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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 $\bar g_{μν} = g_{μν} - \frac{1}{m^4} \partial_μϕ\partial_νϕ$. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as $\dot ϕ^2 > m^4$, 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 $\dot ϕ_0^2$ as ${\cal N} \simeq \frac13 \ln(\frac{\dot ϕ_0}{m^2})$. The field $ϕ$ 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 $\dot ϕ^2_0 \sim M^4_P$, 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 $ϕ$ to matter via a dimension-8 operator $\frac{1}{m^4}\partial_μϕ\partial_νϕ~ T^