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By conservation laws I mean quantum number conservation, such as baryon and lepton numbers.

As far as I know, we have a reasonable confidence that experimental data confirms a lot of features of our models of the universe back to almost the Big Bang itself, at least in some areas, and I presume that our current conservation laws were included in the models.

So my question is: if the above paragraph is correct, then can we be fairly sure that, that as far back as we can measure, at least some conservation laws have been well, conserved, for 14 billion years?

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    $\begingroup$ That's...a bit difficult to answer, since "back to the Big Bang" implies you want to look at cosmological models which are rather classical GR and know nothing of those quantum numbers you are talking about. That is, the models that allow you to go back that far in time do not, at the same time, model the world in the detail that you would need to meaningfully talk about that. I'm also not sure where you see any connection between conservation laws and running couplings. Even for "simpler" conservation laws such as energy, it gets complicated. $\endgroup$ – ACuriousMind Jul 27 '16 at 22:29
  • $\begingroup$ @ACuriousMind I should have been clearer about which laws I am talking about. I will edit out the coupling reference. I was under the impression that calculations such as matter /antimatter ratios in the early universe, for example or Big Bang nucleosynthesis would have used quantum numbers. Thanks for your comment, I will read more and hopefully post a more informed question. $\endgroup$ – user108787 Jul 27 '16 at 22:41
  • $\begingroup$ Well, I think my point is that we firmly believe that the conservation laws of QFT have been valid back to the Big Bang, but I'm at a loss how to actually substantiate that belief over timescales where we cannot suppose doing QFT in flat space is a sufficiently good approximation. However, I'm no cosmologist, so don't take me too seriously ;) I also see I linked the wrong question in my first comment, I meant to link this one $\endgroup$ – ACuriousMind Jul 27 '16 at 22:51
  • $\begingroup$ @ACuriousMind yes, in my own distorted knowledge way, that energy aspect was what I was trying to avoid re the coupling constants reference. As usual, I need to hit the books and be more coherent before rushing the question. $\endgroup$ – user108787 Jul 27 '16 at 22:58
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We don't know how the conservation laws will change, if any, under quantum gravity. But quantum gravity is not really determinative until we go back to about the Planck era. Before that a general relativistic treatment of spacetime, with QFT representing the other three interactions, and the relevant particles, works well enough. And then the issues wind up being how the QFT theory beyond our current standard model of the particles would look like at the much higher energies and temperatures at earlier times in the universe.

Now, problems with the QFT standard model (SM) will arise way before the Planck era that will require going Beyond the Standard Model (BSM), and the new physics may introduce some other factors or asymmetries. The SM is best seen as an effective theory, good probably to somewhere around or above the 1, 10 or 100 TEV, but other effects will enter in then. They will be consistent with the SM symmetries and physics for lower energies.

[BSM physics is in research, and will depend much on what we find from the LHC or higher energy accelerators. Quantum gravity also is in research, with little available experimental data and more dependent on astrophysical data]

[And really, how to treat energy in GR is well understood, using the other known physics and GR, up to those same energy levels. We knew how to treat it for the 2 merging black holes, and know how to treat it even during the inflation era soon after the Big Bang. It is not an issue other than for speculations. See any cosmology book or the BH calculations for the energy in the gravitational waves expected or seen]

So, to energies or temperatures of maybe 1, 10, or 100 TEV the conservation laws we know in particle physics will work well enough. Energy conservation is different because in general relativity (GR) energy in general is not conserved. Energy conservation has to do with time symmetry (timelike Killing vectors in GR) which does nothing exist in the cosmological solution of GR with the isotropy and homogeneity observed. But particle symmetries in QFT are not a problem until the BSM has to be taken into account.

Before then, to energies of that level mentioned, baryon and lepton conservation holds. Also color symmetries. Electroweak symmetry is in that range also. You go much above those energies, and it becomes more questionable. But it has nothing to do with GR, it's the BSM issue. Thus you can do cosmology with classical or semi classical GR, taking the QFT and SM physics to do a lot of it. When you get into the inflation era you need a now unknown inflation field. Even in our times dark matter and dark energy involves something beyond the SM we don't know anything about.

Now, this QFT physics in curved spacetimes needs calculations to be done with that spacetime accounted for. This was done by Hawking in his calculations for blackbody radiation from black holes (BHs) where the strong gravity had the vacuum virtual particles cause the effect of particle radiation from the BHs. Similarly, in the higher energies and temperatures at earlier cosmological times, like the inflation era, you do need to deal with those possible different quantum field in a GR background.

So, it's not just symmetries, it may all come to what symmetries emerge at higher energies, it's whatever new physics comes out at higher energies, and how well we can understand it.

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  • $\begingroup$ No problem. Appreciate your vote of confidence on this answer. But it's interesting that in the BSM investigations symmetries or gauge symmetries don't seem to be a guiding factor, like it was for instance in EW and in the strong force. That's been a guiding light for a long time, seems like BSM is explorations in the dark ages. Depending so much on new experimental result maybe means we've also for now exhausted our ideas, so much vested over the last 10-20 years on supersymmetry and String Theory. Gravity is not too different except we know there a quantum gravity out there somewhere. $\endgroup$ – Bob Bee Aug 2 '16 at 1:55

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