$SL(2,\mathbb{Z})$ Cosmological Attractors

Abstract

We study cosmological theory where the kinetic term and potential have $SL(2,\mathbb{Z})$ 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 $SL(2,\mathbb{Z})$ potentials, the theory exhibits an $\hat{I}\pm$-attractor behavior: its cosmological predictions are stable with respect to significant modifications of the $SL(2,\mathbb{Z})$ invariant potentials. We present a supersymmetric version of this theory in the framework of $\overline{D3}$ induced geometric inflation. The choice of $\hat{I}\pm$ is determined by underlying string compactification. For example, in a CY compactification with $T^2$, one has $3\hat{I}\pm =1$, the lowest discrete Poincaré disk target for LiteBIRD

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