Has anyone done a PPN formalism on Dark Matter? Or other non-GR?

[mollwollfumble]

TL;DR Summary

Any signs of a factor of two difference between Dark Matter mass calculated using gravitational lensing vs calculated from the virial theorem?

This thought surprisingly came from thinking about the definition of temperature and the symmetry breaking that separated time from temperature. Which led to thoughts about symmetry breaking that separated QM from GR. Which led to to the symmetry breaking that separated dark energy from baryonic matter from dark matter. ie. the fine tuning there may be a result of symmetry breaking rather than just a statistical freak.

Although gravity between baryonic matter and baryonic matter has been confirmed using Parameterized post-Newtonian formalism to agree to high accuracy with General Relativity, I haven't seen evidence confirming that gravity between Dark Matter and baryonic matter acts using General Relativity.

Gravity between DM and baryonic matter could, for instance, act through gravitons in QM rather than through GR. If so, then the DM mass calculated from the virial theorem would differ by a factor of two from that calculated by gravitational lensing. Has this been tested? Any signs of a factor of two difference between Dark Matter mass calculated using different methods?

 

[ohwilleke]

Not answering the question, but providing a link to the PPN for background reference.

 

[Vanadium 50]

Dark Matter is GR. So its PPN parameters are the same as GR's.

 

[ohwilleke]

Dark Matter is GR. So its PPN parameters are the same as GR's.

Dark matter theories, at the galaxy and galaxy cluster scale where a lot of the study of DM is being done, aren't really GR. They are really just straight up Newtonian gravity justified by the assumption that GR effects are negligible, which literature being discussing in a different PF thread right now, disputes.

I think what the OP is really asking is whether the improvements on unmodified Newtonian gravity used to approximate GR in most astronomy applications from the Post-Newtonian expansion (or equivalently, the PPN with GR parameters) could reproduce dark matter effects without resort to dark matter.

In other words, if considering some of the GR effects neglected in a purely Newtonian approximation, without using the mathematically intractable fully GR without any simplifying assumptions, as the post-Newtonian expansion and PPN with standard GR parameters do, could explain or partially explain phenomena usually attributed to dark matter.

The main non-Newtonian effects in GR which have been proposed to possibly account for phenomena in galaxies and galaxy clusters that are attributed dark matter have been gravitational field self-interactions and the GEM (gravitomagentic) effects that are both well recognized but have historically been discounted in weak field galaxy and galaxy cluster systems.

I'm not certain whether the PN expansion or PPN approach captures these GR specific effects in a way that would work for galaxy and galaxy cluster scale systems. But I think that this is what the OP wants to know.

 

[Vanadium 50]

I think what the OP is really asking

Then let him ask it. Answering questions he didn't ask rather than the one he did ask is unlikely to be helpful.