SL(2,ℤ) cosmological attractors

Abstract We study cosmological theory where the kinetic term and potential have SL(2,ℤ) symmetry. Potentials have a plateau at large values of the inflaton field, where the axion forms a flat direction. Due to the underlying hyperbolic geometry and special features of SL(2,ℤ) potentials, the theory exhibits an α-attractor behavior: its cosmological predictions are stable with respect to significant modifications of the SL(2,ℤ) invariant potentials. We present a supersymmetric version of this theory in the framework of D 3 induced geometric inflation. The choice of α is determined by underlying string compactification. For example, in a CY compactification with T 2 , one has 3 α = 1, the lowest discrete Poincaré disk target for LiteBIRD.