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Hubble's law (Hubble–Lemaître law): expansion of the universe

An overview of Hubble's law, its historical origin, formulation, measurement methods, cosmological interpretation and important caveats about redshift, distances and the Hubble constant.

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Overview

Hubble's law is the empirical relation that, on sufficiently large scales, galaxies appear to recede from one another with speeds that increase roughly in proportion to their distance. Observationally this relation is seen through the redshift of light from distant sources, often described in simple terms as a Doppler shift. The proportionality between recession speed and distance is usually written as v = H0D, where H0 is the Hubble constant. The law is a direct manifestation of the increasing scale of space-time in the observable portion of the cosmos; the expanding geometry of the observable universe is central to modern cosmology and supports the general framework commonly called the Big Bang model.

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Formulation and key concepts

The simple linear form, that velocity is proportional to distance, is accurate for relatively nearby galaxies (low redshift). The slope is the Hubble constant, conventionally expressed in units such as (km/s)/Mpc. From this constant one can define characteristic scales such as the Hubble time (an order-of-magnitude age) and the Hubble radius (a distance at which recession speed would equal the speed of light in the naive extrapolation). Several distinct distance measures are used in cosmology — proper distance, comoving distance and luminosity distance — and care is required when applying the law to high-redshift objects because the simple velocity–distance picture is replaced by a metric description derived from general relativity.

History and attribution

The theoretical possibility of an expanding universe was derived from general relativity and worked out in published form in the late 1920s by Georges Lemaître, who related cosmic expansion to the redshifts observed in galaxies. Observational confirmation followed from the distance and redshift measurements that astronomers including Vesto Slipher and later Edwin Hubble combined into an empirical linear trend. Because of the complementary theoretical and observational roles, the relation is commonly known today as the Hubble–Lemaître law; both Georges Lemaître and Edwin Hubble are associated with its development.

How the Hubble constant is measured

Determining H0 has employed a variety of distance ladders and independent methods. Typical approaches include:

  • Local distance ladders using Cepheid variable stars and Type Ia supernovae, often relying on observations from space telescopes such as the HST.
  • Large-scale structure and baryon acoustic oscillations, which probe the clustering of matter at cosmological scales.
  • Analysis of the cosmic microwave background and its anisotropies, which infer the expansion rate from early-universe physics.
  • Independent geometric or time-delay methods, such as measurements from gravitational lensing of variable sources.

Different methods have produced slightly different values in recent years, with local-distance measurements tending to give higher numbers and early-universe (CMB-based) inferences yielding lower ones. This discrepancy—often called the "Hubble tension"—is an active area of research because it may indicate unrecognized systematic errors or new physics in cosmology.

Importance, interpretation and caveats

Hubble's law is more than an observational rule: it encapsulates the idea that space itself is stretching so that distant objects increase their separation even when there is no local motion through space. At cosmological distances the redshift should be interpreted as a change in the scale factor of the universe rather than exactly the classical Doppler effect. One striking consequence is that sufficiently remote galaxies can have recession speeds greater than the speed of light without violating relativity, because that limit applies to motion through space, not to the metric expansion of space itself.

Notable facts and practical effects

The Hubble flow—the systematic recession of galaxies—dominates over random or "peculiar" velocities only on large scales; nearby galaxies can show significant local motions that mask the linear relation. For precise cosmological work it is therefore necessary to model peculiar velocities, select appropriate distance indicators, and use the full relativistic framework. Measurements of the expansion rate feed directly into estimates of the universe's age, its energy composition (including dark energy) and its future behaviour, making the Hubble constant one of the most important parameters in modern astronomy.

For further technical introductions and data compilations, readers may consult specialized reviews and survey papers through standard scientific resources.

stages of the universe's evolution. The Hubble parameter indicates the instantaneous rate of expansion at any point in time.
stages of the universe's evolution. The Hubble parameter indicates the instantaneous rate of expansion at any point in time.

Definition

The expansion of the universe is quantitatively described by the scale factor {\displaystyle a(t)}, with the freely defined present-day value {\displaystyle a(t_{0})=1}, whose time evolution is given as a solution of the Friedmann equations of relativistic cosmology. The time-dependent Hubble parameter describes the expansion rate and is defined by

H(t)={\frac {{\dot a}(t)}{a(t)}},

Where is {\dot a}(t)the time derivative of the scale factor.

The present value of the Hubble parameter is called the Hubble constant : H_{0}

{\displaystyle H_{0}=H(t_{0})={\dot {a}}(t_{0})}

with the world age t_{0} . The measured value of the Hubble constant provides the initial condition for solving the Friedmann equations. The Hubble parameter decreases with time because the expansion is slowed down by the gravitation of matter in the universe, so it has always been larger in retrospect than it is today.

The ratio of the Hubble parameter to the present value is given as the expansion factor and can also be {\displaystyle \rho (t)}calculated using the respective total density ρ This relation is the Friedmann equation in general form:

{\displaystyle E(t)={\frac {H(t)}{H(t_{0})}}={\sqrt {\frac {\rho (t)}{\rho (t_{0})}}}}

The time derivative of the Hubble parameter gives:

{\displaystyle {\dot {H}}(t)={\frac {{\ddot {a}}(t)}{a(t)}}-H(t)^{2}}

The Hubble flux denotes the rate at which spatial distances increase for the same world age and, by its very nature, cannot be observed directly because of the transit time of light:

{\displaystyle {\dot {D}}(t)=H(t)\cdot D(t)=H(t)\cdot D(t_{0})\cdot a(t)={\dot {a}}(t)\cdot D(t_{0})}

In the local universe (i.e., over distances that are small compared to the radius of the observable universe), the Hubble constant is the constant of proportionality of the (approximately) linear relationship between the distances Dof galaxies and the redshifts measured from their spectra. z:

c\cdot z\approx H_{0}\cdot D.

Where cthe speed of light.

Often the product c\cdot z is vinterpreted approximately as recession velocity sense of the Doppler effect, one then obtains

{\displaystyle v\approx H_{0}\cdot D.}

The precise relationship between cosmological redshift and distance is nonlinear and requires integration over the time course of the scale factor {\displaystyle a(t)}.

Hubble diagram

The plot of the redshift of astronomical objects against their distance from Earth is called a Hubble diagram. A uniformly expanding universe causes the objects in this diagram to be arranged along a straight line passing through the origin. The slope of this straight line is the Hubble constant.

The first Hubble diagram was published by Edwin Hubble in 1929. In this publication he reported a linear relationship between the distance of galaxies (extragalactic nebula) and their redshift. Determining the distance of a distant astronomical object without recourse to redshift is done from the brightness of standard candles. For this purpose, the image of the object must be so well resolved that no light from other objects distorts the measurement result. This becomes increasingly difficult with increasing distance. The data used in the first Hubble diagram extended to a distance of about 2 Mpc. Almost a century later, measurements up to about 700 Mpc are possible. This allows a much more reliable indication of the Hubble constant.

Questions and answers

Q: What is Hubble's law?

A: Hubble's law, or the Hubble–Lemaître law, is an astronomical observation that all objects observed in deep space have a doppler shift-measured velocity relative to Earth and other interstellar bodies that is proportional to their distance from them. It also states that the space-time volume of the observable universe is expanding.

Q: Who first derived this law?

A: The law was first derived from General Relativity equations by Georges Lemaître in a 1927 article.

Q: Who confirmed its existence?

A: Edwin Hubble confirmed the existence of the law two years later and got a more accurate value for the constant that now bears his name.

Q: How was recession velocity measured?

A: Recession velocity was inferred from redshifts as measured earlier by Vesto Slipher in 1917 and related to velocity by him.

Q: What equation expresses this law?

A: The law is often expressed by the equation v = H0D, with H0 being the constant of proportionality (the Hubble constant) between proper distance D to a galaxy and its velocity v.

Q: What unit does H0 usually come in?

A: H0 is usually quoted in (km/s)/Mpc, which gives the speed in km/s of a galaxy 1 megaparsec (3.09×1019 km) away.

Q: What has been suggested about recent estimates of H0? A Recent 2011 estimate suggests that H0 = 73.8 ± 2.4 (km/s)/Mpc while an alternate approach using data from galactic clusters gave a value of 67 ± 3.2 (km/s)/Mpc with other methods giving figures between 70 and 72 (km/s)/Mpc . A recent 2016 method suggests that it may have been 66.53 km/s per megaparsec soon after expansion began, implying an increasing rate of expansion over time

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