Inhomogeneous models
Due to the very large distances considered, in cosmology we can observe a given place of the universe only at a given moment in time. It is therefore difficult to disentangle temporal evolution from possible spatial variations around us. In order to deal with this problem, the standard approach is to use the Copernican principle which states that humans are not privileged observers of the universe. Along with the observed isotropy, the latter statement implies indeed that the universe is homogeneous on large-enough scales, so it would be sufficient to observe only limited regions of space to infer the overall properties of the universe.
The ITP Cosmology group works on models that feature weak and strong violations of the Copernican principle. Indeed the evolution of dark energy is degenerate with mild (and expected) violations of the Copernican principle. This issue has been recently discussed in relation to the tension between local and global measurements of the Hubble constant by this PRL. The Cosmology group also aims at rooting cosmology on more solid grounds by testing observationally the Copernican principle.