Approaching the Dark Sector through a bounding curvature criterion. Issue 1 (10th November 2018) - Hernandez, X; Sussman, R A; Nasser, L
ABSTRACT: Understanding the observations of dynamical tracers and the trajectories of lensed photons at galactic scales within the context of General Relativity (GR) requires the introduction of a hypothetical dark matter dominant component. The onset of these gravitational anomalies, where the Schwarzschild solution no longer describes observations, closely corresponds to regions where accelerations drop below the characteristic a 0 acceleration of MOND, which occur at a well-established mass-dependent radial distance, R c  ∝ ( GM / a 0 ) 1/2 . At cosmological scales, inferred dynamics are also inconsistent with GR and the observed distribution of mass. The current accelerated expansion rate requires the introduction of a hypothetical dark energy dominant component. We here show that for a Schwarzschild metric at galactic scales, the scalar curvature, K, multiplied by ( r 4 / M ) at the critical MOND transition radius, r  = R c, has an invariant value of κB  = K ( r 4 / M ) = 28 Ga 0 / c 4 . Further, assuming this condition holds for r > R c, is consistent with the full space–time which under GR corresponds to a dominant isothermal dark matter halo, to within observational precision at galactic level. For an FLRW metric, this same constant bounding curvature condition yields for a spatially flat space–time a cosmic expansion history which agrees with the ΛCDM empirical fit for recent epochs, and which similarly tends asymptotically to a de Sitter solution. Thus, a simple covariant purely geometric condition identifies the low-acceleration regime of observed gravitational anomalies, and can be used to guide the development of extended gravity theories at both galactic and cosmological scales.