hobobobo said:
...I don't understand how they calculated critical density. ... what it means to have critical density. Thanx!
They come at these numbers from several different directions, using different kinds of observations----galaxy counts, supernovae, microwave mapping etc.---and the wonder is that different ways of estimating lead to consistent results.
I can only cover a small part of it in one post.
A. assuming uniformity
we assume we don't live in an exceptional part of the universe, with especially low density or high density. we assume the universe is much the same all over, the same in all directions, on largescale average
AA. we can SEE that space is nearly flat
Flat means that the sum of interior angles of any really large triangle has to be 180 degrees. If this weren't true, or nearly true, we would see funny optical effects. Like the number of galaxies in some patch of sky changing unexpectedly fast with distance. Flatness, or near flatness, has been checked repeatedly using various data.
B. assuming Gen Rel is approximately right.
GR is both a theory of gravity and a theory of spacetime geometry. It works to remarkable accuracy-----passes every test we can think of. only breaks down in extreme circumstances like in BH and BB situations. so we assume the main equation of GR relating the density of energy to the changing shape of space is correct.
C. uniformity plus Gen Rel makes Friedmann (A+B=C)
In 1923, Alex Friedmann took Einstein's main GR equation and by assuming uniformity found he could greatly simplify the equation. This produces the two Friedmann equations which relate the density of energy to the changing shape of space, where energy is approximately uniform. It simplifies down to issues of expansion, contraction, and overall curvature.
D. Friedmann equations tell us Rho_crit, density in the flat case.
The Friedmann equations come in three separate versions, for flat, and two kinds of curvature. They are simple equations and can be solved in each of the three cases. Since we can SEE spatial flatness (AA) or near flatness, we can just concentrate on that case. Solving one of the Friedmann equations tells us how to calculate what the energy density must be, in order to have spatial (near) flatness.
This is a great result. Now anybody with a calculator can calculate the energy density of the universe! All you need to know is Newton's constant G, and the Hubble parameter H.
3(cH)
2/8 pi G.
If you get out a calculator and plug in the speed of light, and known values of H and G, then it works out to around 0.85 joules of energy per cubic kilometer.
E. Now all we have to do is compare that 0.85 joules with the OBSERVED density of energy-----that is the energy-equivalent of the matter we can see or can infer is there because of the stability of galaxies and clusters.
F. Well all the matter we can see, or infer is there only amounts to about 0.20 joules per cubic kilometer, when you convert it to energy terms. That includes both ordinary matter and dark matter we infer is there in order to hold galaxies and larger cluster structures together.
So that means either the law of gravity (B.) is wrong, or there is a diffuse non-clumping energy spread out uniformly thru space which amounts to the rest, namely 0.65 joules per cubic kilometer.
But we DON'T HAVE ANY BETTER law of gravity. Einstein Gen Rel works to amazing accuracty in all the tests it's put thru. Until someone comes up with a radically different model of gravity, and spacetime geometry, we have to use the best theory we've got. And that means assuming this dark energy figure of about 0.65 joules per cubic kilometer.
G. And also there is by remarkable coincidence some independent evidence for dark energy. Supernova observations seem to indicate that expansion is accelerating by the amount that would be caused if there were a constant 0.65 joules per cubic kilometer of dark throughout all space.
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I think it is useless to ask for a purely nonmathematical explanation, because all this comes out of the math. Probably the Friedmann equations are the central feature. All cosmology is based on them----that is, based on the simplification of the Gen Rel equation that you get by assuming uniformity.
The basic model has been painstakingly checked ever since 1923 in every detail, repeatedly. It fits reams and reams of data, and continues to be the best we've got.
There must be some popular book you can read about this. Maybe someone can suggest one.
