Power Spectrum Module

The pk module computes galaxy power spectrum multipoles in redshift space, including wide-separation, relativistic, and integrated contributions.

Contribution types:

  • Local contributions: Evaluated at the galaxy position

    • NPP: Newtonian plane-parallel (Kaiser RSD)

    • WA1, WA2: Wide-angle corrections

    • RR1, RR2: Radial-redshift (evolution) corrections

    • WS: Wrapper for combined wide-separation (WA + RR)

    • GR1, GR2: Local relativistic (Doppler, gravitational redshift)

    • Loc, Eq, Orth: PNG scale-dependent bias (local, equilateral, orthogonal)

Note

PNG contributions (Loc, Eq, Orth) require compute_bias=True when initialising ClassWAP.

  • Integrated contributions: Line-of-sight integrals from observer to source

    • Int: Lensing convergence, time delay, integrated Sachs-Wolfe (ISW)

Methods

Each class provides multipole methods:

lx(cosmo_functions, k1, zz=0, t=0, sigma=None)

Compute x-th multipole (l0, l2, l4, etc.).

Parameters:

  • cosmo_functions (object) – ClassWAP instance

  • k1 (array-like) – Wavevector [h/Mpc]

  • zz (float) – Redshift

  • t (float) – LoS parameter t ∈ [0,1] defining endpoint LOS choice

  • sigma (float) – FoG damping

Returns:

Power spectrum multipole [(Mpc/h)^3]

Usage

import numpy as np
import cosmo_wap as cw
import cosmo_wap.pk as pk
from cosmo_wap.lib import utils

cosmo = utils.get_cosmo()
survey = cw.SurveyParams.Euclid(cosmo)
cosmo_funcs = cw.ClassWAP(cosmo, survey)

k = np.linspace(0.01, 0.3, 100)
z = 1.0

# Newtonian multipoles (Kaiser)
P0 = pk.NPP.l0(cosmo_funcs, k, zz=z)
P2 = pk.NPP.l2(cosmo_funcs, k, zz=z)
P4 = pk.NPP.l4(cosmo_funcs, k, zz=z)

# Wide-separation corrections
P0_WS = pk.WS.l0(cosmo_funcs, k, zz=z)

# Relativistic corrections
P0_GR = pk.GR2.l0(cosmo_funcs, k, zz=z)

Numerical \(\mu\) Pipeline

All power spectrum contributions (including standard terms like NPP and GR) can alternatively be computed via the numerical \(\mu\) pipeline in pk_int, which constructs \(P(k,\mu)\) from first-order field kernels and projects onto Legendre multipoles. See Integrated Effects for full details, available kernels, and usage examples.