C2C/EH98_funcs.py at main · henoriega/C2C · GitHub

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import numpy as np
import scipy.constants as conts


def EH98(kvector, redshift, scaling_factor, cosmo=None):
    #This is the link to the paper: https://arxiv.org/pdf/astro-ph/9710252.pdf
    #The input kvector should be in unit of h/Mpc after rescaling by rd.
    cdict = cosmo.get_current_derived_parameters(['z_d'])
    h = cosmo.h()
    H_at_z = cosmo.Hubble(redshift) * conts.c /1000. /(100.*h)
    Omm = cosmo.Omega_m()
    Omb = cosmo.Omega_b()
    #Cannot find the following function.
    # Omc = cosmo.omegach2()/h**2.
    Omc = cosmo.Omega0_cdm()
    Omm_at_z = Omm*(1.+redshift)**3./H_at_z**2.
    OmLambda_at_z = 1.-Omm_at_z
    ns = cosmo.n_s()
    rs = cosmo.rs_drag()*h/scaling_factor
    Omnu = Omm-Omb-Omc
    fnu = Omnu/Omm
    fb = Omb/Omm
    fnub = (Omb+Omnu)/Omm
    fc = Omc/Omm
    fcb = (Omc+Omb)/Omm
    pc = 1./4.*(5-np.sqrt(1+24*fc))
    pcb = 1./4.*(5-np.sqrt(1+24*fcb))
    Neff = cosmo.Neff()
    Omg = cosmo.Omega_g()
    Omr = Omg * (1. + Neff * (7./8.)*(4./11.)**(4./3.))
    aeq = Omr/(Omb+Omc)/(1-fnu)
    zeq = 1./aeq -1.
    Heq = cosmo.Hubble(zeq)/h
    keq = aeq*Heq*scaling_factor
    zd = cdict['z_d']
    yd = (1.+zeq)/(1.+zd)
    growth = cosmo.scale_independent_growth_factor(redshift)

    if (fnu==0):
        Nnu = 0.
    else:
        Nnu = 1.
    #alpha_gamma = 1 - 0.328*np.log(431*Omm*h**2)*Omb/Omm + 0.38*np.log(22.3*Omm*h**2)*(Omb/Omm)**2

    #There seems to be a mistake in this equation.
    # alpha_nu = fc/fcb * (5 - 2*(pc+pcb))/(5-4*pcb) * (1-0.553*fnub + 0.126*fnub**3.) / (1 - 0.193*np.sqrt(fnu)*Nnu**0.2 + 0.169*fnu) \
    #             *(1.+yd)**(pcb-pc) * (1+(pc-pcb)/2*(1+1./(3-4*pc)/(7-4*pcb))*(1.+yd)**(-1.))

    alpha_nu = fc/fcb * (5 - 2*(pc+pcb))/(5-4*pcb) * (1-0.553*fnub + 0.126*fnub**3.) / (1 - 0.193*np.sqrt(fnu*Nnu) + 0.169*fnu*(Nnu)**0.2) \
                *(1.+yd)**(pcb-pc) * (1+(pc-pcb)/2*(1+1./(3-4*pc)/(7-4*pcb))*(1.+yd)**(-1.))

    #eff_shape = (alpha_gamma + (1.-alpha_gamma)/(1+(0.43*kvector*rs)**4.))
    eff_shape = (np.sqrt(alpha_nu) + (1.-np.sqrt(alpha_nu))/(1+(0.43*kvector*rs)**4.))

    #add in q_test.
    q_test = kvector/keq*7.46e-2
    q0 = kvector/(keq/7.46e-2)/eff_shape
    betac = (1.-0.949*fnub)**(-1.)
    L0 = np.log(np.exp(1.)+1.84*np.sqrt(alpha_nu)*betac*q0)
    # C0 = 14.4 + 325./(1+60.5*q0**1.08)
    C0 = 14.4 + 325./(1+60.5*q0**1.11)
    T0 = L0/(L0+C0*q0**2.)
    if (fnu==0):
        yfs=0.
        qnu=3.92*q_test
    else:
        yfs = 17.2*fnu*(1.+0.488*fnu**(-7./6.))*(Nnu*q_test/fnu)**2.
        qnu = 3.92*q_test*np.sqrt(Nnu/fnu)
    D1 = (1.+zeq)/(1.+redshift)*5*Omm_at_z/2./(Omm_at_z**(4./7.) - OmLambda_at_z + (1.+Omm_at_z/2.)*(1.+OmLambda_at_z/70.))
    Dcbnu = (fcb**(0.7/pcb)+(D1/(1.+yfs))**0.7)**(pcb/0.7) * D1**(1.-pcb)
    Bk = 1. + 1.24*fnu**(0.64)*Nnu**(0.3+0.6*fnu)/(qnu**(-1.6)+qnu**0.8)
    #
    Tcbnu = T0*Dcbnu/D1*Bk
    deltah = 1.94e-5 * Omm**(-0.785-0.05*np.log(Omm))*np.exp(-0.95*(ns-1)-0.169*(ns-1)**2.)

    #The output power spectrum will be in the unit of (Mpc/h)^3.
    Pk = 2*np.pi**2. * deltah**2. * (kvector)**(ns) * Tcbnu**2. * growth**2. /cosmo.Hubble(0)**(3.+ns)
    return Pk

def EH98_transfer(kvector, redshift, scaling_factor, cosmo=None):

    #This is the link to the paper: https://arxiv.org/pdf/astro-ph/9710252.pdf
    #The input kvector should be in unit of h/Mpc after rescaling by rd.

    cdict = cosmo.get_current_derived_parameters(['z_d'])
    h = cosmo.h()
    H_at_z = cosmo.Hubble(redshift) * conts.c /1000. /(100.*h)
    Omm = cosmo.Omega_m()
    Omb = cosmo.Omega_b()
    #Cannot find the following function.
    # Omc = cosmo.omegach2()/h**2.
    Omc = cosmo.Omega0_cdm()
    Omm_at_z = Omm*(1.+redshift)**3./H_at_z**2.
    OmLambda_at_z = 1.-Omm_at_z
    ns = cosmo.n_s()
    rs = cosmo.rs_drag()*h/scaling_factor
    Omnu = Omm-Omb-Omc
    fnu = Omnu/Omm
    fb = Omb/Omm
    fnub = (Omb+Omnu)/Omm
    fc = Omc/Omm
    fcb = (Omc+Omb)/Omm
    pc = 1./4.*(5-np.sqrt(1+24*fc))
    pcb = 1./4.*(5-np.sqrt(1+24*fcb))
    Neff = cosmo.Neff()
    Omg = cosmo.Omega_g()
    Omr = Omg * (1. + Neff * (7./8.)*(4./11.)**(4./3.))
    aeq = Omr/(Omb+Omc)/(1-fnu)
    zeq = 1./aeq -1.
    Heq = cosmo.Hubble(zeq)/h
    keq = aeq*Heq*scaling_factor
    zd = cdict['z_d']
    yd = (1.+zeq)/(1.+zd)
    growth = cosmo.scale_independent_growth_factor(redshift)

    if (fnu==0):
        Nnu = 0.
    else:
        Nnu = 1.
    #alpha_gamma = 1 - 0.328*np.log(431*Omm*h**2)*Omb/Omm + 0.38*np.log(22.3*Omm*h**2)*(Omb/Omm)**2

    #There seems to be a mistake in this equation.
    # alpha_nu = fc/fcb * (5 - 2*(pc+pcb))/(5-4*pcb) * (1-0.553*fnub + 0.126*fnub**3.) / (1 - 0.193*np.sqrt(fnu)*Nnu**0.2 + 0.169*fnu) \
    #             *(1.+yd)**(pcb-pc) * (1+(pc-pcb)/2*(1+1./(3-4*pc)/(7-4*pcb))*(1.+yd)**(-1.))

    alpha_nu = fc/fcb * (5 - 2*(pc+pcb))/(5-4*pcb) * (1-0.553*fnub + 0.126*fnub**3.) / (1 - 0.193*np.sqrt(fnu*Nnu) + 0.169*fnu*(Nnu)**0.2) \
                *(1.+yd)**(pcb-pc) * (1+(pc-pcb)/2.0*(1+1./(3-4*pc)/(7-4*pcb))*(1.+yd)**(-1.))

    #eff_shape = (alpha_gamma + (1.-alpha_gamma)/(1+(0.43*kvector*rs)**4.))
    eff_shape = (np.sqrt(alpha_nu) + (1.-np.sqrt(alpha_nu))/(1+(0.43*kvector*rs)**4.))

    #add in q_test.
    q_test = kvector/keq*7.46e-2
    q0 = kvector/(keq/7.46e-2)/eff_shape
    betac = (1.-0.949*fnub)**(-1.)
    L0 = np.log(np.exp(1.)+1.84*np.sqrt(alpha_nu)*betac*q0)
    # C0 = 14.4 + 325./(1+60.5*q0**1.08)
    C0 = 14.4 + 325./(1+60.5*q0**1.11)
    T0 = L0/(L0+C0*q0**2.)
    if (fnu==0):
        yfs=0.
        qnu=3.92*q_test
        # qnu=3.92*q0
    else:
        yfs = 17.2*fnu*(1.+0.488*fnu**(-7./6.))*(Nnu*q_test/fnu)**2.
        qnu = 3.92*q_test*np.sqrt(Nnu/fnu)
        # yfs = 17.2*fnu*(1.+0.488*fnu**(-7./6.))*(Nnu*q0/fnu)**2.
        # qnu = 3.92*q0*np.sqrt(Nnu/fnu)

    #The original code seems to be missing a factor of 5.
    D1 = (1.+zeq)/(1.+redshift)*5*Omm_at_z/2./(Omm_at_z**(4./7.) - OmLambda_at_z + (1.+Omm_at_z/2.)*(1.+OmLambda_at_z/70.))
    Dcbnu = (fcb**(0.7/pcb)+(D1/(1.+yfs))**0.7)**(pcb/0.7) * D1**(1.-pcb)
    Bk = 1. + 1.24*fnu**(0.64)*Nnu**(0.3+0.6*fnu)/(qnu**(-1.6)+qnu**0.8)
    #
    Tcbnu = T0*Dcbnu/D1*Bk

    return Tcbnu

def Primordial(k, A_s, n_s, k_p = 0.05):
    #k_p is in the unit of 1/Mpc, so the input power spectrum also need to be in 1/Mpc.
    P_R = A_s*(k/k_p)**(n_s - 1.0)
    return P_R


def slope_at_x(xvector,yvector):
    #find the slope
    diff = np.diff(yvector)/np.diff(xvector)
    diff = np.append(diff,diff[-1])
    return diff