The video: How Large is the Universe? (20 mins). states that the Universe has a "radius" of 46 Billion Light Years (BLYs) & therefore the maximum distance between two galaxies is at least 92 BLYs. Since the estimated life of the Universe is 13.7 BLYs and both radiation and matter can not travel at speeds in excess of the speed of light, how is it possible to know this?
It turns out that making such a determination is quite simple. in fact, it is quite simple to obtain a graph of the speed at which remote galaxies are receding from our versus their distances from us. The former is obtained by simply passing the light of a remote galaxy through a prism and obtaining its spectrum. In the spectrum one can look for the lines which are proper for the hydrogen (H) and helium (He) atoms. These two elements account for the overhelming share of matter in the Universe. The spectra in question are very well known so it is possible to readily & easily calculate how much any of their spectral lines have red shifted. The amount of red shift is proportional to the observed galaxy recession speed.
Obtaining a measure of the distance to the observed galaxy is not much more complicated. In fact, answering the how far question can be easily done if we have some standard candle of great power (intensity), since if we know the intrinsic intensity of such a candle we can compare the apparent (what we see) intensities to the intrinsic intensities and compute the distance (from us) using the simple equation d = ((I/A)**-2)*r {the square root of ratio I/A times the distance of "nearby" object of intensity equal to I (intrinsic)}. For example, if we have an object (star or galaxy) which shines with intensity I and we also KNOW it is 3 LYs away and if the remote object apparent luminosity is 10**6*I (i.e. a millionth of I) then:
d = ((I/A)**-2)*r = ((1/10**-6)**-2)*3 = 1000*3 = 3,000 light years
Thus determining the distance of galaxies boils down to finding suitable powerful sources of radiation in enough galaxies so that they are visible to us even at distances of billions of LY. Furthermore, such radiation sources should be either of approximately constant power, or such that some other observable parameter correlates strongly with their intrisic luminosity. The latter is the case for cepheids stars whose intrinsic luminosity can be calculated from their period. The former is true for specific classes of Supernovae or exploding stars.
These methods are calibrated by using the previous shorter distance method. The parallax method, that is measuring the apparent angular shift (due to earth motion on its orbit) of the nearby stars, is used to calibrate the cepheid stars that are at the edge of applicability of the parallax method. The cepheid based method is used to calibrate the supernovae based method using galaxies which are at the edge of validity of the cepheid method. These methods can span distances going from a few LYs to several billion LYs. The supernovae standard candles allow us to explore up to the edge of the visible Universe (13.1 BLY vs 13.7 BLY as of end of 2010).
If, for the time being, we assume that the speed of expansion is constant at all times, and that a(t) is the scale factor of the Universe at time t, Then the speed of recession will be proportional to d(a(t))/dt = a' and the distance between us and the observed galaxy would be proportional to a(t). Then the graph of a' vs a is the plot of speed of recession vs position for a given observed galaxy. If this operation is repeated a number of times by getting both values for galaxies at different cosmological distances we will generate a "Hubble graph". Edwin Hubble having generated the first such graph. The Hubble "constant" is given by the formula:
H = a'/a but a = a'T where T is the age of the Universe thus:
H = a'/a = a'/a'T = 1/T or T = 1/H
In other words, if the rate of universal expansion is constant then H is a constant related to the age of the Universe. Namely, its inverse 1/H is the age of the Universe.
If the rate of expansion is constant the Hubble graph will be a straight line whose slope will be the Hubble constant. On the other hand, if the plot of the observed values for a number of galaxies at various distances or depths turns out not to be a straight line then the rate of expansion is variable. In particular if our "telescopes" are weak, as they were in Hubble's time, we will only see the beginning of the graph and be likely to draw the conclusion that the slope is constant (straight line), but as the power of our "telescopes" increases we can see more & more of the real curve & find out that it is NOT a straight line. This is what has happened in the last decade or so with the launch & subsequent fixing of the Hubble space telescope & such other space based observatories such as COBE & WMAP. The actual curve has higher slope for the near space time and progressively lower slope for the far away time & places. That is, the Universe is expanding at an accellerating rate and we should talk of a Hubble parameter & not of a constant. A final point is that we can extrapolate the Hubble graph and estimate the total size of the Universe. This is true even though we can not ever see beyond the horizon where galaxies are moving away from us, at speed greater than the speed of light. Those very large portions of the Universe are as unaccessible by us as the region of a blackhole beyond its event horizon.