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

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ID

oai:arXiv.org:2408.05203

Topic

High Energy Physics - Theory Astrophysics - Cosmology and Nonga... General Relativity and Quantum Cos... High Energy Physics - Phenomenolog...

Author

Kallosh, Renata Linde, Andrei

Year

2024

listing date

10/16/2024

Keywords

potentials $ $sl \mathbb{z}

Metrics

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 $\alpha$-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 $\alpha$ is determined by underlying string compactification.

For example, in a CY compactification with $T^2$, one has $3\alpha=1$, the lowest discrete Poincar\'e disk target for LiteBIRD ;Comment: 20p, 10 Figs. 1 section and 1 figure added, references added

Kallosh, Renata,Linde, Andrei, 2024, $SL(2,\mathbb{Z})$ Cosmological Attractors

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