Hidden symmetries of two-field cosmological models

Abstract

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 $\alpha$-attractor type with a fixed value of the parameter $\alpha$. 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.

74 pages

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• The infrared behavior of tame two-field cosmological models
• Dynamical renormalization and universality in classical multifield cosmological models
• Hesse manifolds and Hessian symmetries of multifield cosmological models
• Noether Symmetries of Two-Field Cosmological Models
• Hidden Symmetries, Rapid Turns and Cosmic Acceleration
• Scaling behavior of observables as a model characteristic in multifield inflation
• Infrared behavior in tame hyperbolizable two-field models