Relaxing the TCC bound on inflationary cosmology?

Abstract We demonstrate that the strict upper bounds on the energy scale of inflation and on the tensor-to-scalar ratio can be somewhat relaxed if we assume that – after an initial period of slow rolling when scales probed today in CMB experiments exit the Hubble radius – the equation of state of the background changes to correspond to an almost marginally accelerating universe. Constructing an actual model in which this happens appears, however, to be unnatural.