Clustering modification (clustering_modification
)¶
Compute modifications to the Newtonian power spectrum in the distant-observer and plane-parallel limits.
Standard Kaiser RSD model¶
Redshift-space distortions induce anisotropy in the power spectrum multipoles
where \(P_\mathrm{m}\) is the matter power spectrum, \(b_1(z)\) is the linear bias and \(f(z)\) is the linear growth rate.
|
Compute the standard Kaiser power spectrum multipoles as multiples of the matter power spectrum, i.e. \(P_\ell/P_\mathrm{m}\). |
Non-Gaussianity scale-dependent modifications¶
Local primordial non-Gaussianty \(f_\mathrm{NL}\) induces scale dependence in the linear bias,
where the scale-dependence kernel is
Here \(H_0\) is the Hubble parameter \(H(z)\) (in km s-1 Mpc-1) at the current epoch \(z = 0\), \(c\) the speed of light, \(\varOmega_\mathrm{m,0}\) the matter density parameter at the current epoch, and \(\delta_\mathrm{c}\) the critical over-density in spherical gravitational collapse. The growth factor \(D(z)\) is normalised to unity at the current epoch (thus the numerical factor 1.27), the transfer function \(T(k)\) is normalised to unity as \(k \to 0\), and \(p\) is a tracer-dependent parameter.
Modifications to power spectrum multipoles as a result of local primordial non-Gaussianty are
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Return the scale-dependence kernel \(A(k, z)\) in the presence of local primordial non-Gaussianity. |
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Compute modifications to the power spectrum multipoles by local primordial non-Gaussianity as multiples of the matter power spectrum, i.e. \(\Delta P_\ell/P_\mathrm{m}\). |
Relativistic corrections¶
Relativistic corrections to the Newtonian clustering mode
are parametrised by the redshift-dependent, dimensionless quantities
with evolution bias \(b_\mathrm{e}(z)\) and magnification bias \(s(z)\), where \(\mathcal{H}(z)\) is the conformal Hubble parameter, \(\chi(z)\) is the comoving distance, and the matter density parameter evolves as
Modifications to power spectrum multipoles from the relativistic corrections are
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Return the relativistic correction function \(g_1(z)\) or \(g_2(z)\). |
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Evaluate the redshift-dependent relativistic correction value \(g_1(z)\) or \(g_2(z)\). |
|
Compute modifications to the power spectrum multipoles by relativistic corrections as multiples of the matter power spectrum, i.e. \(\Delta P_\ell/P_\mathrm{m}\). |
- horizonground.clustering_modification.FIDUCIAL_COSMOLOGY¶
Default Planck15 cosmology.
- Type
nbodykit.cosmology.Cosmology
- horizonground.clustering_modification.standard_kaiser_factor(order, bias, redshift, cosmo=nbodykit.cosmology.Planck15)[source]¶
Compute the standard Kaiser power spectrum multipoles as multiples of the matter power spectrum, i.e. \(P_\ell/P_\mathrm{m}\).
- Parameters
order (int) – Order of the multipole,
order >= 0
.bias (callable or float) – Scale-independent linear bias (at redshift).
redshift (float) – Redshift.
cosmo (
nbodykit.cosmology.Cosmology
, optional) – Cosmological model (default isFIDUCIAL_COSMOLOGY
).
- Returns
factor – Power spectrum multipole as a multiple of the matter power spectrum.
- Return type
- horizonground.clustering_modification.scale_dependence_kernel(redshift, cosmo=nbodykit.cosmology.Planck15)[source]¶
Return the scale-dependence kernel \(A(k, z)\) in the presence of local primordial non-Gaussianity.
- Parameters
redshift (float) – Redshift.
cosmo (
nbodykit.cosmology.Cosmology
, optional) – Cosmological model (default isFIDUCIAL_COSMOLOGY
).
- Returns
Scale-dependence kernel as a function of wavenumber (in \(h/\mathrm{Mpc}\)).
- Return type
callable
- horizonground.clustering_modification.non_gaussianity_correction_factor(wavenumber, order, local_png, bias, redshift, cosmo=nbodykit.cosmology.Planck15, tracer_p=1.0)[source]¶
Compute modifications to the power spectrum multipoles by local primordial non-Gaussianity as multiples of the matter power spectrum, i.e. \(\Delta P_\ell/P_\mathrm{m}\).
- Parameters
wavenumber (float, array_like) – Wavenumber (in \(h/\mathrm{Mpc}\)).
order (int) – Order of the multipole,
order >= 0
.local_png (float) – Local primordial non-Gaussianity.
bias (callable or float) – Scale-independent linear bias (at redshift).
redshift (float) – Redshift.
cosmo (
nbodykit.cosmology.Cosmology
, optional) – Base cosmological model (default isFIDUCIAL_COSMOLOGY
).tracer_p (float, optional) – Tracer parameter (default is 1.).
- Returns
factor – Power spectrum multipole modifications as multiples of the matter power spectrum.
- Return type
float
numpy.ndarray
- horizonground.clustering_modification.relativistic_correction_func(corr_order, cosmo=nbodykit.cosmology.Planck15, evolution_bias=None, magnification_bias=None)[source]¶
Return the relativistic correction function \(g_1(z)\) or \(g_2(z)\).
- Parameters
corr_order ({1, 2}, int) – Order of the correction parameter \(\mathcal{H}/k\).
cosmo (
nbodykit.cosmology.Cosmology
, optional) – Cosmological model (default isFIDUCIAL_COSMOLOGY
).evolution_bias, magnification_bias (callable or None, optional) – Evolution bias or magnification bias as a function of redshift (default is None).
- Returns
Relativistic correction function as a function of redshift (in \(h\)/Mpc).
- Return type
callable
- horizonground.clustering_modification.relativistic_correction_value(redshift, corr_order, cosmo=nbodykit.cosmology.Planck15, evolution_bias=None, magnification_bias=None)[source]¶
Evaluate the redshift-dependent relativistic correction value \(g_1(z)\) or \(g_2(z)\).
- Parameters
redshift (float) – Redshift.
corr_order ({1, 2}, int) – Correction order of the parameter \(\mathcal{H}/k\).
cosmo (
nbodykit.cosmology.Cosmology
, optional) – Base cosmological model (default isFIDUCIAL_COSMOLOGY
).evolution_bias, magnification_bias (float or None, optional) – Evolution bias or magnification bias evaluated at input redshift (default is None).
- Returns
correction_value – Relativistic correction function value (in \(h\)/Mpc) at redshift.
- Return type
- horizonground.clustering_modification.relativistic_correction_factor(wavenumber, order, redshift, bias, correction_value_1=None, correction_value_2=None, cosmo=nbodykit.cosmology.Planck15, evolution_bias=None, magnification_bias=None)[source]¶
Compute modifications to the power spectrum multipoles by relativistic corrections as multiples of the matter power spectrum, i.e. \(\Delta P_\ell/P_\mathrm{m}\).
- Parameters
wavenumber (float, array_like) – Wavenumber (in \(h/\mathrm{Mpc}\)).
order (int) – Order of the multipole,
order >= 0
.redshift (float) – Redshift.
bias (callable or float) – Scale-independent linear bias (at redshift).
correction_value_1, correction_value_2 (float or None, optional) – If not None (default), this is directly used as \(g_1(z)\) or \(g_2(z)\) at redshift in calculations, and evolution_bias, magnification_bias are ignored.
cosmo (
nbodykit.cosmology.Cosmology
, optional) – Cosmological model (default isFIDUCIAL_COSMOLOGY
).evolution_bias (float or callable or None, optional) – Evolution bias as a function of redshift, or evaluated at input redshift (default is None). If callable/float, magnification_bias must also be callable/float.
magnification_bias (float or callable or None, optional) – Magnification bias as a function of redshift, or evaluated at input redshift (default is None). If callable/float, evolution_bias must also be callable/float.
- Returns
factor – Power spectrum multipole modifications as multiples of the matter power spectrum.
- Return type
float
numpy.ndarray