  The possibility has been recently demonstrated to manufacture
(nonrelativistic, Hamiltonian) many-body problems which feature an isochronous
time evolution with an arbitrarily assigned period $T$ yet mimic with good
approximation, or even exactly, any given many-body problem (within a quite
large class, encompassing most of nonrelativistic physics) over times
$\tilde{T}$ which may also be arbitrarily large (but of course such that
$\tilde{T}<T$). In this paper we review and further explore the possibility to
extend this finding to a general relativity context, so that it becomes
relevant for cosmology.
