  We show that the potential of Nambu-Goldstone bosons can have two or more
local minima e.g. at antipodal positions in the vacuum manifold. This happens
in many models of composite Higgs and of composite Dark Matter. Trigonometric
potentials lead to unusual features, such as symmetry non-restoration at high
temperature. In some models, such as the minimal $\rm SO(5)/SO(4)$ composite
Higgs with fermions in the fundamental representation, the two minima are
degenerate giving cosmological domain-wall problems. Otherwise, an unusual
cosmology arises, that can lead to supermassive primordial black holes; to
vacuum or thermal decays; to a high-temperature phase of broken
$\mathrm{SU}(2)_L$, possibly interesting for baryogenesis.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics