Inflationary quasiscale-invariant attractors

In a series of recent papers Kallosh, Linde, and collaborators provide a unified description of single-field inflation with several types of potentials ranging from power law to supergravity, in terms of just one parameter α. These so-called α attractors predict a spectral index ns and a tensor-to-scalar ratio r, which are fully compatible with the latest Planck data. The only common feature of all α attractors is a noncanonical kinetic term with a pole, and a potential analytic around the pole. In this paper, starting from the same Einstein frame with a noncanonical scalar kinetic energy, we explore the case of nonanalytic potentials. We find the functional form that corresponds to quasiscale-invariant gravitational models in the Jordan frame characterized by a universal relation between r and ns that fits the observational data but is clearly distinct from the one of the α attractors. It is known that the breaking of the exact classical scale invariance in the Jordan frame can be attributed to one-loop corrections. Therefore we conclude that there exists a class of nonanalytic potentials in the noncanonical Einstein frame that is physically equivalent to a class of models in the Jordan frame, with scale invariance softly broken by one-loop quantum corrections.