Hubble Constant

The Hubble constant, usually denoted $H_0$, is the present-day rate of expansion of the universe per unit distance. It is a central parameter in cosmology and the proportionality coefficient in the Hubble–Lemaître law, which relates the recession velocities of galaxies participating in the cosmic expansion to their distances. Despite its name, it is not a quantity that must remain constant throughout cosmic history: it is the value of the time-dependent Hubble parameter at the present epoch. (ned.ipac.caltech.edu)

Definition and units

In a homogeneous expanding universe, the scale factor $a(t)$ describes how distances between locations moving with the cosmic expansion change with cosmic time. The Hubble parameter is

where a dot denotes differentiation with respect to time and $t_0$ is the present cosmic time. Thus, $H_0$ measures a fractional expansion rate, rather than an ordinary velocity or an acceleration. Its physical dimension is inverse time. (ned.ipac.caltech.edu)

Astronomers usually express it in kilometres per second per megaparsec:

A megaparsec is one million parsecs, approximately 3.26 million light-years. For illustration, if $H_0=70\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, the ideal expansion contribution to the recession velocity increases by $70\ \mathrm{km\,s^{-1}}$ for each additional megaparsec of distance. Expressed in the International System of Units, this illustrative value is about $2.27\times10^{-18}\ \mathrm{s^{-1}}$. Cosmologists also use the dimensionless quantity $h$, defined by

The value of $h$ must therefore be specified when interpreting distances or masses quoted with factors such as $h^{-1}$. (ned.ipac.caltech.edu)

Expansion, recession velocity, and redshift

For objects at fixed comoving positions, their proper separation $D(t)$, measured on a surface of equal cosmic time, scales with $a(t)$. Differentiating gives

Within this idealized description, the relation is exact. The observational approximation

is restricted to sufficiently small redshifts, where $c$ is the speed of light. At greater redshifts, converting observations into distances requires the expansion history and an appropriate cosmological distance definition, rather than simply identifying recession velocity with $cz$. (wwwmpa.mpa-garching.mpg.de)

Cosmological redshift reflects the stretching of light wavelengths during expansion:

where $t_{\mathrm{em}}$ is the time of emission. A galaxy’s measured redshift also contains contributions from its peculiar velocity—motion relative to the average cosmic expansion. Such motions complicate measurements using nearby galaxies, where they may be substantial compared with the expansion contribution. (ned.ipac.caltech.edu)

Cosmic recession is not identical to local motion through space. Proper-distance recession speeds can exceed $c$ without violating the local speed limit of special relativity. This distinction follows from the treatment of expanding spacetime in general relativity. The Hubble–Lemaître relation also does not imply a preferred center of expansion: in a homogeneous universe, the same relation applies around any comoving observer. (wwwmpa.mpa-garching.mpg.de)

Historical development

Georges Lemaître connected an expanding relativistic universe with a distance–velocity relation in 1927 and estimated its proportionality coefficient from available observations. Edwin Hubble published influential observational evidence for the relation in 1929. In October 2018, the International Astronomical Union recommended the name “Hubble–Lemaître law” to recognize both contributions; “Hubble constant” remains the conventional name of the parameter. (iau.org)

Measuring the coefficient proved much harder than establishing the broad relation. Uncertainties in the astronomical distance scale produced decades of disagreement, with estimates spanning roughly $40$ to $100\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$. Measuring $H_0$ to approximately ten-percent accuracy became a principal objective of the Hubble Space Telescope’s extragalactic distance-scale Key Project, which combined Cepheid distances with several independent secondary distance indicators. (pdg.lbl.gov)

Measurement methods

The cosmic distance ladder

The cosmic distance ladder links nearby objects with geometrically measurable distances to brighter objects observable much farther away. A widely used implementation has three stages:

1. Geometric anchors, including stellar parallaxes, eclipsing binary systems, and water-maser measurements.
2. Cepheid variables, whose pulsation periods correlate with their luminosities and allow distances to galaxies hosting them to be determined.
3. Type Ia supernovae, calibrated using nearby host galaxies and then observed at distances where cosmic expansion dominates peculiar motions.

These supernovae are standardizable candles: their inferred luminosities require corrections based on observed properties rather than being assumed identical. A 2022 analysis by the SH0ES collaboration reported

including its assessed systematic uncertainties. (arxiv.org)

Alternative stellar calibrators include the tip of the red giant branch, a characteristic luminosity boundary in populations of evolving stars. A 2025 Chicago–Carnegie Hubble Program analysis using Hubble and James Webb Space Telescope observations reported $70.39\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, with separately quoted statistical, systematic, and supernova-related uncertainties. The differing central values illustrate why the choice and calibration of distance indicators matter. (doi.org)

Cosmic microwave background inference

The cosmic microwave background provides a different route. Its temperature and polarization patterns constrain early-universe conditions and characteristic physical scales. A cosmological model then connects those conditions to distances and expansion at later times.

Using the base six-parameter Lambda–Cold Dark Matter model, the Planck collaboration’s 2018 data analysis, published in 2020, inferred

This is a model-dependent inference, not a direct measurement of present-day galaxy recession divided by distance. Changing assumptions about spatial curvature, neutrinos, or the expansion history can change the inferred value and its uncertainty. (arxiv.org)

Other approaches

Several techniques provide complementary constraints:

• Inverse distance ladders use baryon acoustic oscillations to establish a distance scale and supernovae to trace relative distances. Their absolute calibration depends on assumptions or information about the early-universe sound horizon.
• Time-delay gravitational lensing uses the different arrival times of variable light seen through multiple images of a background source. The inferred distance depends on modeling the lens’s mass distribution and surrounding matter. (pdg.lbl.gov)
• Standard sirens obtain luminosity distances from gravitational-wave signals. Combining these with source redshifts constrains $H_0$ without the conventional stellar distance ladder. The neutron-star merger GW170817 enabled the first such measurement in 2017. (arxiv.org)

The Hubble tension

The Hubble tension is the discrepancy between some late-universe determinations of $H_0$, especially Cepheid-calibrated supernova measurements, and values inferred from early-universe observations under the standard cosmological model. Both approaches target the same present-day parameter; the discrepancy is not simply the expected difference between expansion rates at different cosmic epochs. Comparing the quoted Planck and 2022 SH0ES results gives a difference of about five combined standard deviations under their stated error assumptions. (arxiv.org)

Its interpretation depends on both observational calibration and model assumptions. Investigations examine stellar crowding, dust, chemical-composition effects, supernova calibration, peculiar motions, and possible changes to early- or late-universe physics. Alternative measurements do not all yield the same central value or achieve the same precision. The Particle Data Group’s December 2025 review described the tension as still under investigation, rather than as an established detection of new physics. (arxiv.org)

Cosmological significance and limitations

The Hubble constant establishes characteristic time and distance scales:

For the illustrative value $70\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, these are approximately 14 billion years and 4.3 gigaparsecs. The Hubble time is not automatically the age of the universe, and the Hubble distance is not generally the boundary of the observable universe. Actual ages and horizons depend on the full expansion history. (ned.ipac.caltech.edu)

The present age in a cosmological model beginning with a Big Bang is obtained from

with the present scale factor normalized to one. The expansion history is governed by the Friedmann equations. In a model with matter, radiation, spatial curvature, and a cosmological constant, it can be written

where the $\Omega$ quantities describe the corresponding present-day contributions. Matter includes ordinary matter and dark matter; the cosmological constant is one possible description of dark energy. (ned.ipac.caltech.edu)

The constant also sets the present critical mass density,

which supplies a reference for cosmological density parameters. It enters the conversion of redshifts and angular sizes into physical distances, and therefore influences inferred galaxy luminosities, sizes, and masses. Nevertheless, $H_0$ alone does not determine the universe’s age, geometry, acceleration, or eventual fate: those require additional information about its contents and their evolution. (ned.ipac.caltech.edu)

References

1. HST Key Project Summary - W. Freedman et al.ned.ipac.caltech.edu
2. TASI Lectures: Introduction to Cosmologyned.ipac.caltech.edu
3. Distance Measures in Cosmology: The Hubble Constantned.ipac.caltech.edu
4. Distance Measures in Cosmology: Redshiftned.ipac.caltech.edu
5. Distance Measures in Cosmology: Cosmological Parametersned.ipac.caltech.edu
6. Distance Measures in Cosmology: Lookback Timened.ipac.caltech.edu
7. Astrophysical Constants and Parameterspdg.lbl.gov
8. IAU members vote to recommend renaming the Hubble law as the Hubble–Lemaître lawiauarchive.eso.org
9. Cosmological Parameterspdg.lbl.gov
10. A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Teamarxiv.org