Gravitational theory of cosmology, galaxies and galaxy clusters
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Regular Article - Theoretical Physics
Gravitational theory of cosmology, galaxies and galaxy clusters J. W. Moffat1,2,a 1 2
Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada Department of Physics and Astronomy, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Received: 15 April 2020 / Accepted: 16 September 2020 © The Author(s) 2020
Abstract A modified gravitational theory explains early universe and late time cosmology, galaxy and galaxy cluster dynamics. The modified gravity (MOG) theory extends general relativity (GR) by three extra degrees of freedom: a scalar field G, enhancing the strength of the Newtonian gravitational constant G N , a gravitational, spin 1 vector graviton field φμ , and the effective mass μ of the ultralight spin 1 graviton. For t < trec , where trec denotes the time of recombination and re-ionization, the density of the vector graviton ρφ > ρb , where ρb is the density of baryons, while for t > trec we have ρb > ρφ . The matter density is parameterized by M = b + φ + r where r = γ + ν . For the cosmological parameter values obtained by the Planck Collaboration, the CMB acoustical oscillation power spectrum, polarization and lensing data can be fitted as in the CDM model. When the baryon density ρb dominates the late time universe, MOG explains galaxy rotation curves, the dynamics of galaxy clusters, galaxy lensing and the galaxy clusters matter power spectrum without dominant dark matter.
1 Introduction Dark matter was introduced to explain the stable dynamics of galaxies and galaxy clusters. General relativity (GR) with only ordinary baryon matter cannot explain the present accumulation of astrophysical and cosmological data without dark matter. However, dark matter has not been observed in laboratory experiments [1]. Therefore, it is important to consider a modified gravitational theory. The observed acceleration of the universe has also complicated the situation by needing a dark energy, either in the form of the cosmological constant vacuum energy or as a modification of GR. The fully relativistic and covariant modified gravity (MOG) theory Scalar–Tensor–Vector–Gravity (STVG) [2–16,23–26] has been successfully applied to explain the a e-mail:
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rotation curves of galaxies and the dynamics of galaxy clusters. It is claimed in Ref. [14] that mass density profiles for galaxies near the centre of the clusters Abell 1689 and Abell 1835 are in conflict with the requirement of no dark matter in the fitting of MOG to the cluster data. The observational data in Fig. 1, Ref. [15], go below r 10 kpc. For r 30 kpc the observational data for the normalized acceleration in Fig. 1 Ref. [15] are well inside a galaxy interior. One should question the observational resolution at small r near the centre of galaxy clusters. While the observational data for r 10 kpc may be correct, the dark matter models, such as the three fitted to the acceleration data of Abell 1689, and the MOG mod
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