Editing Hubble's law (section)

== Units derived from the Hubble constant ==
=== Hubble time ===
The Hubble constant {{math|''H''{{sub|0}}}} has units of inverse time; the '''Hubble time''' {{mvar|t{{sub|H}}}} is simply defined as the inverse of the Hubble constant,<ref>{{cite book |last1=Hawley |first1=John F. |title=Foundations of modern cosmology |last2=Holcomb |first2=Katherine A. |date=2005 |publisher=Oxford University Press |isbn=978-0-19-853096-1 |edition=2nd |location=Oxford [u.a.] |pages=304 |language=en-uk}}</ref> i.e.

<math display="block">t_H \equiv \frac{1}{H_0} = \frac{1}{67.8 \mathrm{~(km/s)/Mpc}} = 4.55\times 10^{17} \mathrm{~s} = 14.4 \text{ billion years}.</math>

This is slightly different from the [[age of the universe]], which is approximately 13.8&nbsp;billion years. The Hubble time is the age it would have had if the expansion had been linear,<ref>{{Cite book |last=Ridpath |first=Ian |title=A Dictionary of Astronomy |publisher=Oxford University Press |year=2012 |isbn=9780199609055 |edition=2nd |page=225 |language=en |doi=10.1093/acref/9780199609055.001.0001}}</ref> and it is different from the real age of the universe because the expansion is not linear; it depends on the energy content of the universe (see {{slink||Derivation of the Hubble parameter}}).

We currently appear to be approaching a period where the expansion of the universe is exponential due to the increasing dominance of [[vacuum energy]]. In this regime, the Hubble parameter is constant, and the universe grows by a factor [[E (mathematical constant)|{{mvar|e}}]] each Hubble time:

<math display="block">H \equiv \frac{\dot a}{a} = \textrm{constant} \quad \Longrightarrow \quad a \propto e^{Ht} = e^{\frac{t}{t_H}}</math>

Likewise, the generally accepted value of 2.27&nbsp;[[Exa-|Es]]<sup>−1</sup> means that (at the current rate) the universe would grow by a factor of {{mvar|e}}{{sup|2.27}} in one [[exasecond]].

Over long periods of time, the dynamics are complicated by general relativity, dark energy, [[Inflation (cosmology)|inflation]], etc., as explained above.

=== Hubble length ===
The Hubble length or Hubble distance is a unit of distance in cosmology, defined as {{math|''cH''{{sup|−1}}}} — the speed of light multiplied by the Hubble time. It is equivalent to 4,420 million parsecs or 14.4 billion light years. (The numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years.) Substituting {{math|1= ''D'' = ''cH''{{sup|−1}}}} into the equation for Hubble's law, {{math|''v'' {{=}} ''H''<sub>0</sub>''D''}} reveals that the Hubble distance specifies the distance from our location to those galaxies which are {{em|currently}} receding from us at the speed of light.

=== Hubble volume ===
{{main|Hubble volume}}
The Hubble volume is sometimes defined as a volume of the universe with a [[Comoving and proper distances|comoving]] size of {{math|''cH''{{sup|−1}}}}. The exact definition varies: it is sometimes defined as the volume of a sphere with radius {{math|''cH''{{sup|−1}}}}, or alternatively, a cube of side {{math|''cH''{{sup|−1}}}}. Some cosmologists even use the term Hubble volume to refer to the volume of the [[observable universe]], although this has a radius approximately three times larger.