We investigate α-attractor models of cosmological inflation with two dynamical scalar fields. In that case the hyperbolic geometry, characterizing the scalar kinetic terms, plays an essential role. We focus on models with a scalar manifold given by the Poincaré disk. We investigate the conditions under which such models can possess a Noether symmetry and derive analytically the form of its generator. Furthermore, we find analytically the form of the scalar potential that is compatible with this symmetry. Interestingly, it also turns out that the requirement for the existence of a Noether symmetry fixes the value of the otherwise arbitrary α-parameter in this class of models.

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