When we have Hubble constant and it's inverse Hubble Time (1/H) what units are they measured in? I know Hubble constant is in "km/s per Mpc" but is there any other units which are popular used with it, and if so is there any conversion between the two? And would Hubble Time unit still be in billion years, seeing it is just displaying a time?
Answer
Although in theory we should all be using SI units, for things that are very large or very small these units are an inconvenient size and it's common to invent new units that are more convenient. So, for example particle physicists measure mass in GeV (strictly speaking GeV/$c^2$) and cosmologists measure distance in light years and/or parsecs.
In the case of the Hubble constant it has dimensions of $T^{-1}$ so the SI unit would be $s^{-1}$. The Hubble time has units of $T$ so the SI unit would be the second. However if we take the value for $H$ measured by Planck, $67 \text{km} \space \text{s}^{-1}/\text{Mpc}$, and convert to units of per second the value is about $2.2 \times 10^{-18} \text{s}^{-1}$, which is a lot harder to remember than the number $67$. That's why cosmologists use those rather strange units. As long as all cosmologists use the same units it doesn't really matter what the units are.
The Hubble constant isn't actually constant and will change in the future. Exactly how it changes depends on the behaviour of dark energy, which is somewhat uncertain at the moment.
Response to comment:
To convert the value of $H$ to $s^{-1}$:
The units of $H$ are (rearranging slightly) $s^{-1}\text{km}/\text{MPc}$. Kilometers and Megaparsecs are both units of length, so their ratio is a dimensionless number. If $N$ is the number of kilometers in a megaparsec then the ratio is just $1/N$. Google helpfully tells us that the number of km in an Mpc is $3.09 \times 10^{19}$, so to convert the Hubble constant to units of per second just divide it by $3.09 \times 10^{19}$.
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