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The FLRW metric is used to model our Universe on large cosmological scale. It is a conformally flat metric and the form of stress energy tensor that we get from Einstein's equations are often equated to stress energy tensor for an ideal fluid. This ideal fluid is interpreted to describe a combination of matter fields (dust) and radiations. Now, it is generally the case that any local source of energy and matter distribution would produce a non-zero conformal curvature. So is it really justified to interpret stress energy tensor in FLRW cosmology to represent a general matter-energy distribution (dust + radiation)? This model has predicted that percentage of ordinary matter is only 4%, dark matter 24% and dark energy 72%. Should we need to revisit these claims if interpretation of stress energy tensor is inaccurate?

KP99
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    "Now, it is generally the case that any local source of energy and matter distribution would produce a non-zero conformal curvature." It seems like the existence of the FLRW metric is a counterexample to this claim. Do you have any proof or source backing it up? – Javier Jun 08 '21 at 18:55
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    I do not have a proof as such, only some observations: standard examples like - Schwarzschild, Kerr. Reissner-Nordstorm solutions or any solutions describing radiations, or take any standard Lagrangians from QFT (non-conformal fields only). In each of these cases , the stress tensor have a definite physical interpretation and have non-zero conformal curvature. So I really want to confirm if there are any physical Lagrangians which can produce a conformally flat space-time. EFEs are in this sense arbitrary, you can assume any metric, but that doesn't necessarily corresponds to a physical field. – KP99 Jun 08 '21 at 19:15
  • Well, yes, the dust and electromagnetic radiation used in cosmology will produce a conformally flat geometry, as you already know. – Javier Jun 08 '21 at 19:24
  • Yes I have seen how they are treated in cosmology. But conformal curvature described by radiation and dust are always algebraically special and not just Petrov type O (flat), so are we making any approximations in cosmology? I don't know what it means to have a radiation with Petrov type O Weyl curvature. – KP99 Jun 08 '21 at 19:38
  • I do not understand your assumption regarding flatness: "The FLRW metric is used to model our Universe on large cosmological scale. It is a conformally flat metric ..." Depending on a value for k, the model is flat if and only if k=0. Other k values are for universe models that have curvature. – Buzz Jun 09 '21 at 14:44
  • Every Friedmann-Robertson-Walker model is conformally flat. For all those models, there exist at each point a time like vector relative to which space-time is spherically symmetric. Only a Weyl curvature of type O has this property, so it must be conformally flat. – KP99 Jun 10 '21 at 12:24
  • "4%, dark energy 24% and dark energy 72%" This should be: "4%, dark matter 24% and dark energy 72%" – Buzz Jun 29 '21 at 16:06

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