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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 ofD3 induced geometric inflation. The choice ofαis determined by underlying string compactification. For example, in a CY compactification withT2, one has 3α= 1, the lowest discrete Poincaré disk target for LiteBIRD.
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This content will become publicly available on May 1, 2026
Landscape of modular cosmology
Abstract We investigate the global structure of the recently discovered family of SL(2,ℤ)-invariant potentials describing inflationary α-attractors. These potentials have an inflationary plateau consisting of the fundamental domain and its images fully covering the upper part of the Poincaré half-plane. Meanwhile, the lower part of the half-plane is covered by an infinitely large number of ridges, which, at first glance, are too sharp to support inflation. However, we show that this apparent sharpness is just an illusion created by hyperbolic geometry, and each of these ridges is physically equivalent to the inflationary plateau in the upper part of the Poincaré half-plane.
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- Award ID(s):
- 2310429
- PAR ID:
- 10614669
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Volume:
- 2025
- Issue:
- 05
- ISSN:
- 1475-7516
- Page Range / eLocation ID:
- 037
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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