Hubble parameter

The Hubble parameter is the universe’s fractional expansion rate at a given cosmic time, equal to the rate of change of the cosmic scale factor divided by that factor.

Scale factor: A dimensionless quantity describing how cosmological distances change over time relative to a chosen reference epoch. The Hubble parameter is the scale factor’s time derivative divided by the scale factor itself.
Hubble constant: The present-day value of the Hubble parameter, commonly denoted H₀. It is the specific epoch’s expansion rate most directly measured by local distance methods.
Hubble tension: The persistent disagreement between early-universe and late-universe determinations of the present-day expansion rate. It centers on whether distinct methods recover the same present-day Hubble parameter.
Friedmann–Lemaître–Robertson–Walker metric: A homogeneous and isotropic spacetime geometry used to model the large-scale universe. Its scale factor provides the geometric quantity from which the Hubble parameter is defined.
Hubble's law: The observed relation in which a galaxy’s recession velocity is approximately proportional to its distance in the nearby universe. Its proportionality constant at the present epoch is the present-day Hubble parameter.
Cosmic distance ladder: A sequence of calibrated methods for measuring increasingly large astronomical distances. Its nearby-galaxy measurements help determine the present-day expansion rate.
Deceleration parameter: A dimensionless measure of whether the cosmic scale factor’s expansion is slowing down or speeding up. Unlike the Hubble parameter, it describes how the expansion rate changes rather than its fractional rate.
General relativity: A theory of gravity in which matter and energy shape spacetime geometry. The cosmological field equations of general relativity govern expansion in standard models.
Cosmological redshift: The increase in a photon’s wavelength caused by the expansion of the universe during its travel. Redshift records changes in the scale factor and helps infer expansion history.
Type Ia supernova: A thermonuclear stellar explosion whose predictable peak luminosity makes it a standardizable distance indicator. Supernova distances combined with redshifts constrain expansion across cosmic time.

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