Logarithmic Extensions to Inflation Universality Classes

The values of, and connection between, the cosmological observables of the primordial power spectrum tilt $n_s$ and the inflationary tensor to scalar ratio $r$ are key guideposts to the physics of inflation. Universality classes can be defined for the tilt from the scale free value proportional to $1/N$, where $N$ is the number of e-folds. We examine the consequences of a $\ln N$ next to leading order correction rather than an expansion in $1/N$, or introducing a new parameter. While nominally this can lower $r$ for some too-high $r$ simple inflation models (e.g. large field models), there is an interesting cancellation preventing such models from coming back into favor. On the other branch of the universality class, near Starobinsky inflation, $r$ can be raised, making it easier to detect.