Primordial gravitational waves, precisely: The role of thermodynamics in
  the Standard Model
  In this paper, we revisit the estimation of the spectrum of primordial
gravitational waves originated from inflation, particularly focusing on the
effect of thermodynamics in the Standard Model of particle physics. By
collecting recent results of perturbative and non-perturbative analysis of
thermodynamic quantities in the Standard Model, we obtain the effective degrees
of freedom including the corrections due to non-trivial interaction properties
of particles in the Standard Model for a wide temperature interval. The impact
of such corrections on the spectrum of primordial gravitational waves as well
as the damping effect due to free-streaming particles is investigated by
numerically solving the evolution equation of tensor perturbations in the
expanding universe. It is shown that the reevaluation of the effects of
free-streaming photons and neutrinos gives rise to some additional damping
features overlooked in previous studies. We also observe that the continuous
nature of the QCD crossover results in a smooth spectrum for modes that reenter
the horizon at around the epoch of the QCD phase transition. Furthermore, we
explicitly show that the values of the effective degrees of freedom remain
smaller than the commonly used value 106.75 even at temperature much higher
than the critical temperature of the electroweak crossover, and that the
amplitude of primordial gravitational waves at a frequency range relevant to
direct detection experiments becomes $\mathcal{O}(1)\,\%$ larger than previous
estimates that do not include such corrections. This effect can be relevant to
future high-sensitivity gravitational wave experiments such as ultimate DECIGO.
Our results on the temperature evolution of the effective degrees of freedom
are made available as tabulated data and fitting functions, which can also be
used in the analysis of other cosmological relics.
