A general framework of automorphic inflation

Schimmrigk, Rolf

doi:10.1007/jhep05(2016)140

Cited by 12 publications

(25 citation statements)

References 77 publications

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“…This leads to the notion of automorphic inflation as a structured framework of multifield inflation [8,9]. An immediate consequence of the existence of such symmetries is that the space of automorphic field theories acquires a foliation, with leaves that are specified by numerical characteristics, defined in terms of the group theoretic and automorphic structure, specifically the underlying continuous group G, the discrete group Γ in G that extends the shift symmetry, and the types of the automorphic forms that define the building blocks of the inflaton potential.…”

Section: Jhep09(2017)043mentioning

confidence: 99%

“…Automorphic inflation was briefly outlined in [8], and the general framework was described in more detail in [9], with emphasis on the automorphic side of the theory. The purpose of the present paper is to focus in more detail on the class of modular inflation and the particular model of j-inflation.…”

Section: Jhep09(2017)043mentioning

confidence: 99%

“…The general framework was introduced in [8] and its structure described in more detail in [9] in the higher rank case. Classical modular forms [40,41] were introduced in the second half of the 19 th century as functions on the complex upper halfplane because this space is mapped to itself by the modular group SL(2, Z).…”

Section: Modular Inflationmentioning

confidence: 99%

“…Such a framework is described in refs. [8,9]. The result is that in the modular context the group theoretic set-up is given by the pairs of groups (G, Γ), where G = SL(2, R) is semisimple.…”

Section: Modular Inflationmentioning

confidence: 99%

“…The domain theoretic structure is obtained by considering a maximal compact subgroup K ⊂ G, which in this case is the rotation group K = SO(2, R), both of which act via the Möbius transformation. More details can be found in [9].…”

Section: Modular Inflationmentioning

confidence: 99%

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Modular inflation observables and j-inflation phenomenology

Schimmrigk

2017

J. High Energ. Phys.

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Modular inflation is the restriction to two fields of automorphic inflation, a general group based framework for multifield scalar field theories with curved target spaces, which can be parametrized by the comoving curvature perturbation R and the isocurvature perturbation tensor S IJ . This paper describes the dynamics and observables of these perturbations and considers in some detail the special case of modular inflation as an extensive class of two-field inflation theories with a conformally flat target space. It is shown that the nonmodular nature of derivatives of modular forms leads to CMB observables in modular invariant inflation theories that are in general constructed from almost holomorphic modular forms. The phenomenology of the model of j-inflation is compared to the recent observational constraints from the Planck satellite and the BICEP2/Keck Array data.

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Section: Jhep09(2017)043mentioning

confidence: 99%

Section: Jhep09(2017)043mentioning

confidence: 99%

Section: Modular Inflationmentioning

confidence: 99%

Section: Modular Inflationmentioning

confidence: 99%

Section: Modular Inflationmentioning

confidence: 99%

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Modular inflation observables and j-inflation phenomenology

Schimmrigk

2017

J. High Energ. Phys.

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Hidden symmetries of two-field cosmological models

Anguelova

Babalic

Lazaroiu

2019

J. High Energ. Phys.

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We determine the most general time-independent Noether symmetries of two-field cosmological models with rotationally-invariant scalar manifold metrics. In particular, we show that such models can have hidden symmetries, which arise if and only if the scalar manifold metric has Gaussian curvature −3/8, i.e. when the model is of elementary α-attractor type with a fixed value of the parameter α. In this case, we find explicitly all scalar potentials compatible with hidden Noether symmetries, thus classifying all models of this type. We also discuss some implications of the corresponding conserved quantity. arXiv:1905.01611v3 [hep-th] 22 Aug 2019 C Solution of the Hesse equation for rotationally-invariant surfaces 61 C.1 Solving the Hesse equation 61 C.2 Reduction to standard cases 66 D Elementary hyperbolic surfaces 68 -1 -2 The minisuperspace Lagrangian of two-field cosmological modelsIn this section, we recall briefly the definition of two-field cosmological models and their constrained Lagrangian description in the minisuperspace approach.

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Generalized two-field α-attractor models from geometrically finite hyperbolic surfaces

Lazaroiu¹,

Shahbazi

2018

Nuclear Physics B

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We consider four-dimensional gravity coupled to a non-linear sigma model whose scalar manifold is a non-compact geometrically finite surface Σ endowed with a Riemannian metric of constant negative curvature. When the space-time is an FLRW universe, such theories produce a very wide generalization of two-field α-attractor models, being parameterized by a positive constant α, by the choice of a finitely-generated surface group Γ ⊂ PSL(2, R) (which is isomorphic with the fundamental group of Σ) and by the choice of a scalar potential defined on Σ. The traditional two-field α-attractor models arise when Γ is the trivial group, in which case Σ is the Poincaré disk. We give a general prescription for the study of such models through uniformization in the so-called "non-elementary" case and discuss some of their qualitative features in the gradient flow approximation, which we relate to Morse theory. We also discuss some aspects of the SRST approximation in these models, showing that it is generally not well-suited for studying dynamics near cusp ends. When Σ is non-compact and the scalar potential is "well-behaved" at the ends, we show that, in the naive local one-field truncation, our generalized models have the same universal behavior as ordinary one-field α-attractors if inflation happens near any of the ends of Σ where the extended potential has a local maximum, for trajectories which are well approximated by non-canonically parameterized geodesics near the ends; we also discuss spiral trajectories near the ends. Generalized two field α-attractors illustrate interesting consequences of nonlinear sigma models whose scalar manifold is not simply connected. They provide a large class of tractable cosmological models with non-trivial topology of the scalar field space.

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A general framework of automorphic inflation

Cited by 12 publications

References 77 publications

Modular inflation observables and j-inflation phenomenology

Modular inflation observables and j-inflation phenomenology

Hidden symmetries of two-field cosmological models

Generalized two-field α-attractor models from geometrically finite hyperbolic surfaces

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