The standard model of cosmology is based on the existence of homogeneous surfaces as the background arena for structure formation. Homogeneity underpins both general relativistic and modified gravity models and is central to the way in which we inter
pret observations of the CMB and the galaxy distribution. However, homogeneity cannot be directly observed in the galaxy distribution or CMB, even with perfect observations, since we observe on the past lightcone and not on spatial surfaces. We can directly observe and test for isotropy, but to link this to homogeneity, we need to assume the Copernican Principle. First, we discuss the link between isotropic observations on the past lightcone and isotropic spacetime geometry: what observations do we need to be isotropic in order to deduce spacetime isotropy? Second, we discuss what we can say with the Copernican assumption. The most powerful result is based on the CMB: the vanishing of the dipole, quadrupole and octupole of the CMB is sufficient to impose homogeneity. Real observations lead to near-isotropy on large scales - does this lead to near-homogeneity? There are important partial results, and we discuss why this remains a difficult open question. Thus we are currently unable to prove homogeneity of the Universe on large-scales, even with the Copernican Principle. However we can use observations of the CMB, galaxies and clusters to test homogeneity itself.
We examine the dynamical consequences of homogeneous cosmological magnetic fields in the framework of loop quantum cosmology. We show that a big-bounce occurs in a collapsing magnetized Bianchi I universe, thus extending the known cases of singularit
y-avoidance. Previous work has shown that perfect fluid Bianchi I universes in loop quantum cosmology avoid the singularity via a bounce. The fluid has zero anisotropic stress, and the shear anisotropy in this case is conserved through the bounce. By contrast, the magnetic field has nonzero anisotropic stress, and shear anisotropy is not conserved through the bounce. After the bounce, the universe enters a classical phase. The addition of a dust fluid does not change these results qualitatively.
