information:classification
Time-dependence of Hubble parameter

The parameter 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 H denoting the present-day value.

Another common source of confusion is that the accelerating universe does not imply that the Hubble parameter is actually increasing with time; since H (t) ≡ a ˙ (t) / a (t) {\displaystyle H(t)\equiv {\dot {a}}(t)/a(t)}, in most accelerating models a {\displaystyle a} increases relatively faster than a ˙ {\displaystyle {\dot {a}}}, so 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 q ≡ − a ¨ a a ˙ 2 {\textstyle q\equiv -{\frac {{\ddot {a}}\,a}{{\dot {a}}^{2}}}}, it follows that

d H d t = − H 2 (1 + q) {\displaystyle {\frac {dH}{dt}}=-H^{2}(1+q)}

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

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