pybird.symbolic_pofk_linear module

pybird.symbolic_pofk_linear.plin_emulated(k, As, Om, Ob, h, ns, mnu, w0, wa, a=1, max_precision=False)

Compute the emulated linear matter power spectrum by combining the Eisenstein & Hu model, an approximation for the growth factor D, the fit from Bartlett et al. (2023), and corrections to both the present-day linear power spectrum and the growth factor.

:param : k (ndarray): k values to evaluate P(k) at [h / Mpc] :param : As (float): 10^9 times the amplitude of the primordial P(k) :param : Om (float): The z=0 total matter density parameter, Om :param : Ob (float): The z=0 baryonic density parameter, Omega_b :param : h (float): Hubble constant, H0, divided by 100 km/s/Mpc :param : ns (float): Spectral tilt of primordial power spectrum :param : mnu (float): Sum of neutrino masses [eV / c^2] :param : w0 (float): Time independent part of the dark energy EoS :param : wa (float): Time dependent part of the dark energy EoS :param : a (float, default=1): The scale factor to evaluate P(k) at

Returns:

pk_lin (ndarray): The emulated linear P(k) [(Mpc/h)^3]

pybird.symbolic_pofk_linear.get_eisensteinhu_nw(k, As, Om, Ob, h, ns, mnu, w0, wa)

Compute the no-wiggles Eisenstein & Hu approximation to the linear P(k) at redshift zero.

:param : k (ndarray): k values to evaluate P(k) at [h / Mpc] :param : As (float): 10^9 times the amplitude of the primordial P(k) :param : Om (float): The z=0 total matter density parameter, Omega_m :param : Ob (float): The z=0 baryonic density parameter, Omega_b :param : h (float): Hubble constant, H0, divided by 100 km/s/Mpc :param : ns (float): Spectral tilt of primordial power spectrum

Returns:

pk (ndarray): Approxmate linear power spectrum at corresponding k values [(Mpc/h)^3]

pybird.symbolic_pofk_linear.logF_fiducial(k, As, Om, Ob, h, ns, mnu, w0, wa, max_precision=False)

Compute the emulated logarithm of the ratio between the true linear power spectrum and the Eisenstein & Hu 1998 fit for LCDM as given in Bartlett et al. 2023.

This calls the logF_fiducial function from symbolic_pofk.linear but extrapolates to all k considered

:param : k (ndarray): k values to evaluate P(k) at [h / Mpc] :param : As (float): 10^9 times the amplitude of the primordial P(k) :param : Om (float): The z=0 total matter density parameter, Omega_m :param : Ob (float): The z=0 baryonic density parameter, Omega_b :param : h (float): Hubble constant, H0, divided by 100 km/s/Mpc :param : ns (float): Spectral tilt of primordial power spectrum :param : mnu (float): Sum of neutrino masses [eV / c^2] :param : w0 (float): Time independent part of the dark energy EoS :param : wa (float): Time dependent part of the dark energy EoS :param : a (float): Scale factor to consider

Returns:

logF (ndarray): The emulated logarithm of the ratio between the true linear power spectrum

pybird.symbolic_pofk_linear.sigma8_to_As(sigma8, Om, Ob, h, ns, mnu, w0, wa, max_precision=False)

pybird.symbolic_pofk_linear.As_to_sigma8(As, Om, Ob, h, ns, mnu, w0, wa, max_precision=False)

pybird.symbolic_pofk_linear.growth_correction_R(As, Om, Ob, h, ns, mnu, w0, wa, a)

Correction to the growth factor

:param : As (float): 10^9 times the amplitude of the primordial P(k) :param : Om (float): The z=0 total matter density parameter, Om :param : Ob (float): The z=0 baryonic density parameter, Ob :param : h (float): Hubble constant, H0, divided by 100 km/s/Mpc :param : ns (float): Spectral tilt of primordial power spectrum :param : mnu (float): Sum of neutrino masses [eV / c^2] :param : w0 (float): Time independent part of the dark energy EoS :param : wa (float): Time dependent part of the dark energy EoS :param : a (float): The scale factor to evaluate P(k) at

Returns:

result (float): correction to the growth factor

pybird.symbolic_pofk_linear.log10_S(k, As, Om, Ob, h, ns, mnu, w0, wa)

Corrections to the present-day linear power spectrum

:param : k (ndarray): k values to evaluate P(k) at [h / Mpc] :param : As (float): 10^9 times the amplitude of the primordial P(k) :param : Om (float): The z=0 total matter density parameter, Omega_m :param : Ob (float): The z=0 baryonic density parameter, Omega_b :param : h (float): Hubble constant, H0, divided by 100 km/s/Mpc :param : ns (float): Spectral tilt of primordial power spectrum :param : mnu (float): Sum of neutrino masses [eV / c^2] :param : w0 (float): Time independent part of the dark energy EoS :param : wa (float): Time dependent part of the dark energy EoS :param : a (float): Scale factor to consider

Returns:

result (ndarray): Corrections to the present-day linear power spectrum

pybird.symbolic_pofk_linear.get_approximate_D(k, As, Om, Ob, h, ns, mnu, w0, wa, a)

Approximation to the growth factor using the results of Bond et al. 1980, Lahav et al. 1992, Carrol et al. 1992 and Eisenstein & Hu 1997 (D_cbnu).

There are two differences between our method and theirs. First, in Eisenstein & Hu 1997 D is chosen to be (1 + zeq) a at early times, whereas we instead choose D -> a at early times. Second, the formulae reported there assume that w=-1, whereas we change the Omega_Lambda terms to include a w0-wa parameterisation.

:param : k (ndarray): k values to evaluate P(k) at [h / Mpc] :param : As (float): 10^9 times the amplitude of the primordial P(k) :param : Om (float): The z=0 total matter density parameter, Omega_m :param : Ob (float): The z=0 baryonic density parameter, Omega_b :param : h (float): Hubble constant, H0, divided by 100 km/s/Mpc :param : ns (float): Spectral tilt of primordial power spectrum :param : mnu (float): Sum of neutrino masses [eV / c^2] :param : w0 (float): Time independent part of the dark energy EoS :param : wa (float): Time dependent part of the dark energy EoS :param : a (float): Scale factor to consider

Returns:

D (ndarray): Approximate linear growth factor at corresponding k values