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 $\Lambda$CDM model for luminosity distance using the extensive type~Ia 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 $\Lambda$CDM models differ by $^{+0.11}_{-0.15}~\mu_B$~mag. over $z_{cmb}=0.01-1.3$, with overall weighted RMS errors of $\pm0.136$ $\mu_B$~mag for modified GR and $\pm0.151$ $\mu_B$~mag for $\Lambda$CDM respectively. The BAO measures span a range $z=0.106-2.36$, with weighted RMS errors of $\pm0.034$~Mpc with $H_0=67.6\pm0.25$ for the modified GR model, and $\pm0.085$~Mpc with $H_0=70.0\pm0.25$ for the $\Lambda$CDM model. The derived GR metric for this new solution describes both the SNe~1a and the BAO observations with comparable accuracy to the $w'\Lambda$CDM 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.