Disformal Inflation

We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms. This field drives inflation solely by its derivatives, which couple to the matter only through the combination $\bar g_{\mu\nu} = g_{\mu\nu} - \frac{1}{m^4} \partial_\mu \phi \partial_\nu \phi$. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as $\dot \phi^2 > m^4$, and terminates gracefully once the scalar field kinetic energy drops below $m^4$. The total number of e-folds is given by the initial inflaton energy $\dot \phi_0^2$ as ${\cal N} \simeq \frac13 \ln(\frac{\dot \phi_0}{m^2})$. The field $\phi$ can neither efficiently reheat the universe nor produce the primordial density fluctuations. However this could be remedied by invoking the curvaton mechanism. If inflation starts when $\dot \phi^2_0 \sim M^4_P$, and $m \sim m_{EW} \sim TeV$, the number of e-folds is ${\cal N} \sim 25$. Because the scale of inflation is low, this is sufficient to solve the horizon problem if the reheating temperature is $T_{RH} \ga MeV$. In this instance, the leading order coupling of $\phi$ to matter via a dimension-8 operator $\frac{1}{m^4}\partial_\mu \phi \partial_\nu \phi ~ T^{\mu\nu}$ would lead to fermion-antifermion annihilation channels $f\bar f \to \phi \phi$ accessible to the LHC, while yielding very weak corrections to the Newtonian potential and to supernova cooling rates, that are completely within experimental limits.