This approach is similar to Deur's approach.
[Submitted on 17 May 2018]
Nonlinear Effects of Gravity in Cosmology
We consider some nonlinear effects of gravity in cosmology. Possible physically interesting consequences include: non-requirement of dark matter and dark energy, asymmetric gravitational matter-creation, emergent homogeneity/isotropy & asymptotic flatness, resolution of "cosmic coincidence" Omega_m \sim Omega_lambda, effective cutoff of gravitational interaction at the scale of cosmic voids.
has gravitational energy in a galaxy like the milky way been calculated ?
Yes. But there are legitimate disputes about whether it has been done right. Most studies use a Newtonian model and use back of napkin type analysis to suggest that the gravitational energy is minimal, without rigorously analyzing the question to the extent necessary. In the same vein a paper today is also on point:
Could dark matter be a natural consequence of a dynamical universe?
Zhi-Wei Wang, Samuel L. Braunstein
Comments: 8 pages, 1 figure
Subjects: General Relativity and Quantum Cosmology (gr-qc)
We construct the gravitating mass of an isolated composite system on asymptotically-flat spacetimes within conventional general relativity and investigate when this quantity is well defined. For stationary spacetimes, this quantity is known to exactly equal the physical (ADM) mass. However, it remains an open question whether these two masses are equal in the absence of a timelike Killing vector. This is especially apropos since our universe has an `origin' and hence no such Killing vector. Further, if these masses failed to agree then composite systems could behave as if they had a `dark component,' whose gravitating mass would not equal the physical mass-energy present. The existence of such an apparent discrepancy is indeed ubiquitous in galaxies and galaxy clusters, though currently it is attributed to the presence of dark matter. We conclude that the theoretical question of the relation between these masses for dynamical spacetimes is ripe for attention."
gravitational energy equal to the mass energy of dark matter which is about 5 times the visible mass needed to explain galaxies rotation seems unlikely Deur's approach or this
The 5x visible mass estimate is model dependent. All of the gravitational approaches are only strengthening the weak fields to get the same dynamics and lensing.
does deur or any gravitational approaches let you calculate from first principles
@neo Deur's approach (in principle) allows you to calculate it from first principles, although, as in GR, the math can be difficult. LambdaCDM modelers use Newtonian gravity and engage in non-rigorous analysis of why the non-Newtonian effects are probably small. Deur's approach makes different choices about effects to ignore to make the math tractable. For one, he is doing a static system approximation which only holds with systems that are reasonably close to stable. It also is a scalar graviton approximation which ignores, for example, EM flux effects. There is good (but again, not entirely rigorous) analysis that holds this together.
@neo You can get more background on Deur's approach and the details of that form the Pages link in the sidebar.
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