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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?

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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 $$\frac{\dot V_{phys}}{V_{phys}}\approx0.2\,\mathrm{Gyr^{-1}}.$$

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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.

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