Cosmological attractors and asymptotic freedom of the inflaton field

We show that the inflaton coupling to all other fields is exponentially suppressed during inflation in the cosmological alpha-attractor models. In the context of supergravity, this feature is a consequence of the underlying hyperbolic geometry of the moduli space which has a flat direction corresponding to the inflaton field. A combination of these factors protects the asymptotic flatness of the inflaton potential.