def growth_rate(a):
gamma = 0.545
z = 1. / a - 1.
# rho_c = 3 * H^2 / (8 * pi G)
# om_m(a) = (rho_m/rho_c) = 8 * pi * G *rho_m(0) * a^-3 / (3 H^2)
# = om_m(a = 1) * a^-3 * (H_0/H)^2
om_ma = params['om_m'] * (cosmo.H(0) / cosmo.H(z))**2. * a**-3.
return om_ma.value**gamma
def Ckk(Pk_interps, Llls, pickle=False, zmax=params['zscatter']):
'''
Given a matter power spectrum interpolator and an array of L values,
return Ckk(L) in the extended Limber approximation.
'''
z = np.linspace(0.001, zmax, 2000)
chis = comoving_distance(z)
## Stores the matter power spectrum for each of (L, z) and therefore k
## in the extended Limber approximation.
result = np.zeros((len(z), len(Llls)))
for i, redshift in enumerate(z):
ks = (Llls + 0.5) / chis[i]
result[i, :] = Pmm(Pk_interps, ks, redshift)
prefactor = (const.c.to('km/s').value /
cosmo.H(z).value) * (lensing_kernel(z) / chis)**2.
integrand = prefactor[:, None] * result
integrand /= params['h_100']**3. ## account for [h^-1 Mpc]^3 of Pmm.
result = simps(integrand, dx=z[1] - z[0], axis=0)
if pickle:
from pickle import dump
## New beam/noise configurations require pickle files to be removed.
dump(result, open("pickle/kk.p", "wb"))
## Ckk at each L, after integrating the lensing kernel over redshift.
return result
def Cgg(Pk_interps, Llls, zmin, zmax, survey_pz, bz, survey_pz2=None, bz2=None, zeff=True):
dz = 0.01
zs = np.arange(zmin, zmax + dz, dz)
## Catch normalisation of p(z). Added 03/01/19.
ps = survey_pz(zs)
norm = np.sum(ps) * dz
ps /= norm
chis = comoving_distance(zs)
if bz2 is None:
bz2 = bz
if survey_pz2 is None:
survey_pz2 = survey_pz
ps2 = np.copy(ps)
else:
ps2 = survey_pz2(zs)
norm = np.sum(ps2) * dz
ps2 /= norm
if zeff:
'''
Compute Cgg in the z_eff and first-order Limber approximations
for a slice of galaxies at zz of width dz; eqn. (5) of
https://arxiv.org/pdf/1511.04457.pdf
'''
zz = dz * np.sum(ps * zs) / (np.sum(ps) * dz) ## Normalisation should already be unity.
ks = (Llls + 0.5) / comoving_distance(zz) ## For the Phh evaluation in the integral, we take a zeff approx.
## i.e. \int dz .... Phh(zeff).
result = Pmm(Pk_interps, ks, zz) * bz(zz) * bz2(zz)
result = np.broadcast_to(result, (len(zs), len(Llls))) ## Broadcast to each redshift.
else:
result = np.zeros((len(zs), len(Llls)))
for i, z in enumerate(zs):
ks = (Llls + 0.5) / chis[i] ## Evaluate Phh for each z and k(ell, z).
result[i,:] = Pmm(Pk_interps, ks, z) * bz(z) * bz2(z)
## Accounts for both spatial to angular mapping as function of z; i.e. k = (l. + 0.5) / chi(z) and redshift evolution of P_mm(k).
prefactor = (cosmo.H(zs).value / const.c.to('km/s').value) * sliced_pz(zs, zmin, zmax, survey_pz)\
* sliced_pz(zs, zmin, zmax, survey_pz2)\
/ chis**2.
integrand = prefactor[:, None] * result
integrand /= params['h_100']
return simps(integrand, dx = dz, axis=0) ## integral over z.
def WCIB(z, nu=353., zc=2., sigmaz=2.):
'''
Input:
nu in GHz; [545, 857, 217, 353] GHz.
'''
result = fv(nu * (1. + z), beta=2., T=34., nup=4955, alpha=0.0)
result *= np.exp(-0.5 * (z - zc)**2. / sigmaz**2.)
result *= comoving_distance(z)**2.
result /= (cosmo.H(z).value * (1. + z)**2.)
result /= result.max()
return result
def Cab(Llls,
spec_z,
surveya='LSST',
surveyb='QSO',
alpha=1.0,
sigma=2.,
zeff=True,
nowiggle=False):
'''
Angular correlation function: i.e. C_sp(L, z).
'''
z = np.arange(0.01, 5.0, 0.01)
chis = comoving_distance(z)
ba = bzs(spec_z, surveya)
bb = bzs(spec_z, surveyb)
if zeff == True:
'''
Compute Cgg in the z_eff and first-order Limber approximations for a slice of galaxies at spec_z of width dz.
eqn. (5) of https://arxiv.org/pdf/1511.04457.pdf
'''
ks = (Llls + 0.5) / comoving_distance(
spec_z
) ## For the Phh evaluation in the integral, we take a zeff approx.
## i.e. \int dz .... Phh(zeff).
result = np.broadcast_to(
Pab(ks, ba, bb, alpha, sigma,
nowiggle), (len(z), len(Llls))) ## Broadcast to each redshift.
else:
result = np.zeros((len(spec_z), len(Llls)))
for i, j in enumerate(z):
ks = (Llls +
0.5) / chis[i] ## Evaluate Phh for each z and k(ell, z).
## Given L mixes at range of k -- washes out BAO.
## accounts for spatial to angular mapping as function of z, i.e. k = (l + 0.5)/chi(z) but neglects redshift evolution of Pps(k).
result[i, :] = Pab(ks, ba, bb, alpha, sigma, nowiggle)
prefactor = (cosmo.H(z).value/const.c.to('km/s').value)*(sliced_pz(z, spec_z, survey_dzs[surveya], surveya, True)/chis) \
*(sliced_pz(z, spec_z, survey_dzs[surveyb], surveyb, True)/chis)
integrand = prefactor[:, None] * result
integrand /= params[
'h_100'] ## account for [h^-1 Mpc]^3 of P(k) and h^-1 Mpc of chi_g.
return simps(integrand, dx=z[1] - z[0], axis=0) ## integral over z.
def projected_crosspower(ks, surveya, surveyb, nowiggle=False, alpha=1.0):
dz = 0.01
zs = np.arange(dz, 6.0, dz)
gzs, gks = np.meshgrid(zs, ks)
prefactor = (cosmo.H(zs).value / const.c.to('km/s').value)
prefactor *= sliced_pz(zs, 0.75, 1.00, surveya, normed=True)
prefactor *= sliced_pz(zs, 0.75, 0.15, surveyb, normed=True) * dz
integrand = Pab(gks,
ba=1.7,
bb=2.0,
alpha=alpha,
sigma=0.0,
nowiggle=nowiggle)
integrand *= prefactor
return np.sum(integrand, axis=1)