NumCosmoDistance

Computes the angular diameter distance from the comoving distance $D_c$, curvature parameter $\Omega_k$, and redshift $z$. This is the _from_Dc version that works directly with distances rather than cosmology objects.

Atomically decrements the reference count of dist by one. If the reference count drops to 0, all memory allocated by dist is released. Set pointer to NULL.

Computes the luminosity distance from the comoving distance $D_c$, curvature parameter $\Omega_k$, and redshift $z$. This is the _from_Dc version that works directly with distances rather than cosmology objects.

Computes the integral of the squared transverse comoving distance, $$ V(D_c, \Omega_k) = \int_0^{D_c} \left[\frac{\mathrm{sinn}(\sqrt{|\Omega_k|}\chi’)}{\sqrt{|\Omega_k|}}\right]^2 d\chi’, $$ where $\mathrm{sinn}(x) = \sinh(x)$ for $\Omega_k > 0$ (open universe), $\mathrm{sinn}(x) = \sin(x)$ for $\Omega_k < 0$ (closed universe), and $\mathrm{sinn}(x) = x$ for $\Omega_k = 0$ (flat universe).

Computes the transverse comoving distance from the comoving distance $D_c$ and curvature parameter $\Omega_k$. This is the _from_Dc version that works directly with distances rather than redshifts.

Computes the ratio between the angular-diameter distance and the sound horizon at the drag epoch, $$\frac{D_A(z)}{c \, r_s(z_d)}.$$.

Computes the ratio between the Hubble (distance) radius and the sound horizon at the drag epoch, $$\frac{R_H}{r_s(z_d)} = \frac{c}{H(z) r_d}.$$.

Computes the ratio between the transverse distance and the sound horizon at the drag epoch, $$\frac{D_t(z)}{c \, r_s(z_d)}.$$.

Compute the acoustic scale $l_A (z_\star)$ at $z_\star$ [nc_distance_decoupling_redshift()], \begin{equation} l_A(z_\star) = \pi \frac{D_t (z_\star)}{r_s (z_\star)}, \end{equation} where $D_t(z_\star)$ is the comoving transverse distance [nc_distance_transverse()] and $r_s(z_\star)$ is the sound horizon [nc_distance_sound_horizon()] both computed at $z_\star$.

Compute the angular diameter $D_A(z)$, defined in Eq. $\eqref{eq:def:Dl}$.

Compute the angular diameter distance $D_A(z)$ for each redshift in z.

We define the angular diameter curvature scale $D_a(z_\star)$ as $$D_a(z_\star) = \frac{E(z_\star)}{1 + z_\star} D_t(z_\star),$$ where $z_\star$ is the decoupling redshift, given by [nc_distance_decoupling_redshift()], $E(z_\star)$ is the normalized Hubble function [Eq. $\eqref{eq:def:Ez}$] and $D_t(z_\star)$ is the transverse comoving distance [Eq. $\eqref{eq:def:Dt}$] both computed at $z_\star$.

Compute the angular diameter distance $D_A(z)$ for each redshift in z.

Compute the angular diameter $D_A(z_1, z_2)$, defined in Eq. $\eqref{eq:def:DA12}$.

This function returns the BAO $A$ parameter. It is defined as $$ A \equiv D_V (z) \frac{\sqrt{\Omega_{m0} H_0^2}}{z c},$$ where $\Omega_{m0}$ is the matter density parameter [nc_hicosmo_Omega_m0()], $c$ is the speed of light [ncm_c_c()], $H_0$ is the Hubble parameter [nc_hicosmo_H0()] and $D_V(z)$ is the dilation scale [nc_distance_dilation_scale()]. See Section 4.5 from [Eisenstein et al. (2005)][XEisenstein2005] [arXiv].

This function computes $r(z_d) / D_V(z)$, where $r(z_d)$ is given by nc_distance_r_zd() and $D_V(z)$ by nc_distance_dilation_scale(). For more information see [Percival et al. (2007)][XPercival2007] [arXiv].

Calculate the comoving distance $D_c (z)$ as defined in Eq. $\eqref{eq:def:Dc}$.

Compute the comoving distance $D_c(z)$ for each redshift in z.

Compute the comoving distance $D_c(z)$ [Eq. \eqref{eq:def:Dc}] at the decoupling redshift $z_\star$ [nc_distance_decoupling_redshift()].

Compute the comoving distance $D_c(z)$ for each redshift in z.

This function computes the comoving volume element per unit solid angle $d\Omega$ given z, namely, $$\frac{\mathrm{d}^2V}{\mathrm{d}z\mathrm{d}\Omega} = \frac{D_t^2(z)}{E(z)} = \frac{(1 + z)^2 D_a^2(z)}{E(z)},$$ where $E(z)$ is the normalized Hubble function and $D_t$ is the transverse comoving distance (and $D_a$ is the angular diameter distance).

Computes the comoving volume radial integral from redshift $z$ using the comoving distance and spatial curvature from the cosmology.

Compute the comoving distance between $z_1$ and $z_2$, $D_c (z_1, z_2)$.

Computes the comoving distance from z to infinity.

Enable/Disable the computation of $z(\xi)$.

This function computes the conformal look-back time $\eta_{lb}(z)$. Within the chosen units it becomes the same as the comoving distance [nc_distance_comoving()], given in Eq. $\eqref{eq:def:dc}$.

This function computes the cosmological conformal time $\eta(z)$ defined as $$ \eta(z) = \int_z^\infty \frac{dz}{E(z)} \, . $$.

This function computes the cosmological time, $t(z)$, defined as \begin{equation} t(z) = \int_z^{\infty} \frac{dx}{(1+x)E(x)}. \end{equation}.

The decoupling redshift $z_\star$ corresponds to the epoch of the last scattering surface of the cosmic microwave background photons.

The dilation scale is the spherically averaged distance for perturbations along and orthogonal to the line of sight, $$D_V(z) = \left[D_{H_0}^2 D_t(z)^2 \frac{cz}{H(z)} \right]^{1/3},$$ where $D_t(z)$ is the transverse comoving distance [Eq. $\eqref{eq:def:Dt}$], $c$ is the speed of light [ncm_c_c()] and $H(z)$ is the Hubble function [nc_hicosmo_H()]. See [Eisenstein et al. (2005)][XEisenstein2005] [arXiv].

Compute the distance modulus $\delta\mu(z)$ defined in Eq. $\eqref{eq:def:dmu}$.

Compute the distance modulus $\delta\mu(z)$ for each redshift in z.

Calculate the distance modulus [Eq. $\eqref{eq:def:dmu}$] using the frame corrected luminosity distance [nc_distance_luminosity_hef()].

Compute the angular diameter distance $D_A(z)$ for each redshift in z.

Drag redshift is the epoch at which baryons were released from photons.

Calculate the sound horizon [nc_distance_sound_horizon()] derivative with respect to $z$, $$\frac{d r_s(z)}{dz} = - \frac{c_s(z)}{E(z)}\, ,$$ where $c_s = \sqrt{c^{b\gamma 2}_s(z)}$ is the baryon-photon plasma speed of sound (see nc_hicosmo_bgp_cs2() for more details) and $E(z)$ is the normalized Hubble function [nc_hicosmo_E()].

Compute the derivative of $D_t(z)$ with respect to $z$ defined in Eq. $\eqref{eq:def:Dt}$.

Atomically decrements the reference count of dist by one. If the reference count drops to 0, all memory allocated by dist is released.

Calculate the curvature scale today as defined in Eq $\eqref{eq:def:DH}$ in units of megaparsec (Mpc) [ncm_c_Mpc()].

Computes the inverse of $\xi(z)$.

This functions computes the look-back time, $t_{lb}(z)$, defined as.

Compute the luminosity distance $D_l(z)$ defined in Eq. $\eqref{eq:def:Dl}$.

Compute the luminosity distance $D_L(z)$ for each redshift in z.

Calculate the luminosity distance $D_l$ corrected to our local frame.

Compute the luminosity distance $D_t(z)$ for each redshift in z.

This function prepares the object dist using cosmo, such that all the available distances functions can be evaluated, e.g. nc_distance_comoving().

This function prepares the object dist using cosmo if it was changed since last preparation.

This function computes the sound horizon [nc_distance_sound_horizon ()] at the drag redshift [nc_distance_drag_redshift()].

Similar as nc_distance_r_zd(), but now in units of $\mathrm{Mpc}$, i.e., $ R_H \times r(z_d)$.

Increases the reference count of dist atomically.

Requires the final redshift of at least zf.

This function sets recomb into dist.

The shift parameter $R(z)$ is defined as \begin{equation} R(z) = \frac{\sqrt{\Omega_{m0} H_0^2}}{c} (1 + z) D_A(z) = \sqrt{\Omega_{m0}} D_t(z), \end{equation} where $\Omega_{m0}$ is the matter density paremeter [nc_hicosmo_Omega_m0()], $D_A(z) = D_{H_0} D_t(z) / (1 + z)$ is the angular diameter distance and $D_t(z)$ is the transverse comoving distance [Eq. $\eqref{eq:def:Dt}$].

Compute the shift parameter $R(z)$ [nc_distance_shift_parameter()] at the decoupling redshift $z_\star$ [nc_distance_decoupling_redshift()].

Computes the critical surface density, \begin{equation}\label{eq:def:SigmaC} \Sigma_c = \frac{c^2}{4\pi G} \frac{D_s}{D_l D_{ls}}, \end{equation} where $c^2$ is the speed of light squared [ncm_c_c2 ()], $G$ is the gravitational constant in units of $m^3/s^2 M_\odot^{-1}$ [ncm_c_G_mass_solar()], $D_s$ ($D_l$) is the angular diameter distance from the observer to the source (lens), and $D_{ls}$ is the angular diameter distance between the lens and the source.

Computes the critical surface density, \begin{equation}\label{eq:def:SigmaC} \Sigma_c = \frac{c^2}{4\pi G} \frac{D_\infty}{D_l D_{l\infty}}, \end{equation} where $c^2$ is the speed of light squared [ncm_c_c2 ()], $G$ is the gravitational constant in units of $m^3/s^2 M_\odot^{-1}$ [ncm_c_G_mass_solar()], $D_\infty$ ($D_l$) is the angular diameter distance from the observer to the source at infinite redshift (lens), and $D_{l\infty}$ is the angular diameter the lens and the source.

Compute the sound horizon $r_s$, \begin{equation} \theta_s (z) = \int_{z}^\infty \frac{c_s(z^\prime)}{E(z^\prime)} dz^\prime, \quad r_s (z) = \frac{\mathrm{sinn}\left(\sqrt{\Omega_{k0}}\theta_s\right)}{\sqrt{\Omega_{k0}}}, \end{equation} where $c_s = \sqrt{c^{b\gamma 2}_s(z)}$ is the baryon-photon plasma speed of sound (see nc_hicosmo_bgp_cs2() for more details) and $E(z)$ is the normalized Hubble function [nc_hicosmo_E()].

Compute the $100\theta_\mathrm{CMB}$ angle at $z_\star$ [nc_distance_decoupling_redshift()], \begin{equation} 100\theta_\mathrm{CMB} = 100 \times \frac{r_s (z_\star)}{D_t (z_\star)}, \end{equation} where $D_t(z_\star)$ is the comoving transverse distance [nc_distance_transverse()] and $r_s(z_\star)$ is the sound horizon [nc_distance_sound_horizon()] both both computed at $z_\star$.

Compute the transverse comoving distance $D_t (z)$ defined in Eq. $\eqref{eq:def:Dt}$.

Compute the transverse comoving distance $D_t(z)$ for each redshift in z.

Compute the transverse distance $D_t(z)$ for each redshift in z.

Compute the transverse comoving distance between $z_1$ and $z_2$, $D_t (z1, z2)$ defined in Eq. $\eqref{eq:def:Dt12}$.

Compute the transverse comoving distance $D_t (z)$ (defined in Eq. $\eqref{eq:def:Dt}$) but from z to infinity.