Dark matter effects look as if at a certain gravitational field strength that the gravitational force shifts from a 1/r^2 effect to a 1/r effect. This effect, which is empirically valid and has produced useful predictions is called "MOND" (for modified gravity).
What could be related to this?
1. It could be a holographic effect, perhaps related to the size of the universe since the cutoff point is roughly equal to the size of the universe times the speed of light.
2. It could be related to self-interaction of a gravitational field with gravitational potential energy, which falls off at 1/r, as this becomes the primary source of matter-energy in the region with weak gravitational fields. A back of napkin calculation ought to be able to determine if this is at all sensible.
3. It could be a function of relativistic graviational effects due to angular momentum that are expressing themselves only in the plane in which the momentum is present, rather than spherically. This could also explain why there are no MOND effects in the solar system (where 99.8% of mass is concentrated in the sun), modest amounts in galaxies (where there is a central black hole and mass bulge, but there are significant amounts of matter beyond the core) and bigger than expected MOND effects in galactic clusters (which may have no center and have massive galaxies circling a center of mass of the system with nothing actually in that center). Some back of napkin calculations ought to be able to see if this makes sense.
Cold dark matter, proposed to explain the situation, has a seemingly intractable problem of requiring cuspy dark matter halos to produce the observed effects that no mechanism has been proposed to explain, in addition to calling for undiscovered types of stable matter that is presumably very weakly interacting. Warm dark matter (basically heavy or numerous objects that would behave like right handed neutrinos) might be a better fit, but also lacks a basis in known processes of baryogenesis or leptogenesis.
Along the same lines, and relevant to both dark energy and dark matter, I wonder if there is adequate accounting in composition of the mass-energy balance in the universe of translational motion, angular momentum, pressure, photons in transit, cosmic background radiation, and the energy content of any other long distance fields of forces (e.g. gravitons, if they exist), stellar gases, and low luminosity baryonic mass (like red dwarf stars) in these calculations.
The Composition of Ordinary Matter In The Universe
The universe (based on the composition of matter in stars and gas giants that seem to make up the vast share of all matter) is about 90% bare hydrogen, and about 10% composed of elements with equal shares of protons and neutrons such as helium, neon, carbon, nitrogen and oxygen. The proportion of the universe made up of elements with more neutrons than protons is tiny and in many of these elements the excess of neutrons over protons is modest. Many of the heaviest isotypes of elements are not found in nature because they are naturally radioactive. So far as we know, there is no sign of large scale charged regions of space, so the number of protons and the number of electrons is extremely evenly balanced on a very fine grained basis over the entire universe. Hence, we have a universe in which there are about 19 protons, 19 electrons and 1 neutron contained in an atomic nucleus, and presumably almost no free neutrons, since they would decay to almost none very quickly in unbound states and there is no known process that produces them in unbound states quickly enough to make up the deficit beyond a very small number. All other mesons, and second or greater generation fundamental particles also decay rapidly, and by hypothesis in QCD there are no free quarks. If protons and electrons were generated from the beta decay of neutrons, then one would expect 19 neutrinos in this proportion of matter in the universe (making up much less than 1% of all matter), but perhaps neutrinos, which oscillate between generations but are otherwise apparently stable, are generated in other processes that a signficant. Neutron stars are presumed to be generated by reverse beta decay (i.e. proton plus electron plus neutrino plus energy produces a neutron). Neutrino mass may also be underestimated, however, if neutrinos are typically moving at relativistic speeds with lots of linear momentum that has a gravitational effect.
Even with recent mass accounting errors that suggest that scientists previously underestimated the amount of ordinary matter in ellipical galaxies so much that ordinary matter and dark matter proportions are actually identical, we still lack good candidates to fill the void. There are indications that dark matter at the supergalactic scale is organized in filaments, but we have no really clue about what those filaments are made out of.
Potential Energy
Could dark matter and dark energy be constant (at least once most baryonic matter forms) and gradually be converting from the former to the latter? If dark energy is proportionate to the size of the universe at a constant density per volume, it would be ever growing, while the matter-energy attributable to dark matter will be ever shrinking. What would a running dark energy amount look like (perhaps via a cosmological constant) and how would corresponding dark matter effect scale shifts impact structure formation in the universe?
Inflation
Cosmology points towards inflation, which is hard to explain, a fraction of the second in the first second of the big bank witnessing massive expansion.
Penrose says that this hypothesis flows from inferences from the implied excessively high uniformity of the universe if one tracks it back that far in time from presently observed states. He suggests based on Second Law of Thermodynamics grounds that the Big Bang should be extremely low in entropy and hence prone to extreme uniformity that does not require a thermal process to reach equilibrium, and that the Big Bang should thus be unlike high entropy black holes. Hence, in his view inflation is not a necessary assumption in Big Bang cosmology. He would rather tinker with the initial conditions of the universe at the dawn of the Big Bang than the laws of nature of inflation seems to.
One stray thought about MOND and inflation is that up to a certain point, there would be no place in the universe where there was a field weak enough for MOND effects to be present. Inflation could be the period until that point was reached. This would take a bit longer to have the same effect, but it would be interesting to model.
I'd also be curious to know how many meters across the universe would be before and after the Big Bang by this hypothesis in a concrete manner. If it is expanding at the speed of light, and is from 10^-35 to 10^-15 or less seconds (approaching a Plank time unit), this is quite small as c equals 186,000 miles per second and 10^-10 seconds would be about six inches at the speed of light. At 10^-15 seconds it should be 100,000 times smaller than that, and at 10^-35 seconds, it should be 100,000,000,000,000,000,000 times smaller than that. It seems that the initial blob doesn't have to be uniform until a very large size at all (all of the matter and energy in the universe condenced into a space much smaller than a grain of sand) to dispense with inflation entirely, and presuming to make meaningful statements that reach back into the first fraction of a second of the Big Bang without more direct evidence seems quite presumptuous. Is it any more of a leap in logic to assume that the Big Bang started from a homogeneous matter-energy spot the size of a tiny grain of sand than to assume that it started to an absolute singularity?
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