Kinematic Constraints to the Key Inflationary Observables

The observables $T\mathrm{/}S$ 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, $T\mathrm{/}S$ and $n-1$. By reformulating the equations governing inflation we show that models generally predict $T\mathrm{/}S\approx -5(n-1)$ or 0, and in particular, if $n>0.85$, $T\mathrm{/}S$ is expected to be $>{10}^{-3}$.