Hoping that I understand Tim Thompson’s post correctly, following are some questions:

- What is the difference between the tensors describing ‘curvature’ and ‘geometry’ of spacetime. Would ‘geometry’ be a set of parameters within which the particular ‘curvature’ takes place? So is this an equation that can be used to describe a local area as well as to describe the entire universe? And do the two tensors and the scalar depend on each other? (Keeping in mind that after reading ‘tensor’ in wikipedia I am unclear just what it is.)

- If ‘spacetime’ incorporates 3 spatial measurements and 1 time measurement, does ‘curvature’ refer exclusively to the time measurement or can it refer to spatial or time measurements, interchangeably or together? In other words, can ‘curvature’ mean curvature in spatial measurements or in time measurement or in both? Apart from that, the possibility of expansion, contraction, or constancy implies an acceleration. Is the ‘original’ empty spacetime expansion an acceleration or a constant expansion? Is there any scenario taking both sides of the equation into account in which a spacetime expanding at a constant rate could be regarded as ‘flat’?

- If the universe is expanding as it currently appears to be (whether accelerated or not), would it be necessary to insert a cosmological constant/vacuum energy term into the equation if it were being written now, or could it be written to include the apparent expansion without vacuum energy?

- Does the left side of the equation (minus cosmological constant/vacuum energy) expand or is it, like the pencil stood on its point, equally likely to contract?

- If local spacetime curvature is an effect of an accelerated frame of reference due to a gravitational field or to other cause, and if the effect of spacetime curvature is in turn to create a variation in spatial or time measurement, and since all observers are in accelerated frames of various strengths, then it seems no two observers can make identical spatial or time measurements. Does this not also present a problem of measuring any object or event? For example a measurement taken to indicate a distant object in a frame of a certain strength could be misinterpreted as a closer or more distant object in a stronger or weaker frame. Is that right?

- Are ‘mass’, ‘matter’ and ‘energy’ treated differently on the right side, or are they given some kind of equivalence? For example, if all the ‘mass’ or ‘matter’ of the universe were treated as ‘energy’, or vice versa, presumably that would change the left side. Is that right? What would the effect be in those cases?

- Could the equation be used to describe a universe expanding at a constant rate at its event horizon (or is the event horizon already observed to be receding at a constant rate)? Specifically at light speed?

- If the universe is not homogenous or isotropic, can the equation still describe it?

- If the original expansion of ‘empty space’ takes place without vacuum energy or matter, where in R(ab) or g(ab) could the (mathematical) cause of this expansion be found?

- Could the idea behind ‘tensor’ be described more simply than it is in wikipedia?