NumCosmo

Homogeneous and Isotropic Primordial Model

HI Primordial Model

Description

Example written in Python to compute Temperature-Temperature angular power spectrum considering an alternative homogeneous and isotropic primordial model. The specific model used in this example is defined here.

Running

To try this example you must have PyGObject installed, and numcosmo built with –enable-introspection option. To run the examples without installing follow the instructions here.

example_hiprim.py:

#!/usr/bin/python2

try:
  import gi
  gi.require_version('NumCosmo', '1.0')
  gi.require_version('NumCosmoMath', '1.0')
except:
  pass

import math
import numpy as np
import matplotlib.pyplot as plt

from gi.repository import GObject
from gi.repository import NumCosmo as Nc
from gi.repository import NumCosmoMath as Ncm

from py_hiprim_example import PyHIPrimExample

#
#  Initializing the library objects, this must be called before
#  any other library function.
#
Ncm.cfg_init ()

#
# Script parameters
#
# maximum multipole
lmax = 2500

#
# Creating a new instance of PyHIPrimExample
#
prim = PyHIPrimExample ()

print "# As        = ", prim.props.As
print "# P (k = 1) = ", prim.SA_powspec_k (1.0)
print "# (a, b, c) = ( ", prim.props.a, ", ", prim.props.b, ", ", prim.props.c, " )"

#
#  New CLASS backend precision object
#  Let's also increase k_per_decade_primordial since we are
#  dealing with a modified spectrum.
#
cbe_prec = Nc.CBEPrecision.new ()
cbe_prec.props.k_per_decade_primordial = 50.0

#
#  New CLASS backend object
#
cbe = Nc.CBE.prec_new (cbe_prec)

Bcbe = Nc.HIPertBoltzmannCBE.full_new (cbe)
Bcbe.set_TT_lmax (lmax)
# Setting which CMB data to use
Bcbe.set_target_Cls (Nc.DataCMBDataType.TT)
# Setting if the lensed Cl's are going to be used or not.
Bcbe.set_lensed_Cls (True)

#
#  New homogeneous and isotropic cosmological model NcHICosmoDEXcdm
#
cosmo = Nc.HICosmo.new_from_name (Nc.HICosmo, "NcHICosmoDEXcdm")
cosmo.omega_x2omega_k ()
cosmo.param_set_by_name ("Omegak", 0.0)

#
#  New homogeneous and isotropic reionization object
#
reion = Nc.HIReionCamb.new ()

#
# Adding submodels to the main cosmological model.
#
cosmo.add_submodel (reion)
cosmo.add_submodel (prim)

#
# Preparing the Class backend object
#
Bcbe.prepare (cosmo)

Cls1 = Ncm.Vector.new (lmax + 1)
Cls2 = Ncm.Vector.new (lmax + 1)

Bcbe.get_TT_Cls (Cls1)

prim.props.a = 0
Bcbe.prepare (cosmo)
Bcbe.get_TT_Cls (Cls2)

Cls1_a = Cls1.dup_array ()
Cls2_a = Cls2.dup_array ()

Cls1_a = np.array (Cls1_a[2:])
Cls2_a = np.array (Cls2_a[2:])

ell = np.array (range (2, lmax + 1))

Cls1_a = ell * (ell + 1.0) * Cls1_a
Cls2_a = ell * (ell + 1.0) * Cls2_a

#
#  Ploting the TT angular power spcetrum
#

plt.title (r'Modified and non-modified $C_\ell$')
plt.xscale('log')
plt.plot (ell, Cls1_a, 'r', label="Modified")
plt.plot (ell, Cls2_a, 'b--', label="Non-modified")

plt.xlabel(r'$\ell$')
plt.ylabel(r'$C_\ell$')
plt.legend(loc=2)

plt.savefig ("hiprim_Cls.svg")

plt.clf ()

Figure 1: TT angular PS

hiprim_Cls.svg

Figure 1: Temperature-Temperature angular power spectrum assuming a power-law primordial power spectrum (non-modified) and a modified primordial spectrum described by \(P_{prim}(k) = A_s \left(\frac{k}{k_\*} \right)^{n_s - 1} \left[1 + a^2 \cos\left(b\frac{k}{k_\*} + c \right)^2 \right],\) where $A_s$ is the normalization, $n_s$ is the spectral index and $k_*$ is the pivot mode.

Example Directory