"""
bias.py
This module contains functions for calculating the halo bias, including a correction
model for the Peak Background Split (PBS) prescription, as described in the provided
cosmological study. The correction accounts for dependencies on Omega_m(z), the slope
of the power spectrum, and the clustering amplitude S_8.
"""
import numpy as np
[docs]
def bias_correction_PBS(Omega_m_z, dlnsigma_dlnR, S8, A0=1.150, a1=0.0929, b1=0.256, b2=0.173, c1=-0.0372):
"""
Compute the correction factor for the linear halo bias based on the PBS prescription.
Parameters:
-----------
Omega_m_z : float
The matter density parameter at redshift z.
dlnsigma_dlnR : float
The logarithmic derivative of the variance with respect to the radius.
S8 : float
The clustering amplitude parameter.
Returns:
--------
float
The correction factor for the halo bias.
References
----------
- [arxiv:2208.02174](https://arxiv.org/pdf/2311.01465): "Euclid preparation. XXIV. Calibration of the halo mass function in Λ(ν)CDM cosmologies",
Castro et al., 2023.
- [arxiv:2409.01877](https://arxiv.org/pdf/2409.01877): "Euclid preparation. Calibration of the linear halo bias in Λ(ν)CDM cosmologies",
Castro et al., 2024.
"""
f0 = 1 + a1 * Omega_m_z
f1 = 1 + b1 * dlnsigma_dlnR + b2 * dlnsigma_dlnR**2
f2 = 1 + c1 * S8
return A0 * f0 * f1 * f2
[docs]
def corrected_bias(b_PBS, Omega_m_z, dlnsigma_dlnR, S8):
"""
Calculate the corrected linear halo bias using the PBS prediction and the correction factor.
Parameters:
-----------
b_PBS : float
The linear halo bias predicted by the PBS model.
Omega_m_z : float
The matter density parameter at redshift z.
dlnsigma_dlnR : float
The logarithmic derivative of the variance with respect to the radius.
S8 : float
The clustering amplitude parameter.
Returns:
--------
float
The corrected linear halo bias.
References
----------
- [arxiv:2208.02174](https://arxiv.org/pdf/2311.01465): "Euclid preparation. XXIV. Calibration of the halo mass function in Λ(ν)CDM cosmologies",
Castro et al., 2023.
- [arxiv:2409.01877](https://arxiv.org/pdf/2409.01877): "Euclid preparation. Calibration of the linear halo bias in Λ(ν)CDM cosmologies",
Castro et al., in prep.
"""
correction_factor = bias_correction_PBS(Omega_m_z, dlnsigma_dlnR, S8)
return b_PBS * correction_factor