What is the current rate of change of the volume of the Universe? Is it possible to know the current rate of change of the volume of the Universe?  If we can't see past the cosmic horizon, can we still get a value for this rate of change, and if so, how would it be calculated?
 A: Physical distances are calculated from comoving distances as $l_{phys}=a\cdot l_{com}$, being $a$ the scale factor at any time. If you calculate the physical volume of the universe from its comoving volume, you get $V_{phys}=a^3\cdot V_{com}$. Of course, we don't know the total volume of the universe, if it exists, so you can calculate the relative rate of change at any time as $$\frac{\dot V_{phys}}{V_{phys}}=\frac{3a^2\dot a V_{com}}{a^3 V_{com}}=\frac{3\dot a}{a}=3H.$$ Then, evaluating today, with $H=H_0\approx 0.069\,\mathrm{Gyr^{-1}}$ you get $$\frac{\dot V_{phys}}{V_{phys}}\approx0.2\,\mathrm{Gyr^{-1}}.$$
A: I have modelled the vacuum as a set of identical, bi-modal, frequency-quantised quantum harmonic oscillators. Using some of the data from the Planck mission and taking the number of baryons in the universe as 10^80 yields the following:
the diameter of the universe is 94.3 x10^9 L yrs ( which compares favourably with that value estimated by Gott et al);
space is currently being created at the rate of 1.54 x 10^59 m^3/s, and this rate is itself currently increasing at the rate of 8.4 x 10^39 m^3/s.
