Hubble Expansion as an Einstein Curvature

Abstract

Extending the spacetime manifold of general relativity (GR) to incorporate the Hubble expansion of space as a specific curvature, generates a modified solution with three additional non-zero Christoffel symbols and a reformulated Ricci tensor and curvature. The observational consequences of this reformulation are compared with the ΛCDM model for luminosity distance using the extensive type 1a supernovae (SNe 1a) data with redshift corrected to the CMB, and for angular diameter distance using the recent baryonic acoustic oscillation (BAO) data. For the SNe 1a data, the modified GR and ΛCDM models differ by mag. over z cmb = 0.01 - 1.3 , with overall weighted RMS errors of ± 0.136 μ B mag for modified GR and ± 0.151 μ B mag for ΛCDM respectively. The BAO measures span a range z = 0.106 - 2.36 , with weighted RMS errors of ±0.034 Mpc with H 0 = 67.6 ± 0.25 for the modified GR model, and ±0.085 Mpc with H 0 = 70.0 ± 0.25 for the ΛCDM model. The derived GR metric for this new solution describes both the SNe 1a and the BAO observations with comparable accuracy to the w ’ΛCDM model. By incorporating the Hubble expansion of space within general relativity as a specific curvature term, these observations may be described without requiring additional parameters for either dark matter or accelerating dark energy.