Heavy-ion colliders have revealed the process of fast thermalization. This experimental breakthrough has led to new theoretical tools to study the thermalization process at both weak and strong coupling. We apply this to the reheating epoch of inflationary cosmology, and the formation of a cosmological quark gluon plasma (QGP). We compute the thermalization time of the QGP at reheating, and find it is determined by the energy scale of inflation and the shear viscosity to entropy ratio $eta/s$; or equivalently, the tensor-to-scalar ratio and the strong coupling constant at the epoch of thermalization. Thermalization is achieved near-instantaneously in low-scale inflation and in strongly coupled systems, and takes of order or less than a single e-fold of expansion for weakly-coupled systems or after high-scale inflation. We demonstrate that the predictions of inflation are robust to the physics of thermalization, and find a stochastic background of gravitational waves at frequencies accessible by interferometers, albeit with a small amplitude.
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