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Abstract We discuss two-stage dilaton-axion inflation models [1] and describe α -attractor models with either exponential or polynomial approach to the plateau.We implement one of the models of primordial black hole production proposed in [2] in the α -attractor context, and develop its supergravity version. The predictions of this model following from its polynomial attractor properties are: n s and r are α -independent, r depends on the mass parameter μ defining the approach to the plateau. The tachyonic instability at the transition point between the two stages of inflation is proportional to the negative curvature of the hyperbolic space ℛ K = -2/3 α . Thereforethe masses of primordial black holes (PBHs) and the frequencies of small-scale gravitational waves (GWs) in this model show significant dependence on α .
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Polynomial α-attractors
Abstract Inflationary α -attractor models can be naturally implemented in supergravity with hyperbolic geometry. They have stable predictions for observables, such as n s = 1 - 2/ N e , assuming that the potential in terms of the original geometric variables, as well as its derivatives, are not singular at the boundary of the hyperbolic disk, or half-plane. In these models, the potential in the canonically normalized inflaton field φ has a plateau, which is approached exponentially fast at large φ . We call them exponential α-attractors . We present a closely related class of models, where the potential is not singular, but its derivative is singular at the boundary. The resulting inflaton potential is also a plateau potential, but it approaches the plateau polynomially. We call them polynomial α-attractors . Predictions of these two families of attractors completely cover the sweet spot of the Planck/BICEP/Keck data. The exponential ones are on the left, the polynomial are on the right.
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- Award ID(s):
- 2014215
- PAR ID:
- 10351169
- Date Published:
- Journal Name:
- Journal of Cosmology and Astroparticle Physics
- Volume:
- 2022
- Issue:
- 04
- ISSN:
- 1475-7516
- Page Range / eLocation ID:
- 017
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1475-7516/2022/04/017
