CAMB: scale factor and adotrad

[Dahee Lee]

Hi.
I want to know reference about exact relation between scale factor and conformal time.
In subroutine initial, a=tau*adotrad*(1+omtau/4).
In CAMB note 12p, regular initial condition series solution S.
In this solution, there is a sentense ‘Following [20]’, but [20] is not found.
What is ‘adotrad’ in module.f90 meaning?
I think ‘adotrad’ is H0*dsqrt(omega_R0), but it’s different value from adotrad.
And, does anyone know reference for scale factor S?

Any help would be appreciated.

[Antony Lewis]

These are just series expansions, you can see some maple code at https://camb.info/maple/. adotrad should indeed just be da/dtau_{tau=0} where tau is conformal time, in Mpc units. You can get it from Omega_R0 as long as you define the latter to include photons and all neutrinos as though they were massless (since they will be relativistic at early times).