wolram said:
I think this is the right place to ask, how much "gravitating", matter
is needed, in LQG and String, for our universe to be as it is. and how
critical is this "density".
wolram, I do not think that either LQG or stringy theories are sufficiently well-developed to provide a figure for the critical density
however, ordinary 1915 Gen. Rel. does provide a basis for calculating the critical density
the formula for calculating it basically just the Friedmann equation and it gives a figure of about
0.83 joules per cubic kilometer.
the usual estimate is that this 0.83 joules is broken down between 73 percent dark energy and 27 percent matter (of which most is dark matter)
so if you want to know how much "matter" (dark and baryonic combined) then it is 27 percent of 0.83 joules
this is about 0.22 joules per cubic kilometer. (baryonic and dark matter combined)
the word "density" just means so-and-so much of something
per unit volume
and there is no certain total volume, one can only guess about whether it is finite or infinite and what it is if it is finite.
so one is better off just talking about density----so and so much per cubic km or cubic lightyear.
besides, it is the density at each point that determines the curvature at that point. So the density is the relevant thing, not the total.
the density, whether it is measured or inferred, turns out to be amazingly sparse by human standards. 0.22 joules is a small amount of energy already and it would seem even more tiny if expressed as a mass equivalent (miniscule fraction of a nanogram)---but all that means is that space, on average, is extraordinarily empty and if it were not so empty then it would not appear flat
what they mean by "critical density" is the value which is necessary for the universe to be flat
and since it appears to be flat (people keep checking this in everyway they can think of) the actual density is believed to be at or close to the critical level.
