# 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?

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