Disformal inflation

AbstractWe 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 ḡμν=gμν−1m4∂μφ∂νφ. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as φ̇2>m4, and terminates gracefully once the scalar field kinetic energy drops below m4. The total number of e-folds is given by the initial inflaton energy φ̇02 as N≃13ln(φ̇0m2). 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 φ̇20∼M4P, and m∼mEW∼TeV, the number of e-folds is N∼25. Because the scale of inflation is low, this is sufficient to solve the horizon problem if the reheating temperature is TRH≳MeV. In this instance, the leading order coupling of φ to matter via a dimension-8 operator 1m4∂μφ∂νφTμν would lead to fermion–antifermion annihilation channels ff̄→φφ accessible to the LHC, while yielding very weak corrections to the Newtonian potential and to supernova cooling rates, that are completely within experimental limits