Tabulated data of the effective degrees of freedom and the transfer function esitimated in this paper are distributed.
You can get the data of the effective degrees of freedom here.
We also provide a c++ code for the fitting functions.
The data of the tansfer function are here.
If you find any problems or request additional data, please contact me (satoshi.shirai_at_ipmu.jp)
Equation of State
The effective degrees of freedom are defined as:
\[
g_{*\rho}(T) \equiv \frac{\rho(T)}{\left[\frac{\pi^2 T^4}{30}\right]},\quad g_{*s}(T) \equiv \frac{s(T)}{\left[\frac{2\pi^2 T^3}{45}\right]}.
\]
Transfer function
The tranfer function is defined as:
\[
T(k) \equiv \frac{1}{12a_0^2 H_0^2}\overline{\left[\chi'(\tau_0,k)\right]^2}h^2.
\]
Using this function, you can produce the spectrum of primordial GWs for a given primordial tensor power spectrum \(\mathcal{P}_T(k)\).
\[
\Omega_{\rm gw}h^2(k) = T(k)\mathcal{P}_T(k).
\]
