard-Smithsonian Center for Astrophysics, enabling extensive parameter-space scans performed by groups involved in the WMAP Science Team and cosmological parameter estimation codes like those at CosmoMC projects. Validation was performed by cross-comparing outputs with independent Boltzmann codes developed at CAMB authorship teams and by comparison against analytic approximations derived in papers by Hu and Sugiyama. Benchmarks on workstations from vendors such as Sun Microsystems and Intel showed typical runtime reductions that made Monte Carlo Markov Chain studies feasible for the first time in high-resolution analyses.

Applications and Impact

CMBFAST underpinned cosmological inference leading to precision measurements of parameters including the baryon density, dark matter density, Hubble parameter, and scalar spectral index reported in results from WMAP Collaboration and Planck Collaboration. Its speed enabled model comparisons involving datasets from Sloan Digital Sky Survey, 2dFGRS, and ground-based CMB experiments like POLARBEAR. The code influenced pedagogical materials and reviews at institutions such as University of Chicago and Caltech, and its methods inspired successor codes and tools used in surveys planned by LSST and Euclid.

Limitations and Successors

CMBFAST is limited by its reliance on fixed-precision Fortran numerics, simplified recombination modules predating advanced multi-level atomic calculations developed by teams at RECFAST and later improvements used in HyRec and CosmoRec. Its treatment of nonlinear effects, lensing, and second-order anisotropies was incomplete compared with successors; therefore, codes like CAMB and CLASS—developed by groups affiliated with Institute for Computational Cosmology and Université Paris-Sud—superseded CMBFAST for modern analyses. Despite this, CMBFAST remains an important milestone cited in foundational papers by researchers at Institute for Theoretical Physics and continues to be referenced in historical and methodological reviews by the International Astronomical Union.

Category:Cosmology software