Hubble Constant = Ho = [d/s]/[d/1] in basic variables, thus it reduces to 1/s which is time inversed, that is, the inverse of the age of the universe at whatever Ho constant value used and further adjustments from the Standard Model equations. The big adjustment is U. acceleration [ and significant deceleration during first 2 billion years]. Thus, for the U to double again, it needs another full universe age ... at least at this instant of time and U size or stretch.
Every part in the U expands, thus any part of it expands like another. Like a loaf of raisin bread, everything expands, and all raisins move apart. Raisins separated by more distance will move apart further, because more expanding bread is between them – expanding at every point. The big bang is not points traveling from a center, but all space however small expanding. Where matter coalesced to stars and proto-galaxies, gravity overcomes matter moving apart, to preserve coalescence, while total U in all parts continues to expand - ?a space fabric expansion, whatever that might be.
So, the Ho needs to be velocity per some chosen distance to define the rate of expansion everywhere. Two points, as you put your question, are distance between, and not related to volume of U, but to linear separation. Linear is related to diameter doubling, also linear.
So, how much time did it take for the U to ‘double diameters’ in the past? Present U age [ = U] in a series of ½ U + ¼ U + 1/8 U + 1/16 U + 1/32 U + 1/64 U etc. as a total is good. Smaller the diameters, the faster it doubles in relation to what it was. Choose any part of the history of the universe and slice it to find how much time was needed to double space between two points, that is, double the size of the observable universe.
We do not know how big is the U. We observe that part of the U that communicates to us with light. Space can expand faster than light. Matter that has a speed limit in relation to itself, but not space. [So what does that mean for matter - galaxies in the part of space moving apart faster than light, one part beyond our view and us in the other galaxy, like 2 super-light fast raisins, and we are one raisin? Does their length disappear to each other, and if so, to what if anything? Better said that they cannot communicate. So, what does that say about relativity and communication?] We are a part of the loaf of bread, but do not know which part, or if or where a center is. We must know some edge to know a center. The U is bigger than we can see and know. U for unknown.
On this topic, have you heard of a writer, Gerald Schroeder, who relates Bible and Genesis creation by a growth-decay formula that uses Bible creation days 1 – 6 as numerical data in the formula to divide the 13.8 billion year history of the universe into six related parts, using diameter doubling for measure? Days can be eras in Hebrew used in the Bible. The six divisions are not equal, but as these fractions given above. The formula is a well accepted growth-decay function with a natural log for universal expansion, and integrated. Data put into the formula is from both nature and Bible, to bridge both with accountability. The nature side relates the age of the U, using a ratio of composed of the Microwave Background Radiation temperature at first matter, that is at quark confinement becoming neutrons [and a little later, protons overlapping], divided by the MBR now. That sets two data points for expansion, and starts the ‘beginning’ in the Bible at first matter. That ratio is related to diameter doublings of the universe. And ‘t’ in the exponent slices all U time into 6 parts, that data number taken from the Bible for 6 creation day-eras. It traces the length of each day-era or ‘slice’ of the whole. An other events fit well on the function graph, such as ‘light of last scattering’ etc. Bible descriptions and nature agree for those slices, especially if using Hebrew correctly to understand Bible words, of which there is much misuse in western Bible translations, and yes, even the Jewish Torah. We must use word roots. The ‘Science of God’ is the book, and his website is his name.
Take care, Steve Huffey