LimberJack.jl

Core

Core performs the main computations of LimberJack.jl. When using LimberJack.jl, the first step is to create an instance of the Cosmology structure. This is as easy as calling:

    using LimberJack
    cosmology = Cosmology()

This will generate the an instance of Cosmology given the vanilla $\Lambda$CDM cosmology of CCL. Cosmology() then computes the value of the comoving distance, the growth factor, the growth rate and matter power spectrum at an array of values and generates interpolators for said quantites. The user can acces the value of these interpolator at an arbitrary input using the public functions of the model. Moreover, the Cosmology structure has its own type called Cosmology.

LimberJack.Settings — Type

Settings(;kwargs...)

Constructor of settings structure constructor.

Kwargs:

nz::Int=300 : number of nodes in the general redshift array.
nk::Int=500: number of nodes in the k-scale array used to compute matter power spectrum grid.
nℓ::Int=300: number of nodes in the multipoles array.
using_As::Bool=false: True if using the As parameter.
cosmo_type::Type=Float64 : type of cosmological parameters.
tk_mode::String=:EisHu : choice of transfer function.
Dz_mode::String=:RK2 : choice of method to compute the linear growth factor.
pk_mode::String=:linear : choice of method to apply non-linear corrections to the matter power spectrum.

Returns:

mutable struct Settings
    nz::Int
    nk::Int
    nℓ::Int

    xs
    zs
    ks
    ℓs
    logk
    dlogk

    using_As::Bool

    cosmo_type::DataType
    tk_mode::Symbol
    Dz_mode::Symbol
    pk_mode::Symbol
end

LimberJack.CosmoPar — Type

CosmoPar(kwargs...)

Cosmology parameters structure constructor.

Kwargs:

Ωm::Dual=0.30 : cosmological matter density.
Ωb::Dual=0.05 : cosmological baryonic density.
h::Dual=0.70 : reduced Hubble parameter.
ns::Dual=0.96 : Harrison-Zeldovich spectral index.
As::Dual=2.097e-9 : Harrison-Zeldovich spectral amplitude.
σ8::Dual=0.81: variance of the matter density field in a sphere of 8 Mpc.
Y_p::Dual=0.24: primordial helium fraction.
N_ν::Dual=3.046: effective number of relativisic species (PDG25 value).
Σm_ν::Dual=0.0: sum of neutrino masses (eV), Planck 15 default ΛCDM value.
θCMB::Dual=2.725/2.7: CMB temperature over 2.7.
Ωg::Dual=2.38163816E-5*θCMB^4/h^2: cosmological density of relativistic species.
Ωr::Dual=Ωg*(1.0 + N_ν * (7.0/8.0) * (4.0/11.0)^(4.0/3.0)): cosmological radiation density.

Returns:

mutable struct CosmoPar{T}
    Ωm::T
    Ωb::T
    h::T
    ns::T
    As::T
    σ8::T
    θCMB::T
    Y_p::T
    N_ν::T
    Σm_ν::T
    Ωg::T
    Ωr::T
    Ωc::T
    ΩΛ::T
end

LimberJack.Cosmology — Type

Cosmology(cpar::CosmoPar, settings::Settings)

Base cosmology structure constructor.

Calculates the LCDM expansion history based on the different species densities provided in CosmoPar.

The comoving distance is then calculated integrating the expansion history.

Depending on the choice of transfer function in the settings, the primordial power spectrum is calculated using:

tk_mode = :EisHu : the Eisenstein & Hu formula (arXiv:astro-ph/9710252)
tk_mode = :EmuPk : the Mootoovaloo et al 2021 emulator EmuPk (arXiv:2105.02256v2)

Depending on the choice of power spectrum mode in the settings, the matter power spectrum is either:

pk_mode = :linear : the linear matter power spectrum.
pk_mode = :halofit : the Halofit non-linear matter power spectrum (arXiv:astro-ph/0207664).

Arguments:

Settings::MutableStructure : cosmology constructure settings.
CosmoPar::Structure : cosmological parameters.

Returns:

mutable struct Cosmology
    settings::Settings
    cpar::CosmoPar
    chi::AbstractInterpolation
    z_of_chi::AbstractInterpolation
    t_of_z::AbstractInterpolation
    chi_max
    chi_LSS
    Dz::AbstractInterpolation
    fs8z::AbstractInterpolation
    PkLz0::AbstractInterpolation
    Pk::AbstractInterpolation
end

Cosmology(;kwargs...)

Short form to call Cosmology(cpar::CosmoPar, settings::Settings). kwargs are passed to the constructors of CosmoPar and Settings. Returns:

Cosmology : cosmology structure.

LimberJack.Ez — Function

Ez(cosmo::Cosmology, z)

Given a Cosmology instance, it returns the expansion rate (H(z)/H0).

Arguments:

cosmo::Cosmology : cosmology structure
z::Dual : redshift

Returns:

Ez::Dual : expansion rate

LimberJack.Hmpc — Function

Hmpc(cosmo::Cosmology, z)

Given a Cosmology instance, it returns the expansion history (H(z)) in Mpc.

Arguments:

cosmo::Cosmology : cosmology structure
z::Dual : redshift

Returns:

Hmpc::Dual : expansion rate

LimberJack.comoving_radial_distance — Function

comoving_radial_distance(cosmo::Cosmology, z)

Given a Cosmology instance, it returns the comoving radial distance.

Arguments:

cosmo::Cosmology : cosmology structure
z::Dual : redshift

Returns:

Chi::Dual : comoving radial distance

LimberJack.growth_factor — Function

growth_factor(cosmo::Cosmology, z)

Given a Cosmology instance, it returns the growth factor (D(z) = log(δ)).

Arguments:

cosmo::Cosmology : cosmological structure
z::Dual : redshift

Returns:

Dz::Dual : comoving radial distance

LimberJack.growth_rate — Function

growth_rate(cosmo::Cosmology, z)

Given a Cosmology instance, it returns growth rate.

Arguments:

cosmo::Cosmology : cosmology structure
z::Dual : redshift

Returns:

f::Dual : f

LimberJack.sigma8 — Function

sigma8(cosmo::Cosmology, z)

Given a Cosmology instance, it returns s8.

Arguments:

cosmo::Cosmology : cosmological structure
z::Dual : redshift

Returns:

s8::Dual : comoving radial distance

LimberJack.fs8 — Function

fs8(cosmo::Cosmology, z)

Given a Cosmology instance, it returns fs8.

Arguments:

cosmo::Cosmology : cosmology structure
z::Dual : redshift

Returns:

fs8::Dual : fs8

LimberJack.lin_Pk — Function

lin_Pk(cosmo::Cosmology, k, z)

Given a Cosmology instance, it returns the linear matter power spectrum (P(k,z))

Arguments:

cosmo::Cosmology : cosmology structure
k::Dual : scale
z::Dual : redshift

Returns:

Pk::Dual : linear matter power spectrum

LimberJack.nonlin_Pk — Function

nonlin_Pk(cosmo::Cosmology, k, z)

Given a Cosmology instance, it returns the non-linear matter power spectrum (P(k,z)) using the Halofit fitting formula (arXiv:astro-ph/0207664).

Arguments:

cosmo::Cosmology : cosmology structure
k::Dual : scale
z::Dual : redshift

Returns:

Pk::Dual : non-linear matter power spectrum

Tracers

In LimberJack.jl each tracer is structure containing at least of three fields:

wint: an interpolator between chis and warr.
F: an interpolator between chis and warr.

On top of these, tracers might contain the value of any nuisance parameter associated with them. Moreover, tracers within LimberJack.jl tracer objects have their own type called Tracer.

LimberJack.NumberCountsTracer — Type

NumberCountsTracer(warr, chis, wint, b, lpre)

Number counts tracer structure. Arguments:

wint::Interpolation : interpolation of the radial kernel over comoving distance.
F::Function : prefactor.

Returns:

NumberCountsTracer::NumberCountsTracer : Number counts tracer structure.

LimberJack.WeakLensingTracer — Type

WeakLensingTracer(cosmo::Cosmology, z_n, nz; kwargs...)

Weak lensing tracer structure constructor. Arguments:

cosmo::Cosmology : cosmology structure.
z_n::Vector{Dual} : redshift array.
nz::Interpolation : distribution of sources over redshift.

Kwargs:

mb::Dual = 1 : multiplicative bias.
IA_params::Vector{Dual} = [A_IA, alpha_IA]: instrinsic aligment parameters.

Returns:

WeakLensingTracer::WeakLensingTracer : Weak lensing tracer structure.

LimberJack.CMBLensingTracer — Type

CMBLensingTracer(warr, chis, wint, lpre)

CMB lensing tracer structure. Arguments:

wint::Interpolation : interpolation of the radial kernel over comoving distance.
F::Function : prefactor.

Returns:

CMBLensingTracer::CMBLensingTracer : CMB lensing tracer structure.

LimberJack.get_IA — Function

get_IA(cosmo::Cosmology, zs, IA_params)

CMB lensing tracer structure. Arguments:

cosmo::Cosmology : cosmology structure.
zs::Vector{Dual} : redshift array.
IA_params::Vector{Dual} : Intrinsic aligment parameters.

Returns:

IA_corr::Vector{Dual} : Intrinsic aligment correction to radial kernel.

Spectra

Performs the computation of the angular power spectra of any two tracers.

LimberJack.Cℓintegrand — Function

Cℓintegrand(cosmo::Cosmology, t1::Tracer, t2::Tracer, logk, ℓ)

Returns the integrand of the angular power spectrum. Arguments:

cosmo::Cosmology : cosmology structure.
t1::Tracer : tracer structure.
t2::Tracer : tracer structure.
logk::Vector{Float} : log scale array.
ℓ::Float : multipole.

Returns:

integrand::Vector{Real} : integrand of the angular power spectrum.

LimberJack.angularCℓs — Function

angularCℓs(cosmo::Cosmology, t1::Tracer, t2::Tracer, ℓs)

Returns the angular power spectrum. Arguments:

cosmo::Cosmology : cosmology structure.
t1::Tracer : tracer structure.
t2::Tracer : tracer structure.
ℓs::Vector{Float} : multipole array.

Returns:

Cℓs::Vector{Real} : angular power spectrum.

Data Utils

Parses sacc and YAML files.

LimberJack.make_data — Function

make_data(sacc_file, yaml_file)

Process sacc and yaml files into a Meta structure containing the instructions of how to compose the theory vector and a npz file with the neccesary redshift distributions of the tracers involved.

Arguments:

sacc_file : sacc file
yaml_file : yaml_file

Returns:

struct Instructions
    names : names of tracers.
    pairs : pairs of tracers to compute angular spectra for.
    types : types of the tracers.
    idx : positions of cls in theory vector.
    data : data vector.
    cov : covariance of the data.
    inv_cov : inverse covariance of the data.
end

-files: npz file

Theory

Performs the computation of complex theory vectors given sacc and YAML files.

LimberJack.Theory — Function

Theory(cosmology::Cosmology,
       instructions::Instructions, files;
       Nuisances=Dict())

Composes a theory vector given a Cosmology object, a Meta objectm, a files npz file and a dictionary of nuisance parameters.

Arguments:

cosmology::Cosmology : Cosmology object.
meta::Meta : Meta object.
files : files npz file.
Nuisances::Dict : dictonary of nuisace parameters.

Returns:

Meta: structure

struct Meta
    names : names of tracers.
    pairs : pairs of tracers to compute angular spectra for.
    types : types of the tracers.
    idx : positions of cls in theory vector.
    data : data vector.
    cov : covariance of the data.
    inv_cov : inverse covariance of the data.
end

files: npz file