Precise WIMP Dark Matter Abundance and Standard Model Thermodynamics

We are now living in the era of precision cosmology. The relic abundance of dark matter (DM) is now observationally well-determined, and its error is smaller than O(1)%. This means that the same or much higher precision is required when we make theoretical predictions.
Weakly Interacting Massive Particle (WIMP) has long been the leading candidate for DM because of its beautiful mechanism to predict the observed relic abundance. WIMP is in the same thermal bath as the Standard Model particles in the beginning. At a certain point when the temperature of the Universe is smaller than the DM mass, it decouples to fix its number density. The yield of the DM is determined by its annihilation cross-section to the Standard Model sector.
It seems that there is no ambiguity in the calculation of this process at first: the cross-section is purely theoretical and all the remainings are described in the Standard Model physics. However, the source of the uncertainty does remain in the Standard Model sector. The dilution of the number density of DM particle depends on the expansion rate of the Universe, which is determined by the Standard Model particles. The effective degree of freedom (d.o.f) of the relativistic species controls this factor. We have to deal with the non-equilibrium dynamics to precisely describe the time-evolution of the d.o.f, in which we need numerical approaches.
In this talk, he introduced his work to update these calculations. By implementing the latest findings in the non-equilibrium dynamics in i) the neutrino decoupling, ii) the QCD phase transition, iii) the electroweak phase transition, and iv) the perturbative calculations, they found that the final d.o.f is smaller than the previous estimate in more than 1%. This is larger than the level of precision in observations. It is also important that the uncertainty is quantified by them.
Another good news is that he makes the calculated d.o.f with its error publically available. With these updates, we now correctly know the points to probe DM!