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A Big Rip is a finite-future-time cosmological singularity at which the scale factor, Hubble parameter, and phantom energy density diverge.

For conformal time $d\tau =dt/a$, the conformal Hubble parameter is $\mathcal{H}=a^{\prime }/a=aH=\dot{a}$, where primes and dots denote conformal and cosmic time derivatives respectively. Its inverse, in units $c=1$, is the comoving Hubble radius. It differs from the ordinary Hubble parameter by one factor of the scale factor.

Cosmic expansion stretches an emitted or absorbed spectral feature's wavelength by $1+z$. A small observed wavelength interval at fixed transition wavelength gives a redshift interval by division by the rest wavelength. Cosmological radial distances then require the Hubble parameter and, for proper distance at that epoch, an extra factor $1/(1+z)$.

Approximately constant positive Hubble parameter gives a nearly de Sitter spacetime expansion in flat slicing. Its scale factor can be approximated by $a=-1/(H\tau )$ with negative conformal time increasing toward zero. Slow variation of the expansion rate limits the accuracy of this approximation.

Suppose a homogeneous scalar field oscillates much faster than the Hubble parameter in a monomial potential $V(\varphi )=\lambda |\varphi {|}^n$. The virial theorem averaged over one oscillation gives $⟨{\dot{\varphi }}^2⟩=n⟨V⟩$, and henceA quadratic minimum therefore behaves like pressureless matter, whereas a quartic minimum behaves like radiation in cosmology.

The Hubble constant is the present value $H_0$ of the Hubble parameter. It sets the local proportionality between recession velocity and distance in the Hubble law.

Hubble friction is the damping term proportional to the Hubble parameter in a field or fluid equation in an expanding universe. A homogeneous scalar field, for example, has the term $3H\dot{\varphi }$ in its equation of motion.