Examples

To use CCToolkit, start by importing the necessary modules and initializing the CosmologyCalculator with your desired cosmological parameters:

from cctoolkit import CosmologyCalculator

# Define cosmological parameters
params = {
    'H0': 70.0,                 # Hubble parameter at z=0 in km/s/Mpc
    'Ob0': 0.05,                # Baryon density parameter
    'Om0': 0.3,                 # Total matter density parameter (Ob0 + Om_c0)
    'sigma8': 0.8,              # rms density fluctuation amplitude at 8 h^-1 Mpc
    'ns': 0.96,                 # Scalar spectral index
    'TCMB': 2.7255,             # CMB Temperature at z=0 in K
    'mnu': 0.06,                # Sum of neutrino masses (eV)
    'num_massive_neutrinos': 1, # Number of massive neutrinos species
    'w0' : -1.1,                # Dark energy equation of state value today
    'wa' : 0.8                  # Dark energy equation of state rate wrt to a
}

# Initialize the calculator
cosmo_calc = CosmologyCalculator(params)

Halo Mass Function

Calculate the Castro et al. 2023 halo mass function for a range of masses:

import numpy as np
import matplotlib.pyplot as plt

masses = np.logspace(13, 15.5, num=100)
hmf = cosmo_calc.dndlnM(masses, 0)
plt.loglog(masses, hmf)
plt.xlabel(r"$M_{\rm vir}\,[M_\odot h^{-1}]$")
plt.ylabel(r"$\frac{{\rm d} n}{{\rm d} \log M}\,[{\rm Mpc}^{-3} h^{3}]$")
plt.show()

Alternatively, one can specify the model Castro et al. 2025 for cosmologies with dynamic dark energy with:

import numpy as np
import matplotlib.pyplot as plt

masses = np.logspace(13, 15.5, num=100)
hmf = cosmo_calc.dndlnM(masses, 0, model='castro25')
plt.loglog(masses, hmf)
plt.xlabel(r"$M_{\rm vir}\,[M_\odot h^{-1}]$")
plt.ylabel(r"$\frac{{\rm d} n}{{\rm d} \log M}\,[{\rm Mpc}^{-3} h^{3}]$")
plt.show()

Halo Bias

Compute the linear halo bias or the at redshift z = 0 for a given mass. CCToolkit can compute both the PBS prescription as well as the corrected model following Castro et al. 2024b

pbs = cosmo_calc.pbs_bias(masses, 0)
bias = cosmo_calc.bias(masses, 0)
plt.loglog(masses, pbs, label=r'${\rm PBS}$')
plt.loglog(masses, bias, label=r'${\rm Castro\, et\,al.\,2022}$')
plt.xlabel(r"$M_{\rm vir}\,[M_\odot h^{-1}]$")
plt.ylabel(r"$b(M)$")
plt.legend()
plt.show()

Impact of Baryons on Cluster and Group masses

Compute the dark-matter only equivalent of a hydro-dynamic simulated object. CCToolkit can compute both the dark-matter only mass at the threshold of equivalence according to the quasi-adibatic model presented in Castro et al. 2024 but also to convert this to the virial definition assuming a concentration mass relation. For any realistic feedback mechanism, the last step is not very sensitive to the assumed mass-concentration relation. The assumed mass-concentration relation is given by Duffy et al. 2008.

import cctoolkit
from cctoolkit import baryons
from cctoolkit.cosmology import CosmologyCalculator
z = 0.0
# Magneticum cosmology
params = {"Om0": 0.272, "Ob0": 0.272 * 0.168, "H0": 70.4, "ns": 0.963, "mnu":0, "num_massive_neutrinos": 0, "sigma8": 0.809}
cosmo_calc = CosmologyCalculator()
# Array of virial masses on hydro
M = np.geomspace(1e13, 3e14)
# Calculating the equivalent DMO mass at the threshold of equivalence according to the quasi-adiabatic model
M_Delta_dmo, Delta = baryons.compute_dmo_mass(M, z, 0.168)
Delta *= cctoolkit.utils.virial_Delta(cosmo_calc.Omega_m(z))
# Converting to the virial mass
mdmo = [baryons.compute_rec_mass(cosmo_calc, m, d, z) for m, d in zip(M_Delta_dmo, Delta)]

Using a tabulated matter power-spectrum

The CosmologyCalculator can also receive a tabulated power-spectrum. This is useful when analysing simulations which, due to backscaling, might have a realized power-spectrum that is not compatible with camb.

from cctoolkit.cosmology import CosmologyCalculator
# Calling colossus to produce a tabulated Pk
from colossus.cosmology import cosmology

params = {'flat': True, 'H0': 67.321, 'Om0': 0.3158, 'Ob0': 0.0494, 'sigma8': 0.8102, 'ns': 0.9661}
cosmo = cosmology.setCosmology("C0", params)
params = {
   'H0': cosmo.H0,           # Hubble parameter at z=0 in km/s/Mpc
   'Ob0': cosmo.Ob0,         # Physical baryon density parameter
   'Om0': cosmo.Om0,         # Physical total matter density parameter (Ob0 + Om_c0)
   'sigma8': cosmo.sigma8,   # rms density fluctuation amplitude at 8 h^-1 Mpc
   'ns': cosmo.ns,           # Scalar spectral index
   'mnu': 0.0,               # Sum of neutrino masses (eV)
   'num_massive_neutrinos': 0,
}
M = np.geomspace(1e13, 1e16, 200)
k = np.geomspace(1e-3, 1e1, 200)
Pk = cosmo.matterPowerSpectrum(k, 0)
cosmo_calc = CosmologyCalculator(params, power_spectrum=[k, Pk])
dndlnM = cosmo_calc.dndlnM(M, 0)

Notice that simulations frequently ignores the radiation contribution. As we use camb as our backend for the CosmologyCalculator, we can not produce a background without radiation. However, we can make its contribution insignificant setting the CMB temperature today to an unrealistic low value.

from cctoolkit.cosmology import CosmologyCalculator

params = {'flat': True, 'H0': 67.321, 'Om0': 0.3158, 'Ob0': 0.0494, 'sigma8': 0.8102, 'ns': 0.9661, 'mnu': 0, 'num_massive_neutrinos': 0, 'TCMB': 0.5}
cosmo_calc = CosmologyCalculator(params)

When using a tabulated power-spectrum, CosmoCalculator will compute the growth factor solving Eq. (11) of Linder and Jenkins 2003. If TCMB is lower than unity, EdS initial conditions are assumed at high-redshift. Otherwise, a radiation dominated solution is assumed.