Approaching the Dark Sector through a bounding curvature criterion
May 17, 20175 pages
Published in:
- Mon.Not.Roy.Astron.Soc. 483 (2019) 1, 147-151
- Published: Feb 11, 2019
e-Print:
- 1705.06356 [astro-ph.GA]
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Abstract: (Oxford University Press)
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 κ_B = K(r^4/M) = 28Ga_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.Note:
- 5 pages, 2 figure.Adjusted criterion now allows for a geometric identification of the MOND a0 constant, is consistent with rotation curve and lensing observations at galactic scales, and with the recent accelerated expansion of the universe at cosmological scales
- gravitation
- galaxies: kinematics and dynamics
- cosmology: theory
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