Goldstone bosons are well-established in physics as taking values in the coset space of spontaneously broken symmetry groups.
Multiple physics papers across different domains (condensed matter, particle physics, holography, and chiral perturbation theory) consistently state and utilize the property that Nambu-Goldstone bosons parameterize a coset space G/H corresponding to the quotient of the full symmetry group by the unbroken subgroup.