Cosmological Calculations (astropy.cosmology)

The astropy.cosmology subpackage provides tools for cosmological calculations based on various cosmological models.

Import paths: Always import classes and functions directly from astropy.cosmology (as shown in all examples below). The old submodule import paths (astropy.cosmology.flrw, .core, .funcs, .connect, .parameter) were deprecated in v7.1 and removed in Astropy 8.0.

Using Built-in Cosmologies

Preloaded cosmologies based on WMAP and Planck observations:

python

from astropy.cosmology import Planck18, Planck15, Planck13
from astropy.cosmology import WMAP9, WMAP7, WMAP5
from astropy import units as u

# Use Planck 2018 cosmology
cosmo = Planck18

# Calculate distance to z=4
d = cosmo.luminosity_distance(4)
print(f"Luminosity distance at z=4: {d}")

# Age of universe at z=0
age = cosmo.age(0)
print(f"Current age of universe: {age.to(u.Gyr)}")

Creating Custom Cosmologies

FlatLambdaCDM (Most Common)

Flat universe with cosmological constant:

python

from astropy.cosmology import FlatLambdaCDM

# Define cosmology
cosmo = FlatLambdaCDM(
    H0=70 * u.km / u.s / u.Mpc,  # Hubble constant at z=0
    Om0=0.3,                      # Matter density parameter at z=0
    Tcmb0=2.725 * u.K             # CMB temperature (optional)
)

LambdaCDM (Non-Flat)

Non-flat universe with cosmological constant:

python

from astropy.cosmology import LambdaCDM

cosmo = LambdaCDM(
    H0=70 * u.km / u.s / u.Mpc,
    Om0=0.3,
    Ode0=0.7  # Dark energy density parameter
)

wCDM and w0wzCDM

Dark energy with equation of state parameter:

python

from astropy.cosmology import FlatwCDM, w0wzCDM

# Constant w
cosmo_w = FlatwCDM(H0=70 * u.km/u.s/u.Mpc, Om0=0.3, w0=-0.9)

# Evolving w(z) = w0 + wz * z
cosmo_wz = w0wzCDM(H0=70 * u.km/u.s/u.Mpc, Om0=0.3, Ode0=0.7,
                   w0=-1.0, wz=0.1)

Distance Calculations

Comoving Distance

Line-of-sight comoving distance:

python

d_c = cosmo.comoving_distance(z)

Luminosity Distance

Distance for calculating luminosity from observed flux:

python

d_L = cosmo.luminosity_distance(z)

# Calculate absolute magnitude from apparent magnitude
M = m - 5*np.log10(d_L.to(u.pc).value) + 5

Angular Diameter Distance

Distance for calculating physical size from angular size:

python

d_A = cosmo.angular_diameter_distance(z)

# Calculate physical size from angular size
theta = 10 * u.arcsec  # Angular size
physical_size = d_A * theta.to(u.radian).value

Comoving Transverse Distance

Transverse comoving distance (equals comoving distance in flat universe):

python

d_M = cosmo.comoving_transverse_distance(z)

Distance Modulus

python

dm = cosmo.distmod(z)
# Relates apparent and absolute magnitudes: m - M = dm

Scale Calculations

kpc per Arcminute

Physical scale at a given redshift:

python

scale = cosmo.kpc_proper_per_arcmin(z)
# e.g., "50 kpc per arcminute at z=1"

Comoving Volume

Volume element for survey volume calculations:

python

vol = cosmo.comoving_volume(z)  # Total volume to redshift z
vol_element = cosmo.differential_comoving_volume(z)  # dV/dz

Time Calculations

Age of Universe

Age at a given redshift:

python

age = cosmo.age(z)
age_now = cosmo.age(0)  # Current age
age_at_z1 = cosmo.age(1)  # Age at z=1

Lookback Time

Time since photons were emitted:

python

t_lookback = cosmo.lookback_time(z)
# Time between z and z=0

Hubble Parameter

Hubble parameter as function of redshift:

python

H_z = cosmo.H(z)  # H(z) in km/s/Mpc
E_z = cosmo.efunc(z)  # E(z) = H(z)/H0

Density Parameters

Evolution of density parameters with redshift:

python

Om_z = cosmo.Om(z)        # Matter density at z
Ode_z = cosmo.Ode(z)      # Dark energy density at z
Ok_z = cosmo.Ok(z)        # Curvature density at z
Ogamma_z = cosmo.Ogamma(z)  # Photon density at z
Onu_z = cosmo.Onu(z)      # Neutrino density at z

Critical and Characteristic Densities

python

rho_c = cosmo.critical_density(z)  # Critical density at z
rho_m = cosmo.critical_density(z) * cosmo.Om(z)  # Matter density

Inverse Calculations

Find redshift corresponding to a specific value:

python

from astropy.cosmology import z_at_value

# Find z at specific lookback time
z = z_at_value(cosmo.lookback_time, 10*u.Gyr)

# Find z at specific luminosity distance
z = z_at_value(cosmo.luminosity_distance, 1000*u.Mpc)

# Find z at specific age
z = z_at_value(cosmo.age, 1*u.Gyr)

Array Operations

All methods accept array inputs:

python

import numpy as np

z_array = np.linspace(0, 5, 100)
d_L_array = cosmo.luminosity_distance(z_array)
H_array = cosmo.H(z_array)
age_array = cosmo.age(z_array)

Neutrino Effects

Include massive neutrinos:

python

from astropy.cosmology import FlatLambdaCDM

# With massive neutrinos
cosmo = FlatLambdaCDM(
    H0=70 * u.km/u.s/u.Mpc,
    Om0=0.3,
    Tcmb0=2.725 * u.K,
    Neff=3.04,  # Effective number of neutrino species
    m_nu=[0., 0., 0.06] * u.eV  # Neutrino masses
)

Note: Massive neutrinos reduce performance by 3-4x but provide more accurate results.

Cloning and Modifying Cosmologies

Cosmology objects are immutable. Create modified copies:

python

# Clone with different H0
cosmo_new = cosmo.clone(H0=72 * u.km/u.s/u.Mpc)

# Clone with modified name
cosmo_named = cosmo.clone(name="My Custom Cosmology")

Common Use Cases

Calculating Absolute Magnitude

python

# From apparent magnitude and redshift
z = 1.5
m_app = 24.5  # Apparent magnitude
d_L = cosmo.luminosity_distance(z)
M_abs = m_app - cosmo.distmod(z).value

Survey Volume Calculations

python

# Volume between two redshifts
z_min, z_max = 0.5, 1.5
volume = cosmo.comoving_volume(z_max) - cosmo.comoving_volume(z_min)

# Convert to Gpc^3
volume_gpc3 = volume.to(u.Gpc**3)

Physical Size from Angular Size

python

theta = 1 * u.arcsec  # Angular size
z = 2.0
d_A = cosmo.angular_diameter_distance(z)
size_kpc = (d_A * theta.to(u.radian)).to(u.kpc)

Time Since Big Bang

python

# Age at specific redshift
z_formation = 6
age_at_formation = cosmo.age(z_formation)
time_since_formation = cosmo.age(0) - age_at_formation

Comparison of Cosmologies

python

# Compare different models
from astropy.cosmology import Planck18, WMAP9

z = 1.0
print(f"Planck18 d_L: {Planck18.luminosity_distance(z)}")
print(f"WMAP9 d_L: {WMAP9.luminosity_distance(z)}")

Performance Considerations

Calculations are fast for most purposes
Massive neutrinos reduce speed significantly
Array operations are vectorized and efficient
Results valid for z < 5000-6000 (depends on model)