How can it be infinite? What nonsense . .

The subject of a flat infinite universe came up again, on the physics forum.  For the first time I expressed my frustration at the claims that the universe might be infinite, and explained that infinity is just a mathematical term that does not have to be realisable.  The discussion highlighted the standard theory that the Big Bang is the point from which everything exists.  The universe does not seem to have been infinite then, so why should it be now?

I made the point that a mass is attributed (around 10^57 kg I believe).  Yes, this is understood to be of the visible universe.  A lot of stuff we can't see due to expansion in the last 13.5Ga, but it all still stems from the Big Bang.  So why do physicists like Brian Cox say, as he did again on TV last night, that the bit we can't see might be infinite?

All it takes is for the boundary to be defined.  The surface of a sphere defines the boundary of the sphere, but the surface itself has no boundary, you could walk round it for ever.  Extend by one dimension, so the volume of the universe has no boundary, but it has to form the boundary of a 4-dimensional entity.  This is the big conundrum, because GR has been defined to work in three spatial dimensions, and a fourth would mean that gravitation would not work as it does.  The inverse square law would be an inverse cube law, and that is not what we see.  Or is it?

There are some problems with GR.  It does not reconcile with quantum, with gravitation being the odd one out in the unification of primary forces.  It should be explaining Dark Matter, instead there are teams of scientists and engineers trying to detect matter that is only detectable through its gravitational effects!  It offers as an option the prospect of the universe being infinite, a nonsense to cover the fact that they don't know the shape of the thing they are talking about.

There is clearly a sense in which GR needs modifying to account for these well-known observations.  Start with an assumption that reality is finite, and that Dark Matter is an artifact of gravitation at the cosmological scale.