Only in the observable universe. The universe as a whole is spatially infinite.ohwilleke said:It follows from the fact that there is a finite amount of mass-energy in the Universe
Which is a local concept in GR, not a global one. In a non-stationary spacetime, such as the spacetime that describes our universe as a whole, there is no conserved global energy.ohwilleke said:conservation of mass-energy
I think you are either misunderstanding or misstating the theory.ohwilleke said:which is very basic and uncontroversial premises of the Big Bang theory of cosmology
This concept of "total energy" is meaningless since it is zero for any spacetime whatever in GR.ohwilleke said:Even if you consider gravitational negative energy as a concept (which I am referencing not as authority but just to clarify my terminology) which is more advanced and controversial, it still gets you only to zero
All of these are speculative quantum gravity models, not mainstream cosmology. Discussion of them belongs in the Beyond the Standard Model forum, not here.ohwilleke said:A good background discussion of asymptotic safety which I oversimplify in my comment can be found in this published open source paper (Eichhorn 2019) (particularly Part 5). See also here and here. Also here (discussing distinction between classical GR singularity Big Bang at infinite temperature and limitations on that in a quantum gravity scenario).
In GR, it's more that there isn't even a well-defined global concept of "energy" except in a special class of spacetimes (the stationary spacetimes).Prishon said:Why should energy not be conserved globally?
This Usenet Physics FAQ article gives a decent overview of the issue:Prishon said:Can you give a link?