dark_emulator.darkemu.de_interface module

class dark_emulator.darkemu.de_interface.base_class

Bases: object

The base class of dark emulator. This holds all the individual emulator class objects for different statistical quantities. By passing to the base class object, the cosmological paramters in all the lower-level objects are updated.

Parameters:

cparam (numpy array) – Cosmological parameters \((\omega_b, \omega_c, \Omega_{de}, \ln(10^{10}A_s), n_s, w)\)

cosmo

A class object dealing with the cosmological parameters and some basic cosmological quantities such as expansion and linear growth.

Type:

class cosmo_class

pkL

A class object that takes care of the linear matter power spectrum

Type:

class pklin_gp

g1

A class object that takes care of the large-scale bias as well as the BAO damping

Type:

class gamma1_gp

xi_cross

A class object that takes care of the halo-matter cross correlation function

Type:

class cross_gp

xi_auto

A class object that takes care of the halo-halo correlation function

Type:

class auto_gp

massfunc

A class object that takes care of the halo mass function

Type:

class hmf_gp

xiNL

A class object that takes care of the nonlinear matter correlation function (experimental)

Type:

class xinl_gp

Dgrowth_from_a(a)

Compute the linear growth factor, D_+, at scale factor a. Normalized to unity at z=0.

Parameters:

a – scale factor normalized to unity at present.

Returns:

linear growth factor

Return type:

float

Dgrowth_from_z(z)

Compute the linear growth factor, D_+, at redshift z. Normalized to unity at z=0.

Parameters:

z – redshift

Returns:

linear growth factor

Return type:

float

dens_to_mass(dens, redshift, nint=20, integration='quad')

Convert the cumulative number density to the halo mass threshold for the current cosmological model at redshift z.

Parameters:

  • dens (float) – halo number density in \((h^{-1}\mathrm{Mpc})^{-3}\)

  • redshift (float) – redshift

  • nint (int, optional) – number of sampling points in log(M) used for interpolation

  • integration (str, optional) – type of integration (default: “quad”, “trapz” is also supported)

Returns:

mass threshold in \([h^{-1}M_{\odot}]\)

Return type:

float

f_from_a(a)

Compute the linear growth rate, \(f = \mathrm{d}\ln D_+/\mathrm{d}\ln a\), at scale factor a.

Parameters:

a – scale factor normalized to unity at present.

Returns:

linear growth rate

Return type:

float

f_from_z(z)

Compute the linear growth rate, \(f = \mathrm{d}\ln D_+/\mathrm{d}\ln a\), at redshift z.

Parameters:

z – redshift

Returns:

linear growth rate

Return type:

float

get_DeltaSigma(R2d, logdens, redshift)

Compute the halo-galaxy lensing signal, the excess surface mass density, \(\Delta\Sigma(R;n_h)\), for a mass threshold halo sample specified by the corresponding cumulative number density.

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \(h^{-1}\mathrm{Mpc}\)

  • logdens (float) – Logarithm of the cumulative halo number density taken from the most massive, \(\log_{10}[n_h/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

excess surface mass density in \([h M_\odot \mathrm{pc}^{-2}]\)

Return type:

numpy array

get_DeltaSigma_mass(R2d, M, redshift)

Compute the halo-galaxy lensing signal, the excess surface mass density, \(\Delta\Sigma(R;M)\), for halos with mass \(M\).

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \(h^{-1}\mathrm{Mpc}\)

  • M (float) – Halo mass in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

excess surface mass density in \([h M_\odot \mathrm{pc}^{-2}]\)

Return type:

numpy array

get_DeltaSigma_massthreshold(R2d, Mthre, redshift)

Compute the halo-galaxy lensing signal, the excess surface mass density, \(\Delta\Sigma(R;>M_\mathrm{th})\), for a mass threshold halo sample.

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \(h^{-1}\mathrm{Mpc}\)

  • Mthre (float) – Minimum halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

excess surface mass density in \([h M_\odot \mathrm{pc}^{-2}]\)

Return type:

numpy array

get_Sigma(R2d, logdens, redshift)

Compute the surface mass density, \(\Sigma(R;n_h)\), for a mass threshold halo sample specified by the corresponding cumulative number density.

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \(h^{-1}\mathrm{Mpc}\)

  • logdens (float) – Logarithm of the cumulative halo number density taken from the most massive, \(\log_{10}[n_h/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

surface mass density in \([h M_\odot \mathrm{pc}^{-2}]\)

Return type:

numpy array

get_Sigma_mass(R2d, M, redshift)

Compute the surface mass density, \(\Sigma(R;M)\), for halos with mass \(M\).

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \(h^{-1}\mathrm{Mpc}\)

  • M (float) – Halo mass in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

surface mass density in \([h M_\odot \mathrm{pc}^{-2}]\)

Return type:

numpy array

get_Sigma_massthreshold(R2d, Mthre, redshift)

Compute the surface mass density, \(\Sigma(R;>M_\mathrm{th})\), for a mass threshold halo sample.

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \(h^{-1}\mathrm{Mpc}\)

  • Mthre (float) – Minimum halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

surface mass density in \([h M_\odot \mathrm{pc}^{-2}]\)

Return type:

numpy array

get_bias(logdens, redshift)

Compute the linear bias for a mass threshold halo sample specified by the corresponding cumulative number density.

Parameters:

  • logdens (float) – Logarithm of the cumulative halo number density taken from the most massive, \(\log_{10}[n_h/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

linear bias factor

Return type:

float

get_bias_mass(M, redshift)

Compute the linear bias for halos with mass \(M\).

Parameters:

  • M (float) – Halo mass in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

linear bias factor

Return type:

float

get_bias_massthreshold(Mth, redshift)

Compute the linear bias, \(b(>M_\mathrm{th})\), for a mass threshold halo sample.

Parameters:

  • Mth (float) – Halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the lens halos are located

Returns:

linear bias factor

Return type:

float

get_cosmology()

Obtain the cosmological parameters currently set to the emulator.

Returns:

Cosmological parameters \((\omega_b, \omega_c, \Omega_{de}, \ln(10^{10}A_s), n_s, w)\)

Return type:

numpy array

get_f_HMF(redshift)

Compute the multiplicity function \(f(\sigma)\), defined through \(dn/dM = f(\sigma)\bar{\rho}_m/M d \ln \sigma^{-1}/dM\).

Parameters:

redshift (float) – redshift

Returns:

tuple containing:

mass(numpy array): \(M_{200b}\)

mass variance(numpy array): \(\sigma(M_{200b)\)

multiplicity function(numpy array): \(f(\sigma)\)

Return type:

(tuple)

get_nhalo(Mmin, Mmax, vol, redshift)

Compute the mean number of halos in a given mass range and volume.

Parameters:

  • Mmin (float) – Minimum halo mass in \([h^{-1}M_\odot]\)

  • Mmax (float) – Maximum halo mass in \([h^{-1}M_\odot]\)

  • vol (float) – Volume in \([(h^{-1}\mathrm{Mpc})^3]\)

Returns:

Number of halos

Return type:

float

get_nhalo_tinker(Mmin, Mmax, vol, redshift)

Compute the mean number of halos in a given mass range and volume based on the fitting formula by Tinker et al. (ApJ 688 (2008) 709).

Parameters:

  • Mmin (float) – Minimum halo mass in \([h^{-1}M_\odot]\)

  • Mmax (float) – Maximum halo mass in \([h^{-1}M_\odot]\)

  • vol (float) – Volume in \([(h^{-1}\mathrm{Mpc})^3]\)

Returns:

Number of halos

Return type:

float

get_phh(ks, logdens1, logdens2, redshift)

Compute the halo-halo power spectrum \(P_{hh}(k;n_1,n_2)\) between 2 mass threshold halo samples specified by the corresponding cumulative number densities.

Parameters:

  • ks (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • logdens1 (float) – Logarithm of the cumulative halo number density of the first halo sample taken from the most massive, \(\log_{10}[n_1/(h^{-1}\mathrm{Mpc})^3]\)

  • logdens2 (float) – Logarithm of the cumulative halo number density of the second halo sample taken from the most massive, \(\log_{10}[n_2/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

halo power spectrum in \([(h^{-1}\mathrm{Mpc})^{3}]\)

Return type:

numpy array

get_phh_mass(ks, M1, M2, redshift)

Compute the halo-halo power spectrum \(P_{hh}(k;M_1,M_2)\) between 2 halo samples with mass \(M_1\) and \(M_2\).

Parameters:

  • ks (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • M1 (float) – Halo mass of the first sample in \([h^{-1}M_\odot]\)

  • M2 (float) – Halo mass of the second sample in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

halo power spectrum in \([(h^{-1}\mathrm{Mpc})^{3}]\)

Return type:

numpy array

get_phh_massthreshold(ks, Mthre, redshift)

Compute the halo-halo auto power spectrum \(P_{hh}(k;>M_\mathrm{th})\) for a mass threshold halo sample.

Parameters:

  • ks (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • Mthre (float) – Minimum halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

halo power spectrum in \([(h^{-1}\mathrm{Mpc})^{3}]\)

Return type:

numpy array

get_phm(ks, logdens, redshift)

Compute the halo-matter cross power spectrum \(P_{hm}(k;n_h)\) for a mass threshold halo sample specified by the corresponding cumulative number density.

Parameters:

  • ks (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • logdens (float) – Logarithm of the cumulative halo number density of the halo sample taken from the most massive, \(\log_{10}[n_h/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

Halo-matter cross power spectrum in \([(h^{-1}\mathrm{Mpc})^{3}]\)

Return type:

numpy array

get_phm_mass(ks, M, redshift)

Compute the halo-matter cross power spectrum \(P_{hm}(k;M)\) for halos with mass \(M\).

Parameters:

  • ks (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • M (float) – Halo mass in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

Halo-matter cross power spectrum in \([(h^{-1}\mathrm{Mpc})^{3}]\)

Return type:

numpy array

get_phm_massthreshold(ks, Mthre, redshift)

Compute the halo-matter cross power spectrum \(P_{hm}(k;>M_\mathrm{th})\) for a mass threshold halo sample.

Parameters:

  • ks (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • Mthre (float) – Minimum halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

Halo-matter cross power spectrum in \([(h^{-1}\mathrm{Mpc})^{3}]\)

Return type:

numpy array

get_pklin(k)

Compute the linear matter power spectrum at z=0.

Parameters:

k (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

Returns:

Linear power spectrum at wavenumbers given in the argument k.

Return type:

numpy array

get_pklin_from_z(k, z)

get_pklin_z

Compute the linear matter power spectrum.

Parameters:

  • k (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • z (float) – redshift

Returns:

Linear power spectrum at wavenumbers given in the argument k.

Return type:

numpy array

get_pknl(k, z)

Compute the nonlinear matter power spectrum. Note that this is still in a development phase, and the accuracy has not yet been fully evaluated.

Parameters:

  • k (numpy array) – Wavenumbers in \([h\mathrm{Mpc}^{-1}]\)

  • z (float) – redshift

Returns:

Nonlinear matter power spectrum at wavenumbers given in the argument k.

Return type:

numpy array

get_sd(z)

Compute the root mean square of the linear displacement, \(\sigma_d\), for the current cosmological model at redshift z.

Parameters:

z (float) – redshift

Returns:

\(\sigma_d\)

Return type:

float

get_sigma8(logkmin=-4, logkmax=1, nint=100)

Compute \(\sigma_8\) for the current cosmology.

Parameters:

  • logkmin (float, optional) – log10 of the minimum wavenumber for the integral (default=-4)

  • logkmin – log10 of the maximum wavenumber for the integral (default=1)

  • nint (int, optional) – Number of samples taken for the trapz integration (default=100)

Returns:

\(\sigma_8\)

Return type:

float

get_wauto(R2d, logdens1, logdens2, redshift)

Compute the projected halo-halo correlation function \(w_{hh}(R;n_1,n_2)\) for 2 mass threshold halo samples specified by the corresponding cumulative number densities.

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \([h^{-1}\mathrm{Mpc}]\)

  • logdens1 (float) – Logarithm of the cumulative halo number density of the first halo sample taken from the most massive, \(\log_{10}[n_1/(h^{-1}\mathrm{Mpc})^3]\)

  • logdens2 (float) – Logarithm of the cumulative halo number density of the second halo sample taken from the most massive, \(\log_{10}[n_2/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

projected halo correlation function in \([h^{-1}\mathrm{Mpc}]\)

Return type:

numpy array

get_wauto_cut(R2d, logdens1, logdens2, redshift, pimax, integration='quad')

Compute the projected halo-halo correlation function \(w_{hh}(R;n_1,n_2)\) for 2 mass threshold halo samples specified by the corresponding cumulative number densities. Unlike get_wauto, this function considers a finite width for the radial integration, from \(-\pi_\mathrm{max}\) to \(\pi_\mathrm{max}\).

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \([h^{-1}\mathrm{Mpc}]\)

  • logdens1 (float) – Logarithm of the cumulative halo number density of the first halo sample taken from the most massive, \(\log_{10}[n_1/(h^{-1}\mathrm{Mpc})^3]\)

  • logdens2 (float) – Logarithm of the cumulative halo number density of the second halo sample taken from the most massive, \(\log_{10}[n_2/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

  • pimax (float) – \(\pi_\mathrm{max}\) for the upper limit of the integral

Returns:

projected halo correlation function in \([h^{-1}\mathrm{Mpc}]\)

Return type:

numpy array

get_wauto_mass(R2d, M1, M2, redshift)

Compute the projected halo-halo correlation function \(w_{hh}(R;M_1,M_2)\) for 2 mass threshold halo samples.

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \([h^{-1}\mathrm{Mpc}]\)

  • M1 (float) – Halo mass of the first sample in \([h^{-1}M_\odot]\)

  • M2 (float) – Halo mass of the second sample in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

projected halo correlation function in \([h^{-1}\mathrm{Mpc}]\)

Return type:

numpy array

get_wauto_mass_cut(R2d, M1, M2, redshift, pimax)

Compute the projected halo-halo correlation function \(w_{hh}(R;M_1,M_2)\) for 2 mass threshold halo samples. Unlike get_wauto_mass, this function considers a finite width for the radial integration, from \(-\pi_\mathrm{max}\) to \(\pi_\mathrm{max}\).

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \([h^{-1}\mathrm{Mpc}]\)

  • M1 (float) – Halo mass of the first sample in \([h^{-1}M_\odot]\)

  • M2 (float) – Halo mass of the second sample in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

  • pimax (float) – \(\pi_\mathrm{max}\) for the upper limit of the integral

Returns:

projected halo correlation function in \([h^{-1}\mathrm{Mpc}]\)

Return type:

numpy array

get_wauto_massthreshold(R2d, Mthre, redshift)

Compute the projected halo-halo correlation function \(w_{hh}(R;>M_\mathrm{th})\) for a mass threshold halo sample.

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \([h^{-1}\mathrm{Mpc}]\)

  • Mthre (float) – Minimum halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

projected halo correlation function in \([h^{-1}\mathrm{Mpc}]\)

Return type:

numpy array

get_wauto_masthreshold_cut(R2d, Mthre, redshift, pimax, integration='quad')

get_wauto_massthreshold_cut

Compute the projected halo-halo correlation function \(w_{hh}(R;>M_\mathrm{th})\) for a mass threshold halo sample. Unlike get_wauto_massthreshold, this function considers a finite width for the radial integration, from \(-\pi_\mathrm{max}\) to \(\pi_\mathrm{max}\).

Parameters:

  • R2d (numpy array) – 2 dimensional projected separation in \([h^{-1}\mathrm{Mpc}]\)

  • Mthre (float) – Minimum halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

  • pimax (float) – \(\pi_\mathrm{max}\) for the upper limit of the integral

Returns:

projected halo correlation function in \([h^{-1}\mathrm{Mpc}]\)

Return type:

numpy array

get_xiauto(xs, logdens1, logdens2, redshift)

Compute the halo-halo correlation function, \(\xi_\mathrm{hh}(x;n_1,n_2)\), bwtween 2 mass threshold halo samples specified by the corresponding cumulative number densities.

Parameters:

  • xs (numpy array) – Separations in \([h^{-1}\mathrm{Mpc}]\)

  • logdens1 (float) – Logarithm of the cumulative halo number density of the first halo sample taken from the most massive, \(\log_{10}[n_1/(h^{-1}\mathrm{Mpc})^3]\)

  • logdens2 (float) – Logarithm of the cumulative halo number density of the second halo sample taken from the most massive, \(\log_{10}[n_2/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – Redshift at which the correlation function is evaluated

Returns:

Halo correlation function

Return type:

numpy array

get_xiauto_mass(xs, M1, M2, redshift)

Compute the halo-halo correlation function, \(\xi_\mathrm{hh}(x;M_1,M_2)\), between 2 halo samples with mass \(M_1\) and \(M_2\). :param xs: Separations in \([h^{-1}\mathrm{Mpc}]\) :type xs: numpy array :param M1: Halo mass of the first sample in \([h^{-1}M_\odot]\) :type M1: float :param M2: Halo mass of the second sample in \([h^{-1}M_\odot]\) :type M2: float :param redshift: Redshift at which the correlation function is evaluated :type redshift: float

Returns:

Halo correlation function

Return type:

numpy array

get_xiauto_massthreshold(xs, Mthre, redshift)

Compute the halo-halo correlation function, \(\xi_\mathrm{hh}(x;>M_\mathrm{th})\), for a mass threshold halo sample.

Parameters:

  • xs (numpy array) – Separations in \([h^{-1}\mathrm{Mpc}]\)

  • Mthre (float) – Minimum halo mass threshold in \([h^{-1}M_\odot]\)

  • redshift (float) – Redshift at which the correlation function is evaluated

Returns:

Halo correlation function

Return type:

numpy array

get_xicross(xs, logdens, redshift)

Compute the halo-matter cross correlation function \(\xi_{hm}(x;n_h)\) for a mass threshold halo sample specified by the corresponding cumulative number density.

Parameters:

  • xs (numpy array) – Separations in \([h^{-1}\mathrm{Mpc}]\)

  • logdens (float) – Logarithm of the cumulative halo number density of the halo sample taken from the most massive, \(\log_{10}[n_h/(h^{-1}\mathrm{Mpc})^3]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

Halo-matter cross correlation function

Return type:

numpy array

get_xicross_mass(xs, M, redshift)

Compute the halo-matter cross correlation function \(\xi_{hm}(x;M)\) for halos with mass \(M\).

Parameters:

  • xs (numpy array) – Separations in \([h^{-1}\mathrm{Mpc}]\)

  • M (float) – Halo mass in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

Halo-matter cross correlation function

Return type:

numpy array

get_xicross_massthreshold(xs, Mthre, redshift)

Compute the halo-matter cross correlation function \(\xi_{hm}(x;>M_\mathrm{th})\) for a mass threshold halo sample.

Parameters:

  • xs (numpy array) – Separations in \([h^{-1}\mathrm{Mpc}]\)

  • Mthre (float) – Minimum mass threshold of a halo sample in \([h^{-1}M_\odot]\)

  • redshift (float) – redshift at which the power spectrum is evaluated

Returns:

Halo-matter cross correlation function

Return type:

numpy array

get_xilin(xs)

Compute the linear matter correlation function at z=0.

Parameters:

xs (numpy array) – Separations in \([h^{-1}\mathrm{Mpc}]\)

Returns:

Correlation function at separations given in the argument xs.

Return type:

numpy array

get_xinl(xs, redshift)

Compute the nonlinear matter correlation function. Note that this is still in a development phase, and the accuracy has not yet been fully evaluated.

Parameters:

xs (numpy array) – Separations in \([h^{-1}\mathrm{Mpc}]\)

Returns:

Correlation function at separations given in the argument xs.

Return type:

numpy array

mass_to_dens(mass_thre, redshift, integration='quad')

Convert the halo mass threshold to the cumulative number density for the current cosmological model at redshift z.

Parameters:

  • mass_thre (float) – mass threshold in \(h^{-1}M_{\odot}\)

  • redshift (float) – redshift

  • integration (str, optional) – type of integration (default: “quad”, “trapz” is also supported)

Returns:

halo number density in \([(h^{-1}\mathrm{Mpc})^{-3}]\)

Return type:

float

set_cosmology(cparam)

Let the emulator know the cosmological parameters. This interface passes the 6 parameters to all the class objects used for the emulation of various halo statistics.

The current version supports wCDM cosmologies specified by the 6 parameters as described below. Other parameters are automatically computed:

\(\Omega_{m}=1-\Omega_{de},\)

\(h=\sqrt{(\omega_b+\omega_c+\omega_{\nu})/\Omega_m},\)

where the neutrino density is fixed by \(\omega_{\nu} = 0.00064\) corresponding to the mass sum of 0.06 eV.

Parameters:

cparam (numpy array) – Cosmological parameters \((\omega_b, \omega_c, \Omega_{de}, \ln(10^{10}A_s), n_s, w)\)