Breaking the cosmological principle into pieces: a prelude to the intrinsically homogeneous and isotropic spacetimes

Abstract

In this manuscript, we show that there are three fundamental building blocks supporting the Cosmological Principle. The first of them states that there is a special frame in the universe where the spatial geometry is intrinsically homogeneous and isotropic. The second demands the existence of a fiducial observer to whom the Hubble parameter is isotropic. The last piece states that matter and radiation behave as a perfect fluid. We show that these three hypotheses give us the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, the central pillar of the standard model of Cosmology. We keep with the first of them and start to investigate the so-called intrinsically homogeneous and isotropic spacetimes. They emerge after the decoupling of the CMB with the geometric frame of reference. Furthermore, a ``$\Lambda$CDM-like" effective theory arises naturally in those backgrounds, together with some new density parameters relating to the local inhomogeneities, the internal energy density, and the local and global magnitudes of the Hubble anisotropy. All those properties make this class of inhomogeneous models, which roughly speaking, keeps "1/3" of the Cosmological Principle, worth investigating in applications to Cosmology, for it can accommodate the same ingredients of the standard model, as a geometric frame and a free-falling isotropic cosmic background radiation, and reduce to the latter when some observable parameters vanish.