Hot New Early Dark Energy#
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import matplotlib.colors as mcolors
import classy as classy
##Define cosmologies:
dict_general = {
# General & Background
'h': 0.67810,
'T_cmb': 2.7255,
'omega_b': 0.02238280,
'omega_cdm': 0.1201075,
'N_ur': 3.044,
'Omega_k': 0.,
'YHe': 'BBN',
'recombination': 'recfast',
# Reionization
'reio_parametrization': 'reio_camb',
'z_reio': 7.6711,
'reionization_exponent': 1.5,
'reionization_width': 0.5,
'helium_fullreio_redshift': 3.5,
'helium_fullreio_width': 0.5,
# Perturbations & Output types
'output': 'tCl,pCl,lCl,mPk',
'modes': 's',
'ic': 'ad',
'gauge': 'synchronous',
'lensing': 'yes',
# Primordial Spectrum
'k_pivot': 0.05,
'A_s': 2.100549e-09,
'n_s': 0.9660499,
'alpha_s': 0.,
# Spectra Limits & LSS
'l_max_scalars': 2500,
'P_k_max_h/Mpc': 1.,
'z_pk': 0,
# Verbosity
'input_verbose': 0,
'background_verbose': 0,
'thermodynamics_verbose': 0,
'perturbations_verbose': 0,
'transfer_verbose': 0,
'primordial_verbose': 0,
'lensing_verbose': 0,
'output_verbose': 0,
'back_integration_stepsize': 1e-3,
'perturb_integration_stepsize': 1e-3
}
# Make some helper functions for cleaner code in the notebook:
def run_cosmo(classy_version, dict_in):
model = classy_version.Class()
model.set(dict_in)
model.compute()
return model
def plot_Cl_TT(model, ax = None,**kwargs):
# Get the computed data dictionary
cl = model.lensed_cl(2500)
l = cl['ell']
# Compute C_l = l(l+1)C_l / 2pi (in muK^2)
factor = l * (l + 1) / (2 * np.pi) * 1e12
cl_TT = factor * cl['tt']
if ax is not None:
ax.plot(l, cl_TT, **kwargs)
return l, cl_TT
Running the Hot NEDE model in CLASS++:#
We can start by running the LCDM model as a baseline:
model_LCDM = run_cosmo(classy, {**dict_general})
To activate Hot NEDE in CLASS++, we need to tell CLASS++ to compute it with four parameters:
G_over_aH_drmd_ini,
delta_Neff_drmd,
f_idm_drmd,
z_stop.
dict_drmd={
'G_over_aH_drmd_ini':1e5, # Interaction strength
'delta_Neff_drmd':1.0, # Extra radiation from the DRMD component
'f_idm_drmd':0.5, # Fraction of DM that is interacting
'z_stop':500, # Redshift at which the interaction stops
}
model_Hot_NEDE = run_cosmo(classy, {**dict_general, **dict_drmd})
We can also extract some output values directly from classy:
print("Hot NEDE model outputs:")
print(f'Fraction of interacting dark radiation (compared to total energy density): f_idr_drmd = {model_Hot_NEDE.f_idr_drmd()}')
print(f'Redshift of decoupling: z_dec_drmd = {model_Hot_NEDE.z_dec_drmd()}')
Hot NEDE model outputs:
Fraction of interacting dark radiation (compared to total energy density): f_idr_drmd = 0.11838235723282768
Redshift of decoupling: z_dec_drmd = 51.83356067095277
N = 25
f_idm_drmds = np.linspace(0.01, 1.0, N)
fig, axs = plt.subplots(2,1, figsize=(10, 8), sharex=True, gridspec_kw={'height_ratios': [3, 1]})
# --- Colormap setup ---
# Restrict range to avoid very light colors
def truncate_cmap(cmap, minval=0.3, maxval=0.9, n=100):
return mcolors.LinearSegmentedColormap.from_list(
f'trunc({cmap.name})',
cmap(np.linspace(minval, maxval, n))
)
cmap_drmd = truncate_cmap(cm.Reds)
cmap_ratio = truncate_cmap(cm.cool)
norm = mcolors.Normalize(vmin=0, vmax=1)
ls_LCDM, cls_LCDM = plot_Cl_TT(model_LCDM, ax=axs[0], label=r'$\Lambda$CDM', color='black')
for f_idm_drmd in f_idm_drmds:
dict_drmd_local = {**dict_general, **dict_drmd, 'f_idm_drmd': f_idm_drmd}
model_drmd_local = classy.Class()
model_drmd_local.set(dict_drmd_local)
model_drmd_local.compute()
color_drmd = cmap_drmd(norm(f_idm_drmd))
color_ratio = cmap_ratio(norm(f_idm_drmd))
ls_drmd, cls_drmd = plot_Cl_TT(
model_drmd_local, axs[0],
color=color_drmd,
alpha = 0.7
)
axs[1].plot(
ls_drmd,
(cls_drmd / cls_LCDM - 1) * 100,
color=color_ratio
)
axs[1].axhline(0, color='black', linestyle='--', alpha=0.7)
# --- Colorbars ---
sm_drmd = cm.ScalarMappable(cmap=cmap_drmd, norm=norm)
sm_drmd.set_array([])
cbar_drmd = fig.colorbar(sm_drmd, ax=axs[0])
cbar_drmd.set_label(r'$f_{\mathrm{idm\_drmd}}$')
sm_ratio = cm.ScalarMappable(cmap=cmap_ratio, norm=norm)
sm_ratio.set_array([])
cbar_ratio = fig.colorbar(sm_ratio, ax=axs[1])
cbar_ratio.set_label(r'$f_{\mathrm{idm\_drmd}}$')
# -------Axes labels and titles-------
axs[0].set_xlabel(r'Multipole $\ell$')
axs[0].set_ylabel(r'$C_\ell^{TT}$ [$\mu K^2$]')
axs[0].set_title('CMB Temperature Power Spectrum')
axs[0].legend()
axs[1].set_xlabel(r'Multipole $\ell$')
axs[1].set_ylabel(r'$\Delta C_\ell^{TT}$ [%]')
axs[1].set_title('Relative Difference to $\Lambda$CDM')
/tmp/ipykernel_3533832/2963136698.py:44: RuntimeWarning: invalid value encountered in divide
(cls_drmd / cls_LCDM - 1) * 100,
Text(0.5, 1.0, 'Relative Difference to $\\Lambda$CDM')
G_over_aH_drmd_inis = np.logspace(-9, 15, N)
fig, axs = plt.subplots(2,1, figsize=(10, 8), sharex=True, gridspec_kw={'height_ratios': [3, 1]})
# --- Colormap setup ---
# Restrict range to avoid very light colors
def truncate_cmap(cmap, minval=0.3, maxval=0.9, n=100):
return mcolors.LinearSegmentedColormap.from_list(
f'trunc({cmap.name})',
cmap(np.linspace(minval, maxval, n))
)
cmap_drmd = truncate_cmap(cm.Reds)
cmap_ratio = truncate_cmap(cm.cool)
norm = mcolors.LogNorm(vmin=G_over_aH_drmd_inis.min(), vmax=G_over_aH_drmd_inis.max())
ls_LCDM, cls_LCDM = plot_Cl_TT(model_LCDM, ax=axs[0], label=r'$\Lambda$CDM', color='black')
for G_over_aH_drmd_ini in G_over_aH_drmd_inis:
dict_drmd_local = {**dict_general, **dict_drmd, 'G_over_aH_drmd_ini': G_over_aH_drmd_ini}
model_drmd_local = classy.Class()
model_drmd_local.set(dict_drmd_local)
model_drmd_local.compute()
color_drmd = cmap_drmd(norm(G_over_aH_drmd_ini))
color_ratio = cmap_ratio(norm(G_over_aH_drmd_ini))
ls_drmd, cls_drmd = plot_Cl_TT(
model_drmd_local, axs[0],
color=color_drmd,
alpha = 0.7
)
axs[1].plot(
ls_drmd,
(cls_drmd / cls_LCDM - 1) * 100,
color=color_ratio
)
axs[1].axhline(0, color='black', linestyle='--', alpha=0.7)
# --- Colorbars ---
sm_drmd = cm.ScalarMappable(cmap=cmap_drmd, norm=norm)
sm_drmd.set_array([])
cbar_drmd = fig.colorbar(sm_drmd, ax=axs[0])
cbar_drmd.set_label(r'$f_{\mathrm{idm\_drmd}}$')
sm_ratio = cm.ScalarMappable(cmap=cmap_ratio, norm=norm)
sm_ratio.set_array([])
cbar_ratio = fig.colorbar(sm_ratio, ax=axs[1])
cbar_ratio.set_label(r'$G/aH_{\mathrm{idm\_drmd}}$')
# -------Axes labels and titles-------
axs[0].set_xlabel(r'Multipole $\ell$')
axs[0].set_ylabel(r'$C_\ell^{TT}$ [$\mu K^2$]')
axs[0].set_title('CMB Temperature Power Spectrum')
axs[0].legend()
axs[1].set_xlabel(r'Multipole $\ell$')
axs[1].set_ylabel(r'$\Delta C_\ell^{TT}$ [%]')
axs[1].set_title('Relative Difference to $\Lambda$CDM')
/tmp/ipykernel_3533832/790192118.py:43: RuntimeWarning: invalid value encountered in divide
(cls_drmd / cls_LCDM - 1) * 100,
Text(0.5, 1.0, 'Relative Difference to $\\Lambda$CDM')
z_stops = np.logspace(2, 5, N)
fig, axs = plt.subplots(2,1, figsize=(10, 8), sharex=True, gridspec_kw={'height_ratios': [3, 1]})
# --- Colormap setup ---
# Restrict range to avoid very light colors
def truncate_cmap(cmap, minval=0.3, maxval=0.9, n=100):
return mcolors.LinearSegmentedColormap.from_list(
f'trunc({cmap.name})',
cmap(np.linspace(minval, maxval, n))
)
cmap_drmd = truncate_cmap(cm.Reds)
cmap_ratio = truncate_cmap(cm.cool)
norm = mcolors.LogNorm(vmin=z_stops.min(), vmax=z_stops.max())
ls_LCDM, cls_LCDM = plot_Cl_TT(model_LCDM, ax=axs[0], label=r'$\Lambda$CDM', color='black')
for z_stop in z_stops:
dict_drmd_local = {**dict_general, **dict_drmd, 'z_stop': z_stop}
model_drmd_local = classy.Class()
model_drmd_local.set(dict_drmd_local)
model_drmd_local.compute()
color_drmd = cmap_drmd(norm(z_stop))
color_ratio = cmap_ratio(norm(z_stop))
ls_drmd, cls_drmd = plot_Cl_TT(
model_drmd_local, axs[0],
color=color_drmd,
alpha = 0.7
)
axs[1].plot(
ls_drmd,
(cls_drmd / cls_LCDM - 1) * 100,
color=color_ratio
)
axs[1].axhline(0, color='black', linestyle='--', alpha=0.7)
# --- Colorbars ---
sm_drmd = cm.ScalarMappable(cmap=cmap_drmd, norm=norm)
sm_drmd.set_array([])
cbar_drmd = fig.colorbar(sm_drmd, ax=axs[0])
cbar_drmd.set_label(r'$z_{\mathrm{stop}}$')
sm_ratio = cm.ScalarMappable(cmap=cmap_ratio, norm=norm)
sm_ratio.set_array([])
cbar_ratio = fig.colorbar(sm_ratio, ax=axs[1])
cbar_ratio.set_label(r'$z_{\mathrm{stop}}$')
# -------Axes labels and titles-------
axs[0].set_xlabel(r'Multipole $\ell$')
axs[0].set_ylabel(r'$C_\ell^{TT}$ [$\mu K^2$]')
axs[0].set_title('CMB Temperature Power Spectrum')
axs[0].legend()
axs[1].set_xlabel(r'Multipole $\ell$')
axs[1].set_ylabel(r'$\Delta C_\ell^{TT}$ [%]')
axs[1].set_title('Relative Difference to $\Lambda$CDM')
/tmp/ipykernel_3533832/3368307376.py:44: RuntimeWarning: invalid value encountered in divide
(cls_drmd / cls_LCDM - 1) * 100,
Text(0.5, 1.0, 'Relative Difference to $\\Lambda$CDM')
delta_Neff_drmds = np.linspace(0.1,3, N)
fig, axs = plt.subplots(2,1, figsize=(10, 8), sharex=True, gridspec_kw={'height_ratios': [3, 1]})
# --- Colormap setup ---
# Restrict range to avoid very light colors
def truncate_cmap(cmap, minval=0.3, maxval=0.9, n=100):
return mcolors.LinearSegmentedColormap.from_list(
f'trunc({cmap.name})',
cmap(np.linspace(minval, maxval, n))
)
cmap_drmd = truncate_cmap(cm.Reds)
cmap_ratio = truncate_cmap(cm.cool)
norm = mcolors.Normalize(vmin=0, vmax=1)
ls_LCDM, cls_LCDM = plot_Cl_TT(model_LCDM, ax=axs[0], label=r'$\Lambda$CDM', color='black')
for delta_Neff_drmd in delta_Neff_drmds:
dict_drmd_local = {**dict_general, **dict_drmd, 'delta_Neff_drmd': delta_Neff_drmd}
model_drmd_local = classy.Class()
model_drmd_local.set(dict_drmd_local)
model_drmd_local.compute()
color_drmd = cmap_drmd(norm(delta_Neff_drmd))
color_ratio = cmap_ratio(norm(delta_Neff_drmd))
ls_drmd, cls_drmd = plot_Cl_TT(
model_drmd_local, axs[0],
color=color_drmd,
alpha = 0.7,
label = ''
)
axs[1].plot(
ls_drmd,
(cls_drmd / cls_LCDM - 1) * 100,
color=color_ratio
)
axs[1].axhline(0, color='black', linestyle='--', alpha=0.7)
# --- Colorbars ---
sm_drmd = cm.ScalarMappable(cmap=cmap_drmd, norm=norm)
sm_drmd.set_array([])
cbar_drmd = fig.colorbar(sm_drmd, ax=axs[0])
cbar_drmd.set_label(r'$\Delta N_{\mathrm{eff}}^{\mathrm{drmd}}$')
sm_ratio = cm.ScalarMappable(cmap=cmap_ratio, norm=norm)
sm_ratio.set_array([])
cbar_ratio = fig.colorbar(sm_ratio, ax=axs[1])
cbar_ratio.set_label(r'$\Delta N_{\mathrm{eff}}^{\mathrm{drmd}}$')
# -------Axes labels and titles-------
axs[0].set_xlabel(r'Multipole $\ell$')
axs[0].set_ylabel(r'$C_\ell^{TT}$ [$\mu K^2$]')
axs[0].set_title('CMB Temperature Power Spectrum')
axs[0].legend()
axs[1].set_xlabel(r'Multipole $\ell$')
axs[1].set_ylabel(r'$\Delta C_\ell^{TT}$ [%]')
axs[1].set_title('Relative Difference to $\Lambda$CDM')
/tmp/ipykernel_3533832/586358244.py:44: RuntimeWarning: invalid value encountered in divide
(cls_drmd / cls_LCDM - 1) * 100,
Text(0.5, 1.0, 'Relative Difference to $\\Lambda$CDM')
