# Hidden symmetries of two-field cosmological models

## TL;DR

This paper classifies two-field cosmological models with rotational symmetry that possess hidden Noether symmetries, revealing that such symmetries occur only for models with a specific scalar manifold curvature, notably in elementary lpha-attractor models.

## Contribution

It explicitly identifies all scalar potentials compatible with hidden Noether symmetries in two-field models with Gaussian curvature -3/8, linking symmetries to lpha-attractor models.

## Key findings

- Hidden symmetries occur only at Gaussian curvature -3/8.
- All compatible scalar potentials are explicitly classified.
- Implications of conserved quantities are discussed.

## 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.