Put a dot by the true statements. Let's see what PF people think about these statements.
1. there is a rest frame in cosmology defined by the expansion
2. this gives us a notion of simultaneity. In principle, observers at rest all over the universe could agree on what is meant by the present moment
3. the basic Hubble law distance (that goes into v = H0 D) is the current distance to objects as measured by observers at rest---sometimes called the "comoving distance"
because it is seen by observers comoving with the expansion
4. the current radius of the observable universe is estimated to be around 40 billion lightyears----this includes all the stuff whose light is reaching us so we can observe it.
5. much of the stuff in the observable universe is currently receding at speeds greater than c. General relativity does not forbid this---indeed it encourages it
6. the expansion of space has chilled down the CMB by a factor of 1000 (more accurately an estimated 1100). That energy is gone. General Relativity does not have a global energy conservation theorem or a consensus as to where that energy may have gone.
7. an observer suspended near the event horizon of a black hole does not see the event horizon rushing at him and (depending on the size of the BH) does not necessarily feel any extreme force of gravity. Gravity near the horizon can be similar to that at the surface of the earth if the BH is large enough.
8. the boundary of the observable universe is currently receding at an estimated speed of around 3c.
9. cosmologists tend not to use the "light travel time" distance for technical work---this distance does not work in the Hubble law---however popularized accounts do use the "light travel time" index of distance.
10. Gmu,nu = 8pi Tmu,nu relates curvature to energy density-----the units on the lefthand side are reciprocal-area units of curvature and the units on the righthand are those of energy-density (formally equivalent to pressure)