NumCosmo

Tensor Power Spectrum

Tensor PS

Description

Example written in Python to compute Temperature-Temperature angular power spectrum (PS) considering (i) the scalar PS and (ii) both scalar and tensor PS.

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_Tmodes.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

#
#  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 HIPrimPowerLaw
#
prim = Nc.HIPrimPowerLaw.new ()
prim.props.T_SA_ratio = 2.0e-1

#
#  New CLASS backend precision object
#  Lets 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)

#
#  New CLASS backend object
#
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)
# Setting if the tensor contribution is going to be used or not. 
Bcbe.set_tensor (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.T_SA_ratio = 1.0e-15
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'With and without tensor contribution to $C_\ell$')
plt.xscale('log')
plt.plot (ell, Cls1_a, 'r', label="with-T")
plt.plot (ell, Cls2_a, 'b--', label="without-T")

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

plt.savefig ("hiprim_tensor_Cls.svg")

plt.clf ()

Figure 1: TT angular PS

hiprim_tensor_Cls.svg

Figure 1: Temperature-Temperature angular power spectrum considering the both tensor and scalar contributions (with-T), and only the scalar one (without-T). The scalar and tensor primordial PS are, respectively,

\begin{equation*} P_{S}(k) = A_s \left(\frac{k}{k_*} \right)^{n_s - 1}, \end{equation*}

\begin{equation*} P_{T}(k) = r A_s \left(\frac{k}{k_*} \right)^{n_T - 1}, \end{equation*} where $A_s$ is the normalization, $n_s$ is the spectral index, $r = \frac{P_T(k_*)}{P_S(k_*)}$ is the tensor-to-scalar ratio and $k_*$ is the pivot mode.

Example Directory