Good wikipedia article on these types of cosmologies including timescape cosmology:
e.g.
Euclidean geometry -> non-euclidean geometry; Classical analysis -> nonstandard analysis; Linearity -> non-linearity; Homogeneity -> inhomogeneity; Flat spacetime -> curved spacetime; Singular probabilities -> superposition.
All of these were loosening of certain criteria that opened up many possibilities. It is certainly erroneous to assume we must, by necessity, have a homogeneous cosmology.