Cosmology

Cosmology parameters are set by the user upfront, once, as a single object — every other module in the package (profiles, kernels, the mass function) takes this object as an argument and computes from it, rather than reading global parameters of its own. If no cosmology is set up, clenspy falls back to its own default. The object itself is a plain astropy.cosmology.FlatLambdaCDM — not a package-specific type — so it composes with the rest of the Astropy/SciPy ecosystem. This page also covers the two background quantities built directly on top of it: distances and the linear growth factor.

Defining a cosmology

fiducial_cosmology() returns an astropy.cosmology.FlatLambdaCDM set to the package’s default parameters — a flat universe with \(H_0=70\,{\rm km\,s^{-1}\,Mpc^{-1}}\), \(\Omega_m=0.3\). Call it with no arguments to get that default, or pass H0/Om0 to set your own:

from clenspy.cosmology import fiducial_cosmology

cosmo = fiducial_cosmology(H0=70.0, Om0=0.3)  # flat LambdaCDM

cosmo is then the one object every other calculation in the package — profiles, kernels, the mass function — takes as an argument, so a single choice of \(H_0\), \(\Omega_m\) propagates consistently through the whole chain. Each call to fiducial_cosmology() returns an independent object, so building cosmo once and passing it everywhere never risks a later call silently changing the cosmology out from under an earlier one.

Using a custom cosmology

fiducial_cosmology() only exposes H0 and Om0 — the two parameters clenspy itself varies. For anything else (baryon density, neutrino mass, \(T_{\rm CMB}\), or a non-flat/non-\(\Lambda\)CDM model), build the astropy.cosmology object yourself and pass it in instead of fiducial_cosmology()’s result — every downstream function only requires the same interface (comoving_distance, H, etc.), not that it came from fiducial_cosmology() specifically:

from astropy.cosmology import FlatLambdaCDM

cosmo = FlatLambdaCDM(H0=67.4, Om0=0.315, Ob0=0.049, Tcmb0=2.7255, m_nu=[0, 0, 0.06])

or reuse one of Astropy’s own published cosmologies directly:

from astropy.cosmology import Planck18 as cosmo

Distances

The comoving distance \(\chi(z)\) and angular diameter distance \(D_A(z) = \chi(z)/(1+z)\) come directly from cosmo. CLensPy adds the angle–distance conversion at fixed lens redshift \(z_l\),

\[ \theta = \frac{D_c}{D_A(z_l)}, \]

used throughout the package to move between a projected physical separation \(R\) and an angular separation on the sky.

Linear growth factor \(D(z)\)

For a flat cosmology with any dark-energy equation of state, the growing mode has the closed-form quadrature (Child et al. 2018, Sec. 4)

\[ D^{+}(a) = \frac{5\Omega_{m,0}}{2}\,\frac{H(a)}{H_0} \int_0^{a} \frac{da'}{\left[a'H(a')/H_0\right]^{3}}, \qquad D(a) = \frac{D^{+}(a)}{D^{+}(a=1)}, \]

normalised so \(D(z{=}0)=1\) — the convention in which \(P_{\rm lin}(k,z) = D^2(z)\,P_{\rm lin}(k,0)\), and the one Halo Mass Function uses to evolve \(\sigma(M,z) = D(z)\,\sigma(M,0)\) instead of recomputing a power spectrum at every redshift.

\(\chi(z)\) and \(D_A(z)\) (left) turn over past \(z\sim1.5\) because a fixed comoving separation subtends a smaller angle as \(D_A\) itself starts to fall; \(D(z)\) (right) falls monotonically from 1.

Example

import numpy as np
from clenspy.cosmology import (
    comoving_to_theta,
    fiducial_cosmology,
    growth_factor,
    theta_to_comoving,
)

# every other layer takes a cosmology object as input; build one first.
# a fresh instance every call -- no shared, mutable module-level default.
cosmo = fiducial_cosmology(H0=70.0, Om0=0.3)  # flat LambdaCDM
print(cosmo)

z_lens = 0.35
D_c = np.array([0.1, 1.0, 10.0])  # comoving separations [Mpc]
theta = comoving_to_theta(D_c, z_lens, cosmo, unit="arcmin")
print("theta [arcmin] =", theta)
print("round trip     =", theta_to_comoving(theta, z_lens, cosmo, unit="arcmin"))

z = np.array([0.0, 0.35, 1.0, 2.0])
print("D(z) =", growth_factor(z, cosmo))  # normalised, D(0) = 1

FlatLambdaCDM(H0=70.0 km / (Mpc s), Om0=0.3, Tcmb0=0.0 K, Neff=3.04, m_nu=None, Ob0=0.0)
theta [arcmin] = [ 0.3373975   3.37397499 33.73974985]
round trip     = [ 0.1  1.  10. ]
D(z) =          [1.         0.834242   0.61180575 0.4214457 ]

See also: API Reference for the full clenspy.cosmology reference, Notation for the symbol table.