Table of contents

Back to the main page 1. Compute Background Evolution 2. Compute Recombination History 3. Compute Perturbations 4. Compute Powerspectrum

Compute Powerspectrum

Here you can select the cosmologically parameters and numerically compute the CMB and matter power-spectrum in $\Lambda$CDM and make some plots. We also show a comparison to Planck 2018 data. NB: The server this runs on have old CPUs and old compilers so the runtime is unfortunately slow. The precision settings are therefore not for perfect (subpercent) accuracy, but fiducial settings are still fairly accurate and runs in ~10sec. Accuracy can be improved, but if settings are improved too much the code might not finish in time (I automatically kill any runs that takes more than a minute or so) so just be aware of that. The results using the fiducial parameters below can also be found here. Important assumptions: 1) for evolution of perturbations and power-spectra the equations implemented assumes $\Omega_k = 0$ (i.e. the curvature is just implemented in the background), 2) neutrinos are always assumed to be massless, 3) for recombination we only use the Saha approximation for Helium and the Peebles for hydrogen.

Background parameters

Hubble parameter ($H_0\equiv 100 h{\rm km/s/ Mpc}$):
Baryon density:
CDM density:
$\Omega_{\rm CDM}$:
Curvature density ($\Omega_k \equiv -k/H_0^2$):
Temperature of the CMB today ($\Omega_\gamma \propto T_{\rm CMB}^4 / h^2$):
$T_{\rm CMB}$ (K):
Effective number of neutrinos ($\Omega_\nu \equiv N_{\rm eff}\frac{7}{8}\left(\frac{4}{11}\right)^{4/3}\Omega_\gamma$):
$N_{\rm eff}$:
Dark energy equation of state (CPL parametrisation) $w = w_0 + w_a(1-a)$:

Recombination parameters

Primordial helium (mass) abundance:
Include Reionization:
Reionization (H and He) redshift:
$z_{\rm reion}$:
Reionization (H and He) redshift width:
$\Delta z_{\rm reion}$:
Include He+ Reionization:
He+ reionization redshift:
$z_{\rm HeReion}$:
He+ reionization redshift width:
$\Delta z_{\rm HeReion}$:

Perturbations parameters

Include polarization:
Include neutrino perturbations:
(Precision) Number of photon multipoles ($3-20$):
(Precision) Number of neutrino multipoles ($3-20$):
(Precision) Minimum wavenumber:
$k_{\rm min}\eta_0$:
(Precision) Maximum wavenumber:
$k_{\rm max}\eta_0$:
(Precision) Number of $k$-values per log-interval ($10-200$):
(Precision) Spacing between points to store while solving:
$\Delta x$:

Powerspectrum parameters

Primordial amplitude:
Spectral index:
Pivot scale:
$k_{\rm pivot}$ (1/Mpc):
Maximum $\ell$ to compute power-spectrum up to:
$\ell_{\rm max}$:
(Precision) Number of points per oscillation to sample Bessel functions on:
(Precision) Number of points per oscillation to sample $C_\ell$ integrand on:
(Precision) Number of samples per oscillation for LOS integration:
(Precision) Number of samples in $\log a$ for LOS integration:
Compute temperature $C_\ell$'s:
Compute E-mode polarization $C_\ell$'s:
Compute correlation function (power-spectrum we always compute):
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