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This code, which requires HEALPix 2.x (ascl:1107.018), allows you to generate power spectrum estimators from WMAP 5-year maps and generate hybrid cross- and auto- power spectrum and covariance from general foreground-cleaned maps. In addition, it allows you to simulate combined maps or combinations of maps for individual detectors and do MPI spherical transforms of arrays of maps, calculate coupling matrices etc. The code includes all of LensPix (ascl:1102.025), the MPI framework used for doing spherical transforms (based on HealPix).
Modelling of the weak lensing of the CMB will be crucial to obtain correct cosmological parameter constraints from forthcoming precision CMB anisotropy observations. The lensing affects the power spectrum as well as inducing non-Gaussianities. We discuss the simulation of full sky CMB maps in the weak lensing approximation and describe a fast numerical code. The series expansion in the deflection angle cannot be used to simulate accurate CMB maps, so a pixel remapping must be used. For parameter estimation accounting for the change in the power spectrum but assuming Gaussianity is sufficient to obtain accurate results up to Planck sensitivity using current tools. A fuller analysis may be required to obtain accurate error estimates and for more sensitive observations. We demonstrate a simple full sky simulation and subsequent parameter estimation at Planck-like sensitivity.
We present a fully covariant and gauge-invariant calculation of the evolution of anisotropies in the cosmic microwave background (CMB) radiation. We use the physically appealing covariant approach to cosmological perturbations, which ensures that all variables are gauge-invariant and have a clear physical interpretation. We derive the complete set of frame-independent, linearised equations describing the (Boltzmann) evolution of anisotropy and inhomogeneity in an almost Friedmann-Robertson-Walker (FRW) cold dark matter (CDM) universe. These equations include the contributions of scalar, vector and tensor modes in a unified manner. Frame-independent equations for scalar and tensor perturbations, which are valid for any value of the background curvature, are obtained straightforwardly from the complete set of equations. We discuss the scalar equations in detail, including the integral solution and relation with the line of sight approach, analytic solutions in the early radiation dominated era, and the numerical solution in the standard CDM model. Our results confirm those obtained by other groups, who have worked carefully with non-covariant methods in specific gauges, but are derived here in a completely transparent fashion.
We relate the observable number of sources per solid angle and redshift to the underlying proper source density and velocity, background evolution and line-of-sight potentials. We give an exact result in the case of linearized perturbations assuming general relativity. This consistently includes contributions of the source density perturbations and redshift distortions, magnification, radial displacement, and various additional linear terms that are small on sub-horizon scales. In addition we calculate the effect on observed luminosities, and hence the result for sources observed as a function of flux, including magnification bias and radial-displacement effects. We give the corresponding linear result for a magnitude-limited survey at low redshift, and discuss the angular power spectrum of the total count distribution. We also calculate the cross-correlation with the CMB polarization and temperature including Doppler source terms, magnification, redshift distortions and other velocity effects for the sources, and discuss why the contribution of redshift distortions is generally small. Finally we relate the result for source number counts to that for the brightness of line radiation, for example 21-cm radiation, from the sources.
We present a fast Markov Chain Monte-Carlo exploration of cosmological parameter space. We perform a joint analysis of results from recent CMB experiments and provide parameter constraints, including sigma_8, from the CMB independent of other data. We next combine data from the CMB, HST Key Project, 2dF galaxy redshift survey, supernovae Ia and big-bang nucleosynthesis. The Monte Carlo method allows the rapid investigation of a large number of parameters, and we present results from 6 and 9 parameter analyses of flat models, and an 11 parameter analysis of non-flat models. Our results include constraints on the neutrino mass (m_nu < 0.3eV), equation of state of the dark energy, and the tensor amplitude, as well as demonstrating the effect of additional parameters on the base parameter constraints. In a series of appendices we describe the many uses of importance sampling, including computing results from new data and accuracy correction of results generated from an approximate method. We also discuss the different ways of converting parameter samples to parameter constraints, the effect of the prior, assess the goodness of fit and consistency, and describe the use of analytic marginalization over normalization parameters.
The main CAMB code supports smooth dark energy models with constant equation of state and sound speed of one, or a quintessence model based on a potential. This modified code generalizes it to support a time-dependent equation of state w(a) that is allowed to cross the phantom divide, i.e. w=-1 multiple times by implementing a Parameterized Post-Friedmann(PPF) prescription for the dark energy perturbations.
cambmag is a modification to CAMB (ascl:1102.026) that calculates the compensated magnetic mode in the scalar, vector and tensor case. Previously CAMB included code only for the vectors. It also corrects for tight-coupling issues and adds in the ability to include massive neutrinos when calculating vector modes.
DecouplingModes calculates the amplitude of the passive modes, which requires solving the Einstein equations on superhorizon scales sourced by the anisotropic stress from the magnetic fields (prior to neutrino decoupling), and the magnetic and neutrino stress (after decoupling). The code is available as a Mathematica notebook.
InitialConditions finds the initial series solutions for perturbations in our Universe. This includes all scalar (1 adiabatic, 4 isocurvature and 2 magnetic modes), vector (1 vorticity mode, 1 magnetic mode), and tensor (1 gravitational wave mode and 1 magnetic mode) perturbations including terms up to second order in the neutrino mass. It can handle the standard species (cdm, baryons, photons), and two neutrino mass eigenstates (1 light, 1 heavy).
GetDist analyzes Monte Carlo samples, including correlated samples from Markov Chain Monte Carlo (MCMC). It offers a point and click GUI for selecting chain files, viewing plots, marginalized constraints, and LaTeX tables, and includes a plotting library for making custom publication-ready 1D, 2D, 3D-scatter, triangle and other plots. Its convergence diagnostics include correlation length and diagonalized Gelman-Rubin statistics, and the optimized kernel density estimation provides an automated optimal bandwidth choice for 1D and 2D densities with boundary and bias correction. It is available as a standalong package and with CosmoMC (ascl:1106.025).
Cobaya (Code for BAYesian Analysis) provides a framework for sampling and statistical modeling and enables exploration of an arbitrary prior or posterior using a range of Monte Carlo samplers, including the advanced MCMC sampler from CosmoMC (ascl:1106.025) and the advanced nested sampler PolyChord (ascl:1502.011). The results of the sampling can be analyzed with GetDist (ascl:1910.018). It supports MPI parallelization and is highly extensible, allowing the user to define priors and likelihoods and create new parameters as functions of other parameters.
It includes interfaces to the cosmological theory codes CAMB (ascl:1102.026) and CLASS (ascl:1106.020) and likelihoods of cosmological experiments, such as Planck, Bicep-Keck, and SDSS. Automatic installers are included for those external modules; Cobaya can also be used as a wrapper for cosmological models and likelihoods, and integrated it in other samplers and pipelines. The interfaces to most cosmological likelihoods are agnostic as to which theory code is used to compute the observables, which facilitates comparison between those codes. Those interfaces are also parameter-agnostic, allowing use of modified versions of theory codes and likelihoods without additional editing of Cobaya’s source.
LoLLiPoP is a Planck low-l polarization likelihood based on cross-power-spectra for which the bias is zero when the noise is uncorrelated between maps. It uses a modified approximation to apply to cross-power spectra and is interfaced with the Cobaya (ascl:1910.019) MCMC sampler. Cross-spectra are computed on the CMB maps from Commander component separation applied on each detset-split Planck frequency maps.