Inflation with nondynamic distortion to leading order in slow roll

Abstract

We study inflation in metric-affine gravity. We write an action that contains all the second order algebraic distortion terms, and all first order distortion terms with a single covariant derivative, coupled to a scalar field. We include the Einstein--Hilbert term with nonminimal coupling, a scalar field potential, and impose projective invariance. The distortion equation of motion is algebraic by construction, and the distortion is integrated out analytically. This yields a kinetic term sourced entirely by distortion, with a kinetic coupling function determined by the 13 free coupling constants of the starting action. We compute inflationary observables for three model classes with a monomial distortion coupling. For a monomial potential, the spectral index and tensor-to-scalar ratio depend only on the ratio of the exponents, with the starting coupling constants dropping out entirely; however, this model lies outside the Planck + BK18 $2σ$ contours. For a potential of the $α$-attractor form, the observables are governed by a single parameter and approach the Starobinsky predictions as a limit. Including a nonminimal coupling to the Ricci scalar with a monomial potential can also yield an asymptotically flat effective potential with the same modified Starobinsky observables.