  The large-scale structure of the universe suggests that the physics
underlying its early evolution is scale-free. This was the historic motivation
for the Harrison-Zel'dovich-Peebles spectrum and for inflation. Based on a
hydrodynamical approach, we identify scale-free forms for the background
equation-of-state for both inflationary and cyclic scenarios and use these
forms to derive predictions for the spectral tilt and tensor-to-scalar ratio of
primordial density perturbations. For the case of inflation, we find three
classes of scale-free models with distinct predictions. Including all classes,
we show that scale-free inflation predicts tensor-to-scalar ratio $r >
10^{-4}$. We show that the observationally favored class is theoretically
disfavored because it suffers from an initial conditions problem and the
hydrodynamical form of an unlikeliness problem similar to that identified
recently for certain inflaton potentials. We contrast these results with those
for scale-free cyclic models.
