Navigator

Creates and reads CMB maps. The program runs with underlying Healpix and Capse's emulator frameworks.

Installation

Step 1: Download the package using git clone https://github.com/ivansladoljev/Navigator.git in the directory you are using.

Step 2: Then create a folder DATA in the Navigator/src/ folder (this can be done by going to the directory where you dowloaded the Navigator file, typing cd Navigator/src in the terminal to go into the right folder and creating DATA using mkdir DATA command to create the folder).

Step 3: In there you will have to download the chain weights for Capse emulator from https://zenodo.org/record/8187935/files/chains_weights.zip?download=1, unzip them and add them to the DATA folder (this can be done by wget https://zenodo.org/record/8187935/files/chains_weights.zip command and unziping them by writing unzip chains_weights.zip in the terminal).

Step 4: Now you successfully downloaded everything you need to operate the code. If you want to use it, just write using Pkg, Pkg.activate("Navigator"), include("Navigator"), using Navigator and you are good to go.

Introduction

With this program you can create your custom CMB temperature maps and analyse them.

CMB power spectrum

To generate the CMB power spectrum use the get_CMBcl() or get_CMBdl() functions which uses Capse's trained neural network to generate a set of CMB power spectra, given the inital cosmological parameters.

get_CMBcl(;As,ns,H0,wb,wc,tau,lmax)

Calculates CMB power spectrum ($C_l$) given the cosmological parameters.

Arguments

• As::Float64 = 3.043: amplitude of primordial perturbations.
• ns::Float64 = 0.964: spectral index of the power spectrum.
• H0::Float64 = 67.54: Hubble expansion rate at current time.
• wb::Float64 = 0.02217: the ratio of baryonic matter ($\Omega_b$).
• wc::Float64 = 0.1191: the ratio of dark matter ($\Omega_c$).
• tau::Float64 = 0.0571: optical depth parameter in the reionisation era.
• lmax::Integer = 5000: maximum multipole moment which the function calculates.

Returns -Vector{Float64}: an array of correlation coefitients[given in $\mu K^2$] starting from l=2 to lmax.

get_CMBdl(;As,ns,H0,wb,wc,tau,lmax)

Calculates the normalised CMB power spectrum ($ D_l= C_l * l(l+1)/2\pi$) given the cosmological parameters.

Arguments

• As::Float64 = 3.043: amplitude of primordial perturbations.
• ns::Float64 = 0.964: spectral index of the power spectrum.
• H0::Float64 = 67.54: Hubble expansion rate at current time.
• wb::Float64 = 0.02217: the ratio of baryonic matter ($\Omega_b *h^2$).
• wc::Float64 = 0.1191: the ratio of dark matter ($\Omega_c *h^2$).
• tau::Float64 = 0.0571: optical depth parameter in the reionisation era.
• lmax::Integer = 5000: maximum multipole moment which the function calculates.

Returns -Vector{Float64}: an array of normalised correlation coefitients [given in $ \mu K^2$] starting from l=2 to lmax.

get_noise_spectrum(;lmax,sigma,Nside)

Gives the theoretical normalized noise power spectrum for gaussian noise with mean 0 and variance $sigma^2$.

Arguments -lmax::Integer = 5000: maximum multipole moment which the function calculates. -sigma::Float64 = 10: dispersion of Gaussian distribution from which the noise is drawn -Nside::Integer, must be a power of 2, default=2048: the Nside parameter related to a number of pixels of a Healpix map

Returns -Vector{Float64}: an array of the theoretical noise power spectrum [given in $\mu K^2$] starting from l=2 to lmax.

Making maps

From the generated set of $C_l$s or $D_l$s you can make your own custom map of the CMB, with differing levels of pixelization, using the make_map() function. You can also make the noise map with make_noise(), or add the gaussian noise to you existing CMB map with make_noisymap() function.

get_Cl(;As,ns,H0,wb,wc,tau,lmax)

Calculates CMB power spectrum ($C_l$) given the cosmological parameters from l=0 to lmax.

Arguments

• As::Float64 = 3.043: amplitude of primordial perturbations.
• ns::Float64 = 0.964: spectral index of the power spectrum.
• H0::Float64 = 67.54: Hubble expansion rate at current time.
• wb::Float64 = 0.02217: the ratio of baryonic matter ($\\Omega_b$).
• wc::Float64 = 0.1191: the ratio of dark matter ($\\Omega_c$).
• tau::Float64 = 0.0571: optical depth parameter in the reionisation era.
• lmax::Integer = 5000: maximum multipole moment which the function calculates.

Returns -Vector{Float64}: an array of correlation coefitients[given in $\mu K^2$] starting from l=0 to lmax. """

make_map(Nside;As,ns,H0,wb,wc,tau,lmax,seed)

Gives the map of the CMB power spectrum.

Arguments

• `Nside::Integer, must be a power of 2``: the Nside parameter for the number of pixels in the map.

• As::Float64 = 3.043: amplitude of primordial perturbations.

• ns::Float64 = 0.964: spectral index of the power spectrum.

• H0::Float64 = 67.54: Hubble expansion rate at current time.

• wb::Float64 = 0.02217: the ratio of baryonic matter ($\Omega_b *h^2$).

• wc::Float64 = 0.1191: the ratio of dark matter ($\Omega_c *h^2$).

• tau::Float64 = 0.0571: optical depth parameter in the reionisation era.

• lmax::Integer = 2*Nside: maximum multipole moment of the power spectrum for which the map is calculated.

• seed::Integer = 1234: fixes the seed for the MersenneTwister random generator

Returns -Healpix.HealpixMap{Float64, Healpix.RingOrder}: returns the Healpix map of the CMB in RingOrdering.

Alternative imput make_map(cl,Nside)

Alternative arguments

• cl::Vector{Float64}: a set of power spectrum $C_l$s for which to calculate a map.

• Nside::Integer, must be a power of 2 : the Nside parameter for the number of pixels in the map.

• seed::Integer = 1234: fixes the seed for the MersenneTwister random generator

Returns -Healpix.HealpixMap{Float64, Healpix.RingOrder}: returns the Healpix map of the CMB in RingOrdering.

make_noise(Nside;sigma)

Gives the map of the Gaussian noise with mean zero and dispersion $sigma$.

Arguments

• Nside::Integer, must be a power of 2 : the Nside parameter for the number of pixels in the map.

• sigma::Float64 = 10: dispersion of Gaussian distribution from which the noise is drawn.

• seed::Integer = 1234: fixes the seed for the MersenneTwister random generator

Returns -Healpix.HealpixMap{Float64, Healpix.RingOrder}: returns the Healpix map of the CMB in RingOrdering.

make_noisymap(Nside;As,ns,H0,wb,wc,tau,lmax,sigma)

Gives the map of the CMB power spectrum with noise added.

Arguments

• Nside::Integer, must be a power of 2 = 2048: the Nside parameter for the number of pixels in the map.

• As::Float64 = 3.043: amplitude of primordial perturbations.

• ns::Float64 = 0.964: spectral index of the power spectrum.

• H0::Float64 = 67.54: Hubble expansion rate at current time.

• wb::Float64 = 0.02217: the ratio of baryonic matter ($\Omega_b *h^2$).

• wc::Float64 = 0.1191: the ratio of dark matter ($\Omega_c *h^2$).

• tau::Float64 = 0.0571: optical depth parameter in the reionisation era.

• lmax::Integer = 5000: maximum multipole moment of the power spectrum for which the map is calculated.

• sigma::Float64 = 10: dispersion of Gaussian distribution from which the noise is drawn.

• seed::Integer = 1234: fixes the seed for the MersenneTwister random generator

Returns -Healpix.HealpixMap{Float64, Healpix.RingOrder}: returns the Healpix map of the CMB in RingOrdering with npise added.

Alternative imput make_noisymap(cl,Nside;sigma)

Alternative arguments

• cl::Vector{Float64}: a set of power spectrum $C_l$s for which to calculate a map.

• Nside::Integer, must be a power of 2 : the Nside parameter for the number of pixels in the map.

• sigma::Float64 = 10: dispersion of Gaussian distribution from which the noise is drawn.

• seed::Integer = 1234: fixes the seed for the MersenneTwister random generator

Returns -Healpix.HealpixMap{Float64, Healpix.RingOrder}: returns the Healpix map of the CMB in RingOrdering with npise added.

Analysing maps

If you already have a Healpix map, you can infere the $C_l$s or the $D_l$s from it with get_clobserved()/get_dlobserved() functions. If you want to remove the theoretical noise from your obsevations and get the pure power spectrum, use the get_clestimate()/get_dlestimate() functions instead.

get_clobserved(map;lmax)

Gives the observed power spectrum coeficients C_l from the given map.

Arguments -Healpix.HealpixMap{Float64, Healpix.RingOrder}: the map from which to infere the power spectrum. Must be in RingOrder.

-lmax::Integer = 2*Nside: maximum multipole moment which the function calculates. Maximum default is 2*Nside parameter of the map.

Returns

• Vector{Float64}: an array of infered power spectrum coeficients $C_l$.

get_dlobserved(map;lmax)

Gives the observed power spectrum coeficients $D_l=C_l * l(l+1)/2\pi$ from the given map.

Arguments -Healpix.HealpixMap{Float64, Healpix.RingOrder}: the map from which to infere the power spectrum. Must be in RingOrder.

-lmax::Integer = 2*Nside: maximum multipole moment which the function calculates. Maximum default is 2*Nside parameter of the map.

Returns

• Vector{Float64}: an array of infered power spectrum coeficients $D_l$.

get_clestimate(map;lmax,sigma)

Gives the infered power spectrum coeficients $C_l$ (with noise removed) from the given map.

Arguments -Healpix.HealpixMap{Float64, Healpix.RingOrder}: the map from which to infere the power spectrum. Must be in RingOrder.

-lmax::Integer = 2*Nside: maximum multipole moment which the function calculates. Maximum default is 2*Nside parameter of the map.

-sigma::Float64 = 10: dispersion of Gaussian distribution from which the theoretical noise is drawn

Returns

• Vector{Float64}: an array of infered power spectrum coeficients $C_l$ with noise removed.

get_dlestimate(map;lmax,sigma)

Gives the infered power spectrum coeficients $D_l=C_l * l(l+1)/2\pi$ (with noise removed) from the given map.

Arguments -Healpix.HealpixMap{Float64, Healpix.RingOrder}: the map from which to infere the power spectrum. Must be in RingOrder.

-lmax::Integer = 2*Nside: maximum multipole moment which the function calculates. Maximum default is 2*Nside parameter of the map.

-sigma::Float64 = 10.0: dispersion of Gaussian distribution from which the theoretical noise is drawn.

Returns

• Vector{Float64}: an array of infered power spectrum coeficients $D_l$ with noise removed.