Scale independent $R^2$ inflation
  Weyl (scale) invariant theories of scalars and gravity can generate all mass
scales spontaneously. In this paper we study a particularly simple version --
scale invariant $R^2$ gravity -- and show that, during an inflationary period,
it leads to fluctuations which, for a particular parameter choice, are almost
indistinguishable from normal $R^2$ inflation. Current observations place tight
constraints on the primary coupling constant of this theory and predict a
tensor to scalar ratio, $0.0033 > r > 0.0026$, which is testable with the next
generation of cosmic microwave background experiments.
