Editing Hubble's law (section)

=== Time-dependence of Hubble parameter ===

The parameter {{mvar|H}} is commonly called the "Hubble constant", but that is a misnomer since it is constant in space only at a fixed time; it varies with time in nearly all cosmological models, and all observations of far distant objects are also observations into the distant past, when the "constant" had a different value. "Hubble parameter" is a more correct term, with {{math|''H''{{sub|0}}}} denoting the present-day value.

Another common source of confusion is that the accelerating universe does {{em|not}} imply that the Hubble parameter is actually increasing with time; since {{nowrap|<math> H(t) \equiv \dot{a}(t)/a(t) </math>,}} in most accelerating models <math>a</math> increases relatively faster than {{nowrap|<math>\dot{a}</math>,}} so {{mvar|H}} decreases with time. (The recession velocity of one chosen galaxy does increase, but different galaxies passing a sphere of fixed radius cross the sphere more slowly at later times.)

On defining the dimensionless [[deceleration parameter]] {{nowrap|<math display="inline"> q \equiv - \frac {\ddot{a}\, a} {\dot{a}^2} </math>,}} it follows that

<math display="block"> \frac{dH}{dt} = -H^2 (1+q) </math>

From this it is seen that the Hubble parameter is decreasing with time, unless {{math|''q'' < -1}}; the latter can only occur if the universe contains [[phantom energy]], regarded as theoretically somewhat improbable.

However, in the standard [[Lambda-CDM model|Lambda cold dark matter model]] (Lambda-CDM or ΛCDM model), {{mvar|q}} will tend to −1 from above in the distant future as the cosmological constant becomes increasingly dominant over matter; this implies that {{mvar|H}} will approach from above to a constant value of ≈&nbsp;57&nbsp;(km/s)/Mpc, and the scale factor of the universe will then grow exponentially in time.