Kinematic constraints to the key inflationary observables

The observables $T/S$ and $n-1$ are key to testing and understanding inflation. $(T,$ S, and $n-1$ respectively quantify the gravity-wave and density-perturbation contributions to CMB anisotropy and the deviation of the density perturbations from the scale-invariant form.) Absent a standard model, there is no definite prediction for, or relation between, $T/S$ and $n-1.$ By reformulating the equations for slow-roll inflation, we show that in the $T/S-\left(n-1\right)$ plane there are excluded regions, regions in which the density perturbations are not well approximated by a power law, and regions in which models with a “featureless” potential must lie.