### redshift at the drag epoch

Posted:

**September 17 2020**According to Eq. 2 in Thepsuriya & Lewis JCAP 01 34 (2015)

the baryon drag optical depth is defined as

\tau_d \int_{\eta_0}^{\eta} d\eta' dtau/d\eta'/R

where dtau/d\eta= sigma_T n_p x_e a and R=\rho_b/rho_{\gamma}

where sigma_T is Thompson scattering cross section, x_e the fraction of free electros, n_p the number density of protons today and a the scale factor, rho_b is the baryon density and \rho_{gamma} the total radiation density

This quantity is caculated in the latest version of the fortran version of camb in the function ddragoptdepth_dz as

ddragoptdepth_dz = noreion_doptdepth_dz(this,z)/this%ThermoData%r_drag0/a

where

noreion_doptdepth_dz = this%CP%Recomb%x_e(a)*this%akthom*dtauda(this,a)

Here ThermoData%r_drag0*a =R akthom=sigma_T*n_e x_e=xe and dtauda= d\eta/da

and my question is if there is not a factor a missing from dtau/d\eta

the baryon drag optical depth is defined as

\tau_d \int_{\eta_0}^{\eta} d\eta' dtau/d\eta'/R

where dtau/d\eta= sigma_T n_p x_e a and R=\rho_b/rho_{\gamma}

where sigma_T is Thompson scattering cross section, x_e the fraction of free electros, n_p the number density of protons today and a the scale factor, rho_b is the baryon density and \rho_{gamma} the total radiation density

This quantity is caculated in the latest version of the fortran version of camb in the function ddragoptdepth_dz as

ddragoptdepth_dz = noreion_doptdepth_dz(this,z)/this%ThermoData%r_drag0/a

where

noreion_doptdepth_dz = this%CP%Recomb%x_e(a)*this%akthom*dtauda(this,a)

Here ThermoData%r_drag0*a =R akthom=sigma_T*n_e x_e=xe and dtauda= d\eta/da

and my question is if there is not a factor a missing from dtau/d\eta