Functions
ncm_c_sqrt_1_4pi ()
long double
ncm_c_sqrt_1_4pi (void
);
Returns
sqrt (1 / (4 * pi))
ncm_c_sqrt_2pi ()
long double
ncm_c_sqrt_2pi (void
);
ncm_c_sqrt_3_4pi ()
long double
ncm_c_sqrt_3_4pi (void
);
Returns
sqrt (3 / (4 * pi))
ncm_c_lnpi_4 ()
long double
ncm_c_lnpi_4 (void
);
Returns
ln (pi) / 4
1.8378770664093454835606594728112352797227949472755668256343
ncm_c_ln2pi ()
long double
ncm_c_ln2pi (void
);
ncm_c_pi ()
long double
ncm_c_pi (void
);
ncm_c_tan_1arcsec ()
long double
ncm_c_tan_1arcsec (void
);
Returns
tan (2 * pi/ (360 * 60 * 60))
ncm_c_degree_to_radian ()
gdouble
ncm_c_degree_to_radian (const gdouble d
);
ncm_c_radian_to_degree ()
gdouble
ncm_c_radian_to_degree (const gdouble r
);
ncm_c_radian_0_2pi ()
gdouble
ncm_c_radian_0_2pi (const gdouble r
);
Returns
the angle in the interval [0, 2pi]
ncm_c_sign_sin ()
gdouble
ncm_c_sign_sin (const gdouble r
);
Returns
the sign of the value of sin(d).
ncm_c_c ()
gdouble
ncm_c_c (void
);
Returns
Speed of light $\left[ \frac{m}{s} \right]$.
ncm_c_hbar ()
gdouble
ncm_c_hbar (void
);
Returns
Planck constant over 2 pi.
ncm_c_fine_struct ()
gdouble
ncm_c_fine_struct (void
);
Returns
Fine structure constant.
ncm_c_kb ()
gdouble
ncm_c_kb (void
);
Returns
Boltzmann constant.
ncm_c_G ()
gdouble
ncm_c_G (void
);
\begin{equation}
G = 6.67428 \times 10^{-11} \, \frac{\text{m}^3}{\text{kg} \, \text{s}^2}
\end{equation}
Returns
Newton's (or gravitational) constant $G$.
ncm_c_planck_length ()
gdouble
ncm_c_planck_length (void
);
ncm_c_thomson_cs ()
gdouble
ncm_c_thomson_cs (void
);
Returns
Thomson cross section.
ncm_c_stefan_boltzmann ()
gdouble
ncm_c_stefan_boltzmann (void
);
Returns
Stefan Boltzmann constant.
ncm_c_mass_e ()
gdouble
ncm_c_mass_e (void
);
ncm_c_mass_p ()
gdouble
ncm_c_mass_p (void
);
ncm_c_mass_n ()
gdouble
ncm_c_mass_n (void
);
ncm_c_mass_ratio_alpha_p ()
gdouble
ncm_c_mass_ratio_alpha_p (void
);
Returns
The proton and alpha particle (helium-4) mass ratio.
ncm_c_hc ()
gdouble
ncm_c_hc (void
);
Returns
Planck constant times the speed of light.
ncm_c_fine_struct_square ()
gdouble
ncm_c_fine_struct_square (void
);
Returns
The square of the fine struct constant.
ncm_c_kpc ()
gdouble
ncm_c_kpc (void
);
ncm_c_Mpc ()
gdouble
ncm_c_Mpc (void
);
ncm_c_AR ()
gdouble
ncm_c_AR (void
);
Returns
Radiation constant AR.
ncm_c_c2 ()
gdouble
ncm_c_c2 (void
);
Returns
Square of the speed of light.
ncm_c_planck_length2 ()
gdouble
ncm_c_planck_length2 (void
);
Returns
Square of the Planck length.
ncm_c_rest_energy_e ()
gdouble
ncm_c_rest_energy_e (void
);
Returns
Electron's rest energy.
ncm_c_rest_energy_p ()
gdouble
ncm_c_rest_energy_p (void
);
Returns
Proton's rest energy.
ncm_c_rest_energy_n ()
gdouble
ncm_c_rest_energy_n (void
);
Returns
Neutron's rest energy.
ncm_c_decay_H_rate_2s_1s ()
gdouble
ncm_c_decay_H_rate_2s_1s (void
);
FIXME: Cite source.
Returns
Decay rate of Hydrogen from 2s -> 1s.
ncm_c_decay_He_rate_2s_1s ()
gdouble
ncm_c_decay_He_rate_2s_1s (void
);
FIXME: Cite source.
Returns
Decay rate of Helium from 2s -> 1s.
ncm_c_HeI_bind_1s ()
gdouble
ncm_c_HeI_bind_1s (void
);
FIXME: Cite source.
Returns
HeI binding energy 1s.
ncm_c_HeII_bind_1s ()
gdouble
ncm_c_HeII_bind_1s (void
);
FIXME: Cite source.
Returns
HeII binding energy 1s.
ncm_c_HeI_Lyman_2s ()
gdouble
ncm_c_HeI_Lyman_2s (void
);
FIXME: Cite source.
Returns
HeI Lyman 2s energy.
ncm_c_HeI_Lyman_2p ()
gdouble
ncm_c_HeI_Lyman_2p (void
);
FIXME: Cite source.
Returns
HeI Lyman 2p energy.
ncm_c_HeI_Lyman_2s_wl ()
gdouble
ncm_c_HeI_Lyman_2s_wl (void
);
FIXME: Cite source.
Returns
HeI Lyman 2s wave length.
ncm_c_HeI_Lyman_2p_wl ()
gdouble
ncm_c_HeI_Lyman_2p_wl (void
);
FIXME: Cite source.
Returns
HeI Lyman 2p wave length.
ncm_c_HeI_bind_2s ()
gdouble
ncm_c_HeI_bind_2s (void
);
FIXME: Cite source.
Returns
HeI binding energy 2s.
ncm_c_HeI_bind_2p ()
gdouble
ncm_c_HeI_bind_2p (void
);
FIXME: Cite source.
Returns
HeI binding energy 2p.
ncm_c_HeI_2s_m_2p ()
gdouble
ncm_c_HeI_2s_m_2p (void
);
FIXME: Cite source.
Returns
HeI energy difference between states 2s and 2p.
ncm_c_HeI_2s_m_2p_kb ()
gdouble
ncm_c_HeI_2s_m_2p_kb (void
);
FIXME: Cite source.
Returns
HeI energy difference between states 2s and 2p divided by Boltzmann constant.
ncm_c_HeI_Lyman_2s_wl3_8pi ()
gdouble
ncm_c_HeI_Lyman_2s_wl3_8pi (void
);
FIXME: Cite source.
Returns
Cubic power of HeI Lyman 2s wave length divided by (8 * pi).
ncm_c_HeI_Lyman_2p_wl3_8pi ()
gdouble
ncm_c_HeI_Lyman_2p_wl3_8pi (void
);
FIXME: Cite source.
Returns
Cubic power of HeI Lyman 2p wave length divided by (8 * pi).
ncm_c_H_reduced_mass ()
gdouble
ncm_c_H_reduced_mass (void
);
FIXME: Cite source.
Returns
Hydrogen reduced mass.
ncm_c_H_reduced_energy ()
gdouble
ncm_c_H_reduced_energy (void
);
FIXME: Cite source.
Returns
Hydrogen reduced energy.
ncm_c_H_bind ()
gdouble
ncm_c_H_bind (const gdouble n
,
const gdouble j
);
Returns
Hydrogen binding energy.
ncm_c_H_bind_1s ()
gdouble
ncm_c_H_bind_1s (void
);
FIXME: Cite source.
Returns
Hydrogen 1s binding energy.
ncm_c_H_bind_2s ()
gdouble
ncm_c_H_bind_2s (void
);
FIXME: Cite source.
Returns
Hydrogen 2s binding energy.
ncm_c_H_bind_2p ()
gdouble
ncm_c_H_bind_2p (void
);
FIXME: Cite source.
Returns
Hydrogen 2p binding energy.
ncm_c_H_Lyman_series ()
gdouble
ncm_c_H_Lyman_series (const gdouble n
,
const gdouble j
);
Energy difference between levels 1s and n,j.
FIXME: Cite source.
Returns
Hydrogen Lyman series.
ncm_c_H_Lyman_2s ()
gdouble
ncm_c_H_Lyman_2s (void
);
FIXME: Cite source.
Returns
Energy difference between levels 1s and 2s.
ncm_c_H_Lyman_2p ()
gdouble
ncm_c_H_Lyman_2p (void
);
FIXME: Cite source.
Returns
Energy difference between levels 1s and 2p.
ncm_c_H_Lyman_series_wl ()
gdouble
ncm_c_H_Lyman_series_wl (const gdouble n
,
const gdouble j
);
FIXME: Cite source.
Returns
Wavelenght relative to the energy difference between levels 1s and n,j.
ncm_c_H_Lyman_2s_wl ()
gdouble
ncm_c_H_Lyman_2s_wl (void
);
FIXME: Cite source.
Returns
Wavelenght relative to the energy difference between levels 1s and 2s.
ncm_c_H_Lyman_2p_wl ()
gdouble
ncm_c_H_Lyman_2p_wl (void
);
FIXME: Cite source.
Returns
Wavelenght relative to the energy difference between levels 1s and 2s.
ncm_c_H_Lyman_2s_wl3_8pi ()
gdouble
ncm_c_H_Lyman_2s_wl3_8pi (void
);
FIXME: Cite source.
Returns
Cubic power of the Wavelenght relative to the energy difference between levels 1s and 2s divided by (8*pi).
ncm_c_H_Lyman_2p_wl3_8pi ()
gdouble
ncm_c_H_Lyman_2p_wl3_8pi (void
);
FIXME: Cite source.
Returns
Cubic power of the wavelenght relative to the energy difference between levels 1s and 2p divided by (8*pi).
ncm_c_thermal_wl_e ()
gdouble
ncm_c_thermal_wl_e (void
);
FIXME: Cite source.
Returns
Thermal electron wavelenght.
ncm_c_thermal_wl_p ()
gdouble
ncm_c_thermal_wl_p (void
);
FIXME: Cite source.
Returns
Thermal proton wavelenght.
ncm_c_thermal_wl_n ()
gdouble
ncm_c_thermal_wl_n (void
);
FIXME: Cite source.
Returns
Thermal neutron wavelenght.
ncm_c_thermal_wn_e ()
gdouble
ncm_c_thermal_wn_e (void
);
FIXME: Cite source.
Returns
Thermal eletron wavenumber.
ncm_c_thermal_wn_p ()
gdouble
ncm_c_thermal_wn_p (void
);
FIXME: Cite source.
Returns
Thermal proton wavenumber.
ncm_c_thermal_wn_n ()
gdouble
ncm_c_thermal_wn_n (void
);
FIXME: Cite source.
Returns
Thermal neutron wavenumber.
ncm_c_boltzmann_factor_H_1s ()
gdouble
ncm_c_boltzmann_factor_H_1s (const gdouble T
);
FIXME: Cite source.
Returns
Boltzmann factor for Hydrogen 1s level.
ncm_c_boltzmann_factor_H_2s ()
gdouble
ncm_c_boltzmann_factor_H_2s (const gdouble T
);
FIXME: Cite source.
Returns
Boltzmann factor for Hydrogen 2s level.
ncm_c_boltzmann_factor_H_2p ()
gdouble
ncm_c_boltzmann_factor_H_2p (const gdouble T
);
FIXME: Cite source.
Returns
Boltzmann factor for Hydrogen 2p level.
ncm_c_boltzmann_factor_HeI_1s ()
gdouble
ncm_c_boltzmann_factor_HeI_1s (const gdouble T
);
FIXME: Cite source.
Returns
Boltzmann factor for HeI 1s level.
ncm_c_boltzmann_factor_HeI_2s ()
gdouble
ncm_c_boltzmann_factor_HeI_2s (const gdouble T
);
FIXME: Cite source.
Returns
Boltzmann factor for HeI 2s level.
ncm_c_boltzmann_factor_HeI_2p ()
gdouble
ncm_c_boltzmann_factor_HeI_2p (const gdouble T
);
FIXME: Cite source.
Returns
Boltzmann factor for HeI 2p level.
ncm_c_AU ()
gdouble
ncm_c_AU (void
);
Returns
Astronomical unit (http://ssd.jpl.nasa.gov/?constants).
ncm_c_pc ()
gdouble
ncm_c_pc (void
);
\begin{equation}
1 \text{pc} = 3.085678 \times 10^{16} \, \text{m}
\end{equation}
Returns
Parsec unit 1 AU / tan (1 arcsec) - Copied from CAMB/constants.f90 to facilitate comparison.
ncm_c_mass_solar ()
gdouble
ncm_c_mass_solar (void
);
\begin{equation}
1 M_\odot = 1.98892 \times 10^{30} \, \text{kg}
\end{equation}
ncm_c_stats_1sigma ()
long double
ncm_c_stats_1sigma (void
);
The integral of a Gaussian distribution with mean $\mu$
and standard deviation $\sigma$ in $(\mu - 1 \sigma, \mu + 1 \sigma)$.
Returns
$P (\mu - 1 \sigma, \mu + 1 \sigma)$
ncm_c_stats_2sigma ()
long double
ncm_c_stats_2sigma (void
);
The integral of a Gaussian distribution with mean $\mu$
and standard deviation $\sigma$ in $(\mu - 2 \sigma, \mu + 2 \sigma)$.
Returns
$P (\mu - 2 \sigma, \mu + 2 \sigma)$
ncm_c_stats_3sigma ()
long double
ncm_c_stats_3sigma (void
);
The integral of a Gaussian distribution with mean $\mu$
and standard deviation sigma in $(\mu - 3 \sigma, \mu + 3 \sigma)$.
Returns
$P (\mu - 3 \sigma, \mu + 3 \sigma)$
ncm_c_wmap3_cmb_z ()
gdouble
ncm_c_wmap3_cmb_z (void
);
Returns
Wmap3 last scatering redshift.
ncm_c_wmap3_cmb_R ()
gdouble
ncm_c_wmap3_cmb_R (void
);
Returns
Wmap3 last scatering shift parameter.
ncm_c_wmap3_cmb_sigma_R ()
gdouble
ncm_c_wmap3_cmb_sigma_R (void
);
Returns
Wmap3 last scatering shift parameter standard deviation.
ncm_c_wmap5_cmb_z ()
gdouble
ncm_c_wmap5_cmb_z (void
);
Returns
Wmap5 last scatering redshift.
ncm_c_wmap5_cmb_R ()
gdouble
ncm_c_wmap5_cmb_R (void
);
Returns
Wmap5 last scatering shift parameter.
ncm_c_wmap5_cmb_sigma_R ()
gdouble
ncm_c_wmap5_cmb_sigma_R (void
);
Returns
Wmap5 last scatering shift parameter standard deviation.
ncm_c_wmap7_cmb_z ()
gdouble
ncm_c_wmap7_cmb_z (void
);
ncm_c_wmap7_cmb_R ()
gdouble
ncm_c_wmap7_cmb_R (void
);
ncm_c_wmap7_cmb_sigma_R ()
gdouble
ncm_c_wmap7_cmb_sigma_R (void
);
ncm_c_wmap5_coadded_I_K ()
gdouble
ncm_c_wmap5_coadded_I_K (void
);
ncm_c_wmap5_coadded_I_Ka ()
gdouble
ncm_c_wmap5_coadded_I_Ka (void
);
ncm_c_wmap5_coadded_I_Q ()
gdouble
ncm_c_wmap5_coadded_I_Q (void
);
ncm_c_wmap5_coadded_I_V ()
gdouble
ncm_c_wmap5_coadded_I_V (void
);
ncm_c_wmap5_coadded_I_W ()
gdouble
ncm_c_wmap5_coadded_I_W (void
);
ncm_c_hubble_cte_wmap ()
gdouble
ncm_c_hubble_cte_wmap (void
);
FIXME
ncm_c_hubble_cte_hst ()
gdouble
ncm_c_hubble_cte_hst (void
);
FIXME
ncm_c_hubble_cte_msa ()
gdouble
ncm_c_hubble_cte_msa (void
);
FIXME
ncm_c_neutrino_n_eff ()
gdouble
ncm_c_neutrino_n_eff (void
);
FIXME
ncm_c_prim_He_Yp ()
gdouble
ncm_c_prim_He_Yp (void
);
The primoridial helium mass fraction
$$Y_p = \frac{m_\text{He}n_\text{He}}
{m_\text{He}n_\text{He}+m_\text{H}n_\text{H}},$$ where $m_\text{He}$,
n_\text{He}, m_\text{H} and m_\text{H} are respectively helium mass and
number density and hydrogen mass and number density.
Returns
The primordial helium mass abundance.
ncm_c_prim_H_Yp ()
gdouble
ncm_c_prim_H_Yp (void
);
The primordial hydrogen mass fraction $$Y_{\text{H}p} = 1 - Y_p,$$
where $Y_p$ is the helium mass fraction, see ncm_c_prim_He_Yp()
.
Returns
The primordial hydrogen mass abundance.
ncm_c_prim_XHe ()
gdouble
ncm_c_prim_XHe (void
);
The primordial helium to hydrogen ratio $$X_\text{He} =
\frac{n_\text{He}}{n_\text{H}} = \frac{m_\text{H}}{m_\text{He}}
\frac{Y_p}{Y_{\text{H}p}},$$ see ncm_c_prim_H_Yp()
and ncm_c_prim_He_Yp()
.
Returns
The primordial helium to hydrogen ratio.
ncm_c_hubble_radius ()
gdouble
ncm_c_hubble_radius (void
);
FIXME
ncm_c_hubble_radius_planck ()
gdouble
ncm_c_hubble_radius_planck (void
);
FIXME
ncm_c_crit_density ()
gdouble
ncm_c_crit_density (void
);
The critical density is defined as
\begin{equation}
\rho_{crit} = \frac{3 c^2 H_0^2}{8\pi G},
\end{equation}
where $G$ is the gravitational constant (ncm_c_G()
), $c$ is the speed of light
(ncm_c_c()
) and $H_0$ is the Hubble parameter,
$$H_0 = 100 \times h \, \frac{\text{km}}{\text{s} \, \text{Mpc}}.$$
Returns
Critical density, $$\left[\rho^h_{crit}\right] = \frac{\left[\rho^h_{crit}\right]}{h^2} = \frac{\text{kg}}{\text{m}^3} \frac{\text{m}^2}{\text{s}^2}.$$
ncm_c_crit_mass_density ()
gdouble
ncm_c_crit_mass_density (void
);
The critical mass density is defined as
\begin{equation}
\rho_{crit} = \frac{3 H_0^2}{8\pi G},
\end{equation}
where $G$ is the gravitational constant (ncm_c_G()
), $c$ is the speed of light
(ncm_c_c()
) and $H_0$ is the Hubble parameter,
$$H_0 = 100 \times h \, \frac{\text{km}}{\text{s} \, \text{Mpc}}.$$
Returns
Critical mass density, $$\left[\rho_{crit}\right] = \frac{\text{kg}}{\text{m}^3}.$$
ncm_c_crit_mass_density_solar_Mpc ()
gdouble
ncm_c_crit_mass_density_solar_Mpc (void
);
This function computes the critical mass density in units of solar mass $M_\odot$ and Mpc, i.e.,
\begin{equation}
\frac{\rho_{crit}}{1.98892 \times 10^{30}} \left(10^6 \times 3.085678 \times 10^{16} \right)^3.
\end{equation}
Returns
Critical mass density in $M_\odot$ and Mpc units.
ncm_c_crit_number_density_p ()
gdouble
ncm_c_crit_number_density_p (void
);
FIXME
Returns
Critical proton number density in ... units.
ncm_c_crit_number_density_n ()
gdouble
ncm_c_crit_number_density_n (void
);
FIXME
Returns
Critical neutron number density in ... units.
ncm_c_blackbody_energy_density ()
gdouble
ncm_c_blackbody_energy_density (void
);
FIXME
Returns
Blackbody energy density in ... units.
ncm_c_radiation_temp_to_h2omega_r ()
gdouble
ncm_c_radiation_temp_to_h2omega_r (const gdouble T
);
ncm_c_radiation_h2Omega_r_to_temp ()
gdouble
ncm_c_radiation_h2Omega_r_to_temp (const gdouble omr
);
FIXME