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skills/astropy/references/cosmology.md

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+# Cosmological Calculations (astropy.cosmology)
+
+The `astropy.cosmology` subpackage provides tools for cosmological calculations based on various cosmological models.
+
+## 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)