Abstract
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 SIJ . This paper describes the dynamics and observables of these per-turbations 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.
Highlights
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, 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
Modular inflation models present the simplest class of theories that allow to embed the shift symmetry into a group, in the process leading to a stratified theory space, in which the individual leaves that provide the building blocks of the resulting foliation are characterized by the weights and levels of the defining modular forms
The field theory space of automorphic inflation in general, and modular inflation in particular, has a nontrivial geometry that is encoded in the Riemannian metric GIJ derived in a canonical way from the underlying group structure
Summary
Automorphic inflation as a group theoretic framework for multifield inflation involves field spaces that are obtained as coset spaces of continuous groups, are curved. In the following the comoving curvature perturbation R will be adopted as the adiabatic mode, while the isocurvature perturbations are encoded in an antisymmetric tensor denoted by SIJ. The focus on the latter is suggested by the dynamics of R, leading to an isocurvature dynamics different from the usual dynamics based on projections of the Sasaki-Mukhanov variables. While the geometry in automorphic inflation is derived from the structure of the underlying Lie group G and certain subgroups, it is best to leave the metric of the inflaton field space arbitrary and the number of fields of the inflaton multiplet φI unconstrained, so as to indicate the general features of the framework.
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