SL(2,Z) Cosmological Attractors

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, a saddle point at τ=i, and a minimum at τ=e2π i 3. Due to the underlying hyperbolic geometry, the theory exhibits an α-attractor behavior: its cosmological predictions are stable with respect to certain modifications of the SL(2,Z) invariant potentials. We present a supersymmetric version of this theory in the framework of D3̄ induced geometric inflation. The choice of α is determined by underlying string compactification. For example, in a CY compactification with T², one has 3α=1, the lowest discrete Poincar\'e disk target for LiteBIRD.