Singular $α$-attractors
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911335699185664 |
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| author | Kallosh, Renata Linde, Andrei |
| author_facet | Kallosh, Renata Linde, Andrei |
| contents | $α$-attractor models naturally appear in supergravity with hyperbolic geometry. The simplest versions of $α$-attractors, T- and E-models, originate from theories with non-singular potentials. In canonical variables, these potentials have a plateau that is approached exponentially fast at large values of the inflaton field $φ$. In a closely related class of polynomial $α$-attractors, or P-models, the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential also has a plateau, but it is approached polynomially. In this paper, we will consider a more general class of potentials, which can be singular at the boundary of the moduli space, S-models. These potentials may have a short plateau, after which the potential may grow polynomially or exponentially at large values of the inflaton field. We will show that this class of models may provide a simple solution to the initial conditions problem for $α$-attractors and may account for a very broad range of possible values of $n_{s}$ matching the recent ACT, SPT, and DESI data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_02969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular $α$-attractors Kallosh, Renata Linde, Andrei High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology $α$-attractor models naturally appear in supergravity with hyperbolic geometry. The simplest versions of $α$-attractors, T- and E-models, originate from theories with non-singular potentials. In canonical variables, these potentials have a plateau that is approached exponentially fast at large values of the inflaton field $φ$. In a closely related class of polynomial $α$-attractors, or P-models, the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential also has a plateau, but it is approached polynomially. In this paper, we will consider a more general class of potentials, which can be singular at the boundary of the moduli space, S-models. These potentials may have a short plateau, after which the potential may grow polynomially or exponentially at large values of the inflaton field. We will show that this class of models may provide a simple solution to the initial conditions problem for $α$-attractors and may account for a very broad range of possible values of $n_{s}$ matching the recent ACT, SPT, and DESI data. |
| title | Singular $α$-attractors |
| topic | High Energy Physics - Theory Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.02969 |