2011/04/30 by Roy Maartens · 116 citations
Physics and Astronomy · #Anisotropy #Astronomy #Astrophysics #Black Holes and Theoretical Physics #Copernican principle #Cosmic microwave background #Cosmological principle #Cosmology #Cosmology and Gravitation Theories #Dark energy #Galaxy #Homogeneity (statistics) #Isotropy #Metric expansion of space #Physics #Quantum mechanics #Relativity and Gravitational Theory #Spacetime #Theoretical physics #astro-ph.CO #gr-qc
paper · pdf · doi:10.1098/rsta.2011.0289
published in Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences 369(1957), 5115-5137 (Royal Society) · Based on an invited talk at a Theo Murphy Meeting "Testing general relativity with cosmology". Minor corrections, references updated. To appear Phil. Trans. R. Soc. A
arxiv created 2011/10/06 · openalex publication_date 2011/11/14 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 interpret observations of the cosmic microwave background (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 light cone 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 (CP). First, we discuss the link between isotropic observations on the past light cone and isotropic space-time geometry: what observations do we need to be isotropic in order to deduce space-time 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 CP. However, we can use observations of the cosmic microwave background, galaxies and clusters to test homogeneity itself.