by David_Wiltshire_VIA on Fri 16 Jan 2015 23:28
There are different aspects to gravitational energy in an expanding universe:
(i) kinetic energy of expansion;
(ii) binding energy of bound structures;
(iii) thermal energy of galaxies in clusters
etc. I do not believe that any of these problems can be treated in a rigid Newtonian sense. Things may be close to Newtonian at some level in a hierarchy, but there is a question of the relative calibration of the rulers and clocks at every level of the hierarchy, over long periods of time, given that spacetime rigidity is not a part of general relativity.
Since kinetic energy of expansion is in principle very different from binding energy etc, my work thus far has coarse-grained over all the problems associated with binding energy, thermal energy within clusters etc. It is my hypothesis that understanding gradients in kinetic energy of expansion between voids and the walls and filaments that contain galaxy cluster explains dark energy. Since this is a qualitatively different problem to binding energy, I have been trying to deal with one problem at a time.
Some or all of the problem of dark matter is very possibly another aspect of understanding gravitational energy. For example, in recent work Mikolaj Korzynski has constructed multiscale exact solutions of Einstein's equations in which this problem is explicitly studied, and within which "backreaction" is very significant. See arXiv:1412.3865. His solutions are of course very idealized, but they explicitly demonstrate the new effects that can arise with coarse-graining in general relativity. Essentially there is a nonlinearity of adding masses together with makes the game very different to Newtonian gravity. Korzynski's work is interesting because it shows how even though things can be close to Newtonian at one level of a hierarchy, the effect of nested structures is to give an overall mass renormalization.
I think the main problem is that we have not been using the full power of general relativity, just because there are lots of very complicated and deep issues. I am completely agnostic about the existence of possible new particles which might solve the dark matter problem to some extent; it's a very reasonable proposition. But the big issue that I see is that the whole present cosmological paradigm is just Newtonian gravity built on top of one very simple exact solution (the FLRW model). GR is not a complete theory, even at the statistical level. Many physicists want to keep space rigid and add all sorts of complex modified forces - because it is conceptually easy and we understand Newton - but real progress can only be made by tackling the problems we know to be conceptually difficult. These are not simple problems to solve, which is why we have to try to identify the key physical elements, and be guided by observation.
MOND is a fascinating phenomenology that appears to hold at one particular level of the hierarchy of structure - galaxies - but not at the next level, clusters of galaxies. That's a piece of the puzzle, no doubt. It so happens that the relative volume deceleration required by the timescape model - a time varying quantity - once one fits to the data turns out to coincide with the MOND acceleration scale at late epochs, where MOND is tested. (It's different in the early universe, as it is not a fixed rigid number.) The timescape model does have a natural relative deceleration scale, but since I have been coarse-graining over all of the internal structure of the walls and filaments in which galaxies are contained, I have no explanation as to why this coincidence should be there. I never expected it until I calculated it. I should point out that since the timescape relative deceleration scale is related to derivatives of the Hubble parameter, it is a more striking coincidence than the numerical coincidence that Milgrom and others have remarked on concerning the present Hubble constant and the MOND scale (which is an order of magnitude less precise than the coincidence I find).
At present such facts are puzzles and mysteries; but are possible hints that new simplifying principles are there to be found.