The theory given in the following article satisfies Einstein's field equations and supports presence of cold dark matter. It provides an alternative to MOND and Tensor-vector-scalar gravity theories. These two theories does not require cold dark matter.
http://ptep-online.com/index_files/2015/PP-40-11.PDF
This study successfully applies GR dynamics to derive the rotation curves of spiral galaxies without evoking dark matter: http://arxiv.org/abs/1101.3224.
@James. Thank you for information. How do you explain the structure formation in your theory. Dark matter was originally proposed for structure formation.
Vikram,
Actually no, dark matter was proposed to explain discrepancies between evaluation of the gravitational dynamics of larges scale, disperse, compound structures. Fritz Zwicky first suggested that much of the mass of galaxy clusters was 'missing'. However, he was unaware of the massive intracluster medium identified through later observations X-ray emissions - now thought to contain ~2/3 of mass from ordinary matter. More importantly, the proposed requirement for DM was more firmly established in the late 1970's from discrepancies between the observed 'flat' rotational dynamics of spiral galaxies and the simple (invalid) expectation that disk galaxies should rotate just like planetary systems - with velocities diminishing as a function of radial distance. As best I can determine, this is still the fundamental basis for identifying the requirement for dark matter in spiral galaxies - as all methods are derived from the discrepancy with this perceived requirement. Please see http://en.wikipedia.org/wiki/Dark_matter#Observational_evidence, for example.
Only after the requirement for DM, especially in spiral galaxies, became generally established in the astrophysics community was its presumed existence extended to cosmological models.
If it is systematic inadequacies in our evaluations of gravitational dynamics that seem to require the presence of either compensatory mass or gravitational effects, then our evaluations of structure formation must be similarly inadequate...
Following article is now published in "Progress in Physics"
Zaveri V.H., Periodic relativity: deflection of light, acceleration, rotation curves. Progress in Physics, 2015, v.11(1), 43-49.
http://ptep-online.com/index_files/2015/PP-40-11.PDF
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