Scale dependence (scale_dependence)

Compute scale-dependence modifications to galaxy clustering from local primordial non-Gausianity \(f_\textrm{NL}\).

The scale-independent linear bias is modified as

\[b_1(z) \mapsto b_1(z) + f_\textrm{NL} [b_1(z) - p] A(k,z) \,,\]

where \(p\) is a tracer-dependent parameter and the scale-dependence modification kernel

\[A(k,z) = 1.3 \left( \frac{H_0}{c} \right)^2 \frac{ 3\varOmega_\textrm{m,0} \delta_\textrm{c} }{k^2 D(z) T(k)}\]

relates to the cosmological model and its growth factor \(D(z)\) (normalised to unity at the current epoch; hence the numerical factor 1.3) and transfer function \(T(k)\) (normalised to unity as \(k \to 0\)). 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.

scale_dependence_modification(cosmo, redshift)

Return the scale-dependence modification kernel \(A(k,z)\) for a given cosmological model.

scale_dependent_bias(b_1, f_nl, cosmo[, ...])

Return the scale-dependent bias modulated by local primordial non-Gaussianity.

modified_power_spectrum(b_1, f_nl, cosmo[, ...])

Return the tracer power spectrum modified by primordial non-Gaussianity.

harmonia.cosmology.scale_dependence.scale_dependence_modification(cosmo, redshift)[source]

Return the scale-dependence modification kernel \(A(k,z)\) for a given cosmological model.

Parameters:
Returns:

Scale-dependence modification kernel as a function of wavenumber (in \(h\)/Mpc).

Return type:

callable

harmonia.cosmology.scale_dependence.scale_dependent_bias(b_1, f_nl, cosmo, redshift=0.0, tracer_p=1.0)[source]

Return the scale-dependent bias modulated by local primordial non-Gaussianity.

Parameters:

  • b_1 (float) – Scale-independent linear bias at input redshift.

  • f_nl (float) – Local primordial on-Gaussianity.

  • cosmo (nbodykit.cosmology.cosmology.Cosmology) – Cosmological model.

  • redshift (float, optional) – Redshift at which quantities are evaluated (default is 0.).

  • tracer_p (float, optional) – Tracer-dependent parameter \(p\) (default is 1.).

Returns:

Scale-dependent bias as a function of wavenumber (in \(h\)/Mpc).

Return type:

callable

harmonia.cosmology.scale_dependence.modified_power_spectrum(b_1, f_nl, cosmo, redshift=0.0, tracer_p=1.0, nbar=None, contrast=None)[source]

Return the tracer power spectrum modified by primordial non-Gaussianity.

Parameters:

  • b_1 (float) – Scale-independent linear bias at input redshift.

  • f_nl (float) – Local primordial non-Gaussianity.

  • cosmo (nbodykit.cosmology.cosmology.Cosmology) – Cosmological model.

  • redshift (float, optional) – Redshift at which quantities are evaluated (default is 0.).

  • tracer_p (float, optional) – Tracer-dependent parameter \(p\) (default is 1.).

  • nbar (float or None, optional) – If not None (default), add 1/nbar as shot noise to the resulting power spectrum.

  • contrast (float or None, optional) – If not None (default), add additional 1/(contrast*nbar) as shot noise to the resulting power spectrum.

Returns:

Tracer power spectrum modified by primordial non-Gaussianity as a function of wavenumber (in \(h\)/Mpc).

Return type:

callable