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Using the quantum chromodynamics (QCD) equation of state (EoS) from latticecalculations we investigate effects from QCD on primordial gravitational waves(PGWs) produced during the inflationary era. We also consider different casesfor vanishing and nonvanishing lepton asymmetry where the latter one isconstrained by cosmic microwave background experiments. Our results show thatthere is up to a few percent deviation in the predicted gravitational wavebackground in the frequency range around the QCD transition ($10^{-10}-10^{-7}$~Hz) for different lattice QCD EoSs, or at larger frequencies fornonvanishing lepton asymmetry using perturbative QCD. Future gravitational waveexperiments with high enough sensitivity in the measurement of the amplitude ofPGWs like SKA, EPTA, DECIGO and LISA can probe these differences and can shedlight on the real nature of the cosmic QCD transition and the existence of anonvanishing lepton asymmetry in the early universe.

Effects of the QCD Equation of State and Lepton Asymmetry on Primordial Gravitational Waves