An analogy for explaining Hubble's law, usingraisins in a rising loaf of bread in place of galaxies. If a raisin is twice as far away from a place as another raisin, then the farther raisin would move away from that place twice as quickly.
Hubble's law, also known as theHubble–Lemaître law,[1] is the observation inphysical cosmology thatgalaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther a galaxy is from the Earth, the faster it moves away. A galaxy'srecessional velocity is typically determined by measuring itsredshift, a shift in the frequency oflight emitted by the galaxy.
The discovery of Hubble's law is attributed to work published byEdwin Hubble in 1929,[2][3][4] but the notion of the universe expanding at a calculable rate was first derived fromgeneral relativity equations in 1922 byAlexander Friedmann. TheFriedmann equations showed the universe might be expanding, and presented the expansion speed if that were the case.[5] Before Hubble, astronomerCarl Wilhelm Wirtz had, in 1922[6] and 1924,[7] deduced with his own data that galaxies that appeared smaller and dimmer had larger redshifts and thus that more distant galaxies recede faster from the observer. In 1927,Georges Lemaître concluded that the universe might be expanding by noting the proportionality of the recessional velocity of distant bodies to their respective distances. He estimated a value for this ratio, which—after Hubble confirmed cosmic expansion and determined a more precise value for it two years later—became known as the Hubble constant.[8][9][10][11][12] Hubble inferred the recession velocity of the objects from theirredshifts, many of which were earlier measured and related to velocity byVesto Slipher in 1917.[13][14][15] Combining Slipher's velocities withHenrietta Swan Leavitt's intergalactic distance calculations and methodology allowed Hubble to better calculate an expansion rate for the universe.[16]
Hubble's law is considered the first observational basis for theexpansion of the universe, and is one of the pieces of evidence most often cited in support of theBig Bang model.[8][17] The motion of astronomical objects due solely to this expansion is known as theHubble flow.[18] It is described by the equationv =H0D, withH0 the constant of proportionality—theHubble constant—between the "proper distance"D to a galaxy (which can change over time, unlike thecomoving distance) and its speed of separationv, i.e. thederivative of proper distance with respect to thecosmic time coordinate.[a] Though the Hubble constantH0 is constant at any given moment in time, theHubble parameterH, of which the Hubble constant is the current value, varies with time, so the termconstant is sometimes thought of as somewhat of a misnomer.[19][20]
The Hubble constant is most frequently quoted inkm/s/Mpc, which gives the speed of a galaxy 1 megaparsec (3.09×1019 km) away as70 km/s. Simplifying the units of the generalized form reveals thatH0 specifies afrequency (SI unit:s−1), leading the reciprocal ofH0 to be known as theHubble time (14.4 billion years). The Hubble constant can also be stated as a relative rate of expansion. In this formH0 = 7%/Gyr, meaning that, at the current rate of expansion, it takes one billion years for an unbound structure to grow by 7%.
In 1912,Vesto M. Slipher measured the firstDoppler shift of a "spiral nebula" (the obsolete term for spiral galaxies) and soon discovered that almost all such objects were receding from Earth. He did not grasp the cosmological implications of this fact, and indeed at the time it washighly controversial whether or not these nebulae were "island universes" outside the Milky Way galaxy.[22][23]
In 1927, two years before Hubble published his own article, the Belgian priest and astronomer Georges Lemaître was the first to publish research deriving what is now known as Hubble's law. According to the Canadian astronomerSidney van den Bergh, "the 1927 discovery of the expansion of the universe by Lemaître was published in French in a low-impact journal. In the 1931 high-impact English translation of this article, a critical equation was changed by omitting reference to what is now known as the Hubble constant."[25] It is now known that the alterations in the translated paper were carried out by Lemaître himself.[10][26]
Before the advent of modern cosmology, there was considerable talk about the size andshape of the universe. In 1920, theShapley–Curtis debate took place betweenHarlow Shapley andHeber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy, and Curtis argued that the universe was much larger. The issue was resolved in the coming decade with Hubble's improved observations.
Edwin Hubble did most of his professional astronomical observing work atMount Wilson Observatory,[27] home to the world's most powerful telescope at the time. His observations ofCepheid variable stars in "spiral nebulae" enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. They continued to be callednebulae, and it was only gradually that the termgalaxies replaced it.
The velocities and distances that appear in Hubble's law are not directly measured. The velocities are inferred from the redshiftz = ∆λ/λ of radiation and distance is inferred from brightness. Hubble sought to correlate brightness with parameterz.
Combining his measurements of galaxy distances with Vesto Slipher andMilton Humason's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality between redshift of an object and its distance. Though there was considerablescatter (now known to be caused bypeculiar velocities—the 'Hubble flow' is used to refer to the region of space far enough out that the recession velocity is larger than local peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 (km/s)/Mpc (much higher than the currently accepted value due to errors in his distance calibrations; seecosmic distance ladder for details).[29]
Hubble's law can be easily depicted in a "Hubble diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer.[30] A straight line of positive slope on this diagram is the visual depiction of Hubble's law.
After Hubble's discovery was published,Albert Einstein abandoned his work on thecosmological constant, aterm he had inserted into his equations of general relativity to coerce them into producing the static solution he previously considered the correct state of the universe. The Einstein equations in their simplest form model either an expanding or contracting universe, so Einstein introduced the constant to counter expansion or contraction and lead to a static and flat universe.[31] After Hubble's discovery that the universe was, in fact, expanding, Einstein called his faulty assumption that the universe is static his "greatest mistake".[31] On its own, general relativity could predict the expansion of the universe, which (throughobservations such as thebending of light by large masses, or theprecession of the orbit of Mercury) could be experimentally observed and compared to his theoretical calculations using particular solutions of the equations he had originally formulated.
In 1931, Einstein went to Mount Wilson Observatory to thank Hubble for providing the observational basis for modern cosmology.[32]
The cosmological constant has regained attention in recent decades as a hypothetical explanation fordark energy.[33]
A variety of possible recessional velocity vs. redshift functions including the simple linear relationv =cz; a variety of possible shapes from theories related to general relativity; and a curve that does not permit speeds faster than light in accordance with special relativity. All curves are linear at low redshifts.[34]
The discovery of the linear relationship between redshift and distance, coupled with a supposed linear relation betweenrecessional velocity and redshift, yields a straightforward mathematical expression for Hubble's law as follows:
where
v is the recessional velocity, typically expressed in km/s.
H0 is Hubble's constant and corresponds to the value ofH (often termed theHubble parameter which is a value that istime dependent and which can be expressed in terms of thescale factor) in the Friedmann equations taken at the time of observation denoted by the subscript0. This value is the same throughout the universe for a givencomoving time.
D is the proper distance (which can change over time, unlike thecomoving distance, which is constant) from thegalaxy to the observer, measured inmegaparsecs (Mpc), in the 3-space defined by givencosmological time. (Recession velocity is justv =dD/dt).
Hubble's law is considered a fundamental relation between recessional velocity and distance. However, the relation between recessional velocity and redshift depends on the cosmological model adopted and is not established except for small redshifts.
Since the Hubble "constant" is a constant only in space, not in time, the radius of the Hubble sphere may increase or decrease over various time intervals. The subscript '0' indicates the value of the Hubble constant today.[28] Current evidence suggests that the expansion of the universe is accelerating (seeAccelerating universe), meaning that for any given galaxy, the recession velocitydD/dt is increasing over time as the galaxy moves to greater and greater distances; however, the Hubble parameter is actually thought to be decreasing with time, meaning that if we were to look at somefixed distanceD and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones.[35]
Redshift can be measured by determining the wavelength of a known transition, such as hydrogen α-lines for distant quasars, and finding the fractional shift compared to a stationary reference. Thus, redshift is a quantity unambiguously acquired from observation. Care is required, however, in translating these to recessional velocities: for small redshift values, a linear relation of redshift to recessional velocity applies, but more generally the redshift-distance law is nonlinear, meaning the co-relation must be derived specifically for each given model and epoch.[36]
The redshiftz is often described as aredshift velocity, which is the recessional velocity that would produce the same redshiftif it were caused by a linearDoppler effect (which, however, is not the case, as the velocities involved are too large to use a non-relativistic formula for Doppler shift). This redshift velocity can easily exceed the speed of light.[37] In other words, to determine the redshift velocityvrs, the relation:
is used.[38][39] That is, there isno fundamental difference between redshift velocity and redshift: they are rigidly proportional, and not related by any theoretical reasoning. The motivation behind the "redshift velocity" terminology is that the redshift velocity agrees with the velocity from a low-velocity simplification of the so-calledFizeau–Doppler formula[40]
Here,λo,λe are the observed and emitted wavelengths respectively. The "redshift velocity"vrs is not so simply related to real velocity at larger velocities, however, and this terminology leads to confusion if interpreted as a real velocity. Next, the connection between redshift or redshift velocity and recessional velocity is discussed.[41]
SupposeR(t) is called thescale factor of the universe, and increases as the universe expands in a manner that depends upon thecosmological model selected. Its meaning is that all measured proper distancesD(t) between co-moving points increase proportionally toR. (The co-moving points are not moving relative to their local environments.) In other words:
wheret0 is some reference time.[42] If light is emitted from a galaxy at timete and received by us att0, it is redshifted due to the expansion of the universe, and this redshiftz is simply:
Suppose a galaxy is at distanceD, and this distance changes with time at a ratedtD. We call this rate of recession the "recession velocity"vr:
We now define the Hubble constant as
and discover the Hubble law:
From this perspective, Hubble's law is a fundamental relation between (i) the recessional velocity associated with the expansion of the universe and (ii) the distance to an object; the connection between redshift and distance is a crutch used to connect Hubble's law with observations. This law can be related to redshiftz approximately by making aTaylor series expansion:
If the distance is not too large, all other complications of the model become small corrections, and the time interval is simply the distance divided by the speed of light:
or
According to this approach, the relationcz =vr is an approximation valid at low redshifts, to be replaced by a relation at large redshifts that is model-dependent. Seevelocity-redshift figure.
Strictly speaking, neitherv norD in the formula are directly observable, because they are propertiesnow of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it.
For relatively nearby galaxies (redshiftz much less than one),v andD will not have changed much, andv can be estimated using the formulav = zc wherec is the speed of light. This gives the empirical relation found by Hubble.
For distant galaxies,v (orD) cannot be calculated fromz without specifying a detailed model for howH changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation:(1 +z) is the factor by which the universe has expanded while the photon was traveling towards the observer.
In using Hubble's law to determine distances, only the velocity due to the expansion of the universe can be used. Since gravitationally interacting galaxies move relative to each other independent of the expansion of the universe,[43] these relative velocities, called peculiar velocities, need to be accounted for in the application of Hubble's law. Such peculiar velocities give rise toredshift-space distortions.
The parameterH 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, withH0 denoting the present-day value.
Another common source of confusion is that the accelerating universe doesnot imply that the Hubble parameter is actually increasing with time; since, in most accelerating models increases relatively faster than, soH 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.)
From this it is seen that the Hubble parameter is decreasing with time, unlessq < -1; the latter can only occur if the universe containsphantom energy, regarded as theoretically somewhat improbable.
However, in the standardLambda 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 thatH 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.
The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensionalCartesian/Newtonian coordinate space, which, considered as ametric space, is entirelyhomogeneous and isotropic (properties do not vary with location or direction). Simply stated, the theorem is this:
Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.
In fact, this applies to non-Cartesian spaces as long as they are locally homogeneous and isotropic, specifically to the negatively and positively curved spaces frequently considered as cosmological models (seeshape of the universe).
An observation stemming from this theorem is that seeing objects recede from us on Earth is not an indication that Earth is near to a center from which the expansion is occurring, but rather thatevery observer in an expanding universe will see objects receding from them.
Theage andultimate fate of the universe can be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterized by values of density parameters (ΩM formatter andΩΛ for dark energy). Aclosed universe withΩM > 1 andΩΛ = 0 comes to an end in aBig Crunch and is considerably younger than its Hubble age. Anopen universe withΩM ≤ 1 andΩΛ = 0 expands forever and has an age that is closer to its Hubble age. For the accelerating universe with nonzeroΩΛ that we inhabit, the age of the universe is coincidentally very close to the Hubble age.
The value of the Hubble parameter changes over time, either increasing or decreasing depending on the value of the so-calleddeceleration parameterq, which is defined by
In a universe with a deceleration parameter equal to zero, it follows thatH = 1/t, wheret is the time since the Big Bang. A non-zero, time-dependent value ofq simply requiresintegration of the Friedmann equations backwards from the present time to the time when thecomoving horizon size was zero.
It was long thought thatq was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than1/H (which is about 14 billion years). For instance, a value forq of 1/2 (once favoured by most theorists) would give the age of the universe as2/(3H). The discovery in 1998 thatq is apparently negative means that the universe could actually be older than1/H. However, estimates of theage of the universe are very close to1/H.
The expansion of space summarized by the Big Bang interpretation of Hubble's law is relevant to the old conundrum known asOlbers' paradox: If the universe wereinfinite in size,static, and filled with a uniform distribution ofstars, then every line of sight in the sky would end on a star, and the sky would be asbright as the surface of a star. However, the night sky is largely dark.[44][45]
Since the 17th century, astronomers and other thinkers have proposed many possible ways to resolve this paradox, but the currently accepted resolution depends in part on the Big Bang theory, and in part on the Hubble expansion: in a universe that existed for a finite amount of time, only the light of a finite number of stars has had enough time to reach us, and the paradox is resolved. Additionally, in an expanding universe, distant objects recede from us, which causes the light emanated from them to be redshifted and diminished in brightness by the time we see it.[44][45]
Instead of working with Hubble's constant, a common practice is to introduce thedimensionless Hubble constant, usually denoted byh and commonly referred to as "little h",[29] then to write Hubble's constantH0 ash × 100 km⋅s−1⋅Mpc−1, all the relative uncertainty of the true value ofH0 being then relegated toh.[46] The dimensionless Hubble constant is often used when giving distances that are calculated from redshiftz using the formulad ≈c/H0 ×z. SinceH0 is not precisely known, the distance is expressed as:
In other words, one calculates 2998 ×z and one gives the units as Mpc h-1 orh-1 Mpc.
Occasionally a reference value other than 100 may be chosen, in which case a subscript is presented afterh to avoid confusion; e.g.h70 denotesH0 = 70h70(km/s)/Mpc, which impliesh70 =h / 0.7.
This should not be confused with thedimensionless value of Hubble's constant, usually expressed in terms ofPlanck units, obtained by multiplyingH0 by1.75×10−63 (from definitions of parsec andtP), for example forH0 = 70, a Planck unit version of1.2×10−61 is obtained.
A value forq measured fromstandard candle observations ofType Ia supernovae, which was determined in 1998 to be negative, surprised many astronomers with the implication that the expansion of the universe is currently "accelerating"[47] (although the Hubble factor is still decreasing with time, as mentioned above in theInterpretation section; see the articles ondark energy and the ΛCDM model).
whereH is the Hubble parameter,a is thescale factor,G is thegravitational constant,k is the normalised spatial curvature of the universe and equal to −1, 0, or 1, andΛ is the cosmological constant.
Matter-dominated universe (with a cosmological constant)
If the universe ismatter-dominated, then the mass density of the universeρ should be taken to include just matter so
whereρm0 is the density of matter today. From the Friedmann equation and thermodynamic principles we know for non-relativistic particles that their mass density decreases proportional to the inverse volume of the universe, so the equation above must be true. We can also define (seedensity parameter forΩm)
therefore:
Also, by definition,
where the subscript0 refers to the values today, anda0 = 1. Substituting all of this into the Friedmann equation at the start of this section and replacinga witha = 1/(1+z) gives
If the universe is both matter-dominated and dark energy-dominated, then the above equation for the Hubble parameter will also be a function of theequation of state of dark energy. So now:
whereρde is the mass density of the dark energy. By definition, an equation of state in cosmology isP =wρc2, and if this is substituted into the fluid equation, which describes how the mass density of the universe evolves with time, then
Ifw is constant, then
implying:
Therefore, for dark energy with a constant equation of statew,. If this is substituted into the Friedman equation in a similar way as before, but this time setk = 0, which assumes a spatially flat universe, then (seeshape of the universe)
If the dark energy derives from a cosmological constant such as that introduced by Einstein, it can be shown thatw = −1. The equation then reduces to the last equation in the matter-dominated universe section, withΩk set to zero. In that case the initial dark energy densityρde0 is given by[48]
If dark energy does not have a constant equation-of-statew, then
and to solve this,w(a) must be parametrized, for example ifw(a) =w0 +wa(1−a), giving[49]
The Hubble constantH0 has units of inverse time; theHubble timetH is simply defined as the inverse of the Hubble constant,[50] i.e.
This is slightly different from theage of the universe, which is approximately 13.8 billion years. The Hubble time is the age it would have had if the expansion had been linear,[51] and it is different from the real age of the universe because the expansion is not linear; it depends on the energy content of the universe (see§ Derivation of the Hubble parameter).
We currently appear to be approaching a period where the expansion of the universe is exponential due to the increasing dominance ofvacuum energy. In this regime, the Hubble parameter is constant, and the universe grows by a factore each Hubble time:
Likewise, the generally accepted value of 2.27 Es−1 means that (at the current rate) the universe would grow by a factor ofe2.27 in oneexasecond.
Over long periods of time, the dynamics are complicated by general relativity, dark energy,inflation, etc., as explained above.
The Hubble length or Hubble distance is a unit of distance in cosmology, defined ascH−1 — the speed of light multiplied by the Hubble time. It is equivalent to 4,420 million parsecs or 14.4 billion light years. (The numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years.) SubstitutingD =cH−1 into the equation for Hubble's law,v =H0D reveals that the Hubble distance specifies the distance from our location to those galaxies which arecurrently receding from us at the speed of light.
The Hubble volume is sometimes defined as a volume of the universe with acomoving size ofcH−1. The exact definition varies: it is sometimes defined as the volume of a sphere with radiuscH−1, or alternatively, a cube of sidecH−1. Some cosmologists even use the term Hubble volume to refer to the volume of theobservable universe, although this has a radius approximately three times larger.
The value of the Hubble constant in (km/s)/Mpc, including measurement uncertainty, for recent surveys[52]
The value of the Hubble constant,H0, cannot be measured directly, but is derived from a combination of astronomical observations and model-dependent assumptions. Increasingly accurate observations and new models over many decades have led to two sets of highly precise values which do not agree. This difference is known as the "Hubble tension".[8][53]
For the original 1929 estimate of the constant now bearing his name, Hubble used observations ofCepheid variable stars as "standard candles" to measure distance.[54] The result he obtained was500 (km/s)/Mpc, much larger than the value astronomers currently calculate. Later observations by astronomerWalter Baade led him to realize that there were distinct "populations" for stars (Population I and Population II) in a galaxy. The same observations led him to discover that there are two types of Cepheid variable stars with different luminosities. Using this discovery, he recalculated Hubble constant and the size of the known universe, doubling the previous calculation made by Hubble in 1929.[55][56][54] He announced this finding to considerable astonishment at the 1952 meeting of theInternational Astronomical Union in Rome.
For most of the second half of the 20th century, the value ofH0 was estimated to be between50 and 90 (km/s)/Mpc.
The value of the Hubble constant was the topic of a long and rather bitter controversy betweenGérard de Vaucouleurs, who claimed the value was around 100, andAllan Sandage, who claimed the value was near 50.[57] In one demonstration of vitriol between the parties, when Sandage and his colleagueGustav Andreas Tammann formally acknowledged the shortcomings of confirming the systematic error of their method in 1975, Vaucouleurs responded: "It is unfortunate that this sober warning was so soon forgotten and ignored by most astronomers and textbook writers".[58] In 1996, a debate moderated byJohn Bahcall between Sidney van den Bergh and Gustav Tammann was held in similar fashion to the earlier Shapley–Curtis debate over these two competing values.
This previously wide variance in estimates was partially resolved with the introduction of theΛCDM model of the universe in the late 1990s. Incorporating the ΛCDM model, observations of high-redshift clusters at X-ray and microwave wavelengths using theSunyaev–Zel'dovich effect, measurements of anisotropies in thecosmic microwave background radiation, and optical surveys all gave a value of around 50–70 km/s/Mpc for the constant.[59]
By the late 1990s, advances in ideas and technology allowed higher precision measurements.[60]However, two major categories of methods, each with high precision, fail to agree."Late universe" measurements using calibrated distance ladder techniques have converged on a value of approximately73 (km/s)/Mpc. Since 2000, "early universe" techniques based on measurements of thecosmic microwave background have become available, and these agree on a value near67.7 (km/s)/Mpc.[61] (This accounts for the change in the expansion rate since the early universe, so is comparable to the first number.) Initially, this discrepancy was within the estimatedmeasurement uncertainties and thus no cause for concern. However, as techniques have improved, the estimated measurement uncertainties have shrunk, but the discrepancies havenot, to the point that the disagreement is now highlystatistically significant. This discrepancy is called theHubble tension.[62][63]
An example of an "early" measurement, thePlanck mission published in 2018 gives a value forH0 = of67.4±0.5 (km/s)/Mpc.[64] In the "late" camp is the higher value of74.03±1.42 (km/s)/Mpc determined by theHubble Space Telescope[65] and confirmed by theJames Webb Space Telescope in 2023.[66][67]The "early" and "late" measurements disagree at the >5σ level, beyond a plausible level of chance.[68][69] The resolution to this disagreement is an ongoing area of active research.[70]
The landscape of H0 measurements around 2021, with the 2018 results from CMB measurements highlighted in pink and 2020 distance ladder values highlighted in cyan.[63]
Since 2013, extensive checks for possible systematic errors and improvements in reproducibility have been undertaken.[53]
The "late universe" or distance ladder measurements typically employ three stages or "rungs". In the first rung, distances toCepheids are determined while trying to reduce luminosity errors from dust and correlations ofmetallicity with luminosity. The second rung usesType Ia supernova, explosions of almost constant amounts of mass. Thusly, these produce very similar amounts of light; the primary systematic error in this case is the limited number of objects that can be observed. The third rung of the distance ladder measures the red-shift of supernovae to extract the Hubble flow, and from that the constant. At this rung, corrections due tomotion other than expansion are applied.[53]: 2.1 As an example of the kind of work needed to reduce systematic errors, photometry on observations from the James Webb Space Telescope of extra-galactic Cepheids confirm the findings from the HST. The higher resolution avoided confusion from crowding of stars in the field of view but came to the same value for H0.[71][53]
The "early universe" or inverse distance ladder measures the observable consequences of spherical sound waves on primordial plasma density. These pressure waves – calledbaryon acoustic oscillations (BAO) – ceased once the universe cooled enough for electrons to stay bound to nuclei, ending the plasma and allowing the photons trapped by interaction with the plasma to escape. The subsequent pressure waves are evident in very small perturbations in the density imprinted on the cosmic microwave background, and on the large-scale density of galaxies across the sky. Detailed structure in high-precision measurements of the CMB can be matched to physics models of the oscillations. These models depend upon the Hubble constant such that a match reveals a value for the constant. Similarly, the BAO affects the statistical distribution of matter, observed as distant galaxies across the sky.
These two independent measurements produce similar values for the constant from the current models, giving strong evidence that systematic errors in the measurements themselves do not affect the result.[53]: Sup. B
In addition to measurements based on calibrated distance ladder techniques or measurements of the CMB, other methods have been used to determine the Hubble constant.
One alternative method for constraining the Hubble constant involves transient events seen in multiple images of astrongly lensed object. A transient event, such as a supernova, is seen at different times in each of the lensed images, and if thistime delay between each image can be measured, it can be used to constrain the Hubble constant. This method is commonly known as "time-delay cosmography", and was first proposed byRefsdal in 1964,[72] years before the first strongly lensed object was observed. The first strongly lensed supernova to be discovered was namedSN Refsdal in his honor. While Refsdal suggested this could be done with supernovae, he also noted that extremely luminous and distant star-like objects could also be used. These objects were later namedquasars, and to date (April 2025) the majority of time-delay cosmography measurements have been done with strongly lensed quasars. This is because current samples of lensed quasars vastly outnumber known lensed supernovae, of which <10 are known. This is expected to change dramatically in the next few years, with surveys such asLSST expected to discover ~10 lensed SNe in the first three years of observation.[73] For example time-delay constraints on H0, see the results from STRIDES and H0LiCOW in the table below.
In July 2019, astronomers reported that a new method to determine the Hubble constant, and resolve the discrepancy of earlier methods, has been proposed based on the mergers of pairs ofneutron stars, following the detection of the neutron star merger of GW170817, an event known as adark siren.[76][77] Their measurement of the Hubble constant is73.3+5.3 −5.0 (km/s)/Mpc.[78]
In February 2020, the Megamaser Cosmology Project published independent results based onastrophysical masers visible at cosmological distances and which do not require multi-step calibration. That work confirmed the distance ladder results and differed from the early-universe results at a statistical significance level of 95%.[82]
In July 2020, measurements of the cosmic background radiation by theAtacama Cosmology Telescope predict that the Universe should be expanding more slowly than is currently observed.[83]
In July 2023, an independent estimate of the Hubble constant was derived from akilonova, the optical afterglow of aneutron star merger, using theexpanding photosphere method.[84] Due to the blackbody nature of early kilonova spectra,[85] such systems provide strongly constraining estimators of cosmic distance. Using the kilonovaAT2017gfo (the aftermath of, once again, GW170817), these measurements indicate a local-estimate of the Hubble constant of67.0±3.6 (km/s)/Mpc.[86][84]
Estimated values of the Hubble constant, 2001–2020. Estimates in black represent calibrated distance ladder measurements which tend to cluster around73 (km/s)/Mpc; red represents early universe CMB/BAO measurements with ΛCDM parameters which show good agreement on a figure near67 (km/s)/Mpc, while blue are other techniques, whose uncertainties are not yet small enough to decide between the two.
The cause of the Hubble tension is unknown,[87] and there are many possible proposed solutions. The most conservative is that there is an unknown systematic error affecting either early-universe or late-universe observations. Although intuitively appealing, this explanation requires multiple unrelated effects regardless of whether early-universe or late-universe observations are incorrect, and there are no obvious candidates. Furthermore, any such systematic error would need to affect multiple different instruments, since both the early-universe and late-universe observations come from several different telescopes.[53]
Alternatively, it could be that the observations are correct, but some unaccounted-for effect is causing the discrepancy. If thecosmological principle fails (seeLambda-CDM model § Violations of the cosmological principle), then the existing interpretations of the Hubble constant and the Hubble tension have to be revised, which might resolve the Hubble tension.[88] In particular, we would need to be located within a very large void, up to about a redshift of 0.5, for such an explanation to conflate with supernovae andbaryon acoustic oscillation observations.[63] Yet another possibility is that the uncertainties in the measurements could have been underestimated, but given the internal agreements this is neither likely, nor resolves the overall tension.[53]
Finally, another possibility is new physics beyond the currently accepted cosmological model of the universe, theΛCDM model.[63][89] There are very many theories in this category, for example, replacing general relativity witha modified theory of gravity could potentially resolve the tension,[90][91] as can a dark energy component in the early universe,[b][92] dark energy with a time-varyingequation of state,[c][93] ordark matter that decays into dark radiation.[94] A problem faced by all these theories is that both early-universe and late-universe measurements rely on multiple independent lines of physics, and it is difficult to modify any of those lines while preserving their successes elsewhere. The scale of the challenge can be seen from how some authors have argued that new early-universe physics alone is not sufficient;[95][96] while other authors argue that new late-universe physics alone is also not sufficient.[97] Nonetheless, astronomers are trying, with interest in the Hubble tension growing strongly since the mid 2010s.[63]
Timing delay of gravitationally lensed images ofSupernova H0pe. Independent of cosmic distance ladder or the CMB. JWST data. (2023-05-11 cell and this one are the only 2 values with this method so far)
Due to the blackbody spectra of the optical counterpart of neutron-star mergers, these systems provide strongly constraining estimators of cosmic distance.
Use Type II supernovae as standardisable candles to obtain an independent measurement of the Hubble constant—13 SNe II with host-galaxy distances measured from Cepheid variables, the tip of the red giant branch, and geometric distance (NGC 4258).
Combining earlier work onred giant stars, using the tip of the red-giant branch (TRGB) distance indicator, withparallax measurements ofOmega Centauri from Gaia EDR3.
Combination of HSTphotometry and Gaia EDR3 parallaxes for Milky WayCepheids, reducing the uncertainty in calibration of Cepheid luminosities to 1.0%. Overall uncertainty in the value forH0 is 1.8%, which is expected to be reduced to 1.3% with a larger sample of type Ia supernovae in galaxies that are known Cepheid hosts. Continuation of a collaboration known as Supernovae,H0, for the Equation of State of Dark Energy (SHoES).
Eight quadruplylensed galaxy systems are used to determineH0 to a precision of 5%, in agreement with both "early" and "late" universe estimates. Independent of distance ladders and the cosmic microwave background.
Derived from 88 0.02 <z < 0.05 Type Ia supernovae used as standard candle distance indicators. TheH0 estimate is corrected for the effects of peculiar velocities in the supernova environments, as estimated from the galaxy density field. The result assumesΩm = 0.3,ΩΛ = 0.7 and a sound horizon of149.3 Mpc, a value taken from Anderson et al. (2014).[115]
Use Type II supernovae as standardisable candles to obtain an independent measurement of the Hubble constant—7 SNe II with host-galaxy distances measured from Cepheid variables or the tip of the red giant branch.
This is obtained analysing low-redshift cosmological data within ΛCDM model. The datasets used are type-Ia supernovae,baryon acoustic oscillations, time-delay measurements using strong-lensing,H(z) measurements using cosmic chronometers and growth measurements from large scale structure observations.
Measuring the distance toMessier 106 using its supermassive black hole, combined with measurements of eclipsing binaries in the Large Magellanic Cloud.
Updated observations of multiply imaged quasars, now using six quasars, independent of the cosmic distance ladder and independent of the cosmic microwave background measurements.
Precision HST photometry of Cepheids in theLarge Magellanic Cloud (LMC) reduce the uncertainty in the distance to the LMC from 2.5% to 1.3%. The revision increases the tension withCMB measurements to the 4.4σ level (P=99.999% for Gaussian errors), raising the discrepancy beyond a plausible level of chance. Continuation of a collaboration known as Supernovae,H0, for the Equation of State of Dark Energy (SHoES).
Quasar angular size and baryon acoustic oscillations, assuming a flat ΛCDM model. Alternative models result in different (generally lower) values for the Hubble constant.
Additional HSTphotometry of galactic Cepheids with early Gaia parallax measurements. The revised value increases tension with CMB measurements at the 3.8σ level. Continuation of the SHoES collaboration.
Parallax measurements of galactic Cepheids for enhanced calibration of thedistance ladder; the value suggests a discrepancy with CMB measurements at the 3.7σ level. The uncertainty is expected to be reduced to below 1% with the final release of the Gaia catalog. SHoES collaboration.
Standard siren measurement independent of normal "standard candle" techniques; the gravitational wave analysis of a binaryneutron star (BNS) mergerGW170817 directly estimated the luminosity distance out to cosmological scales. An estimate of fifty similar detections in the next decade may arbitrate tension of other methodologies.[132] Detection and analysis of a neutron star-black hole merger (NSBH) may provide greater precision than BNS could allow.[133]
Uses time delays between multiple images of distant variable sources produced bystrong gravitational lensing. Collaboration known asH0 Lenses in COSMOGRAIL's Wellspring (H0LiCOW).
Comparing redshift to other distance methods, includingTully–Fisher, Cepheid variable, and Type Ia supernovae. A restrictive estimate from the data implies a more precise value of75±2.
Baryon acoustic oscillations. An extended survey (eBOSS) began in 2014 and is expected to run through 2020. The extended survey is designed to explore the time when the universe was transitioning away from the deceleration effects of gravity from 3 to 8 billion years after the Big Bang.[137]
Type Ia supernova, the uncertainty is expected to go down by a factor of more than two with upcoming Gaia measurements and other improvements. SHoES collaboration.
Results from an analysis ofPlanck's full mission were made public on 1 December 2014 at a conference inFerrara, Italy. A full set of papers detailing the mission results were released in February 2015.
TheESA Planck Surveyor was launched in May 2009. Over a four-year period, it performed a significantly more detailed investigation of cosmic microwave radiation than earlier investigations usingHEMTradiometers andbolometer technology to measure the CMB at a smaller scale than WMAP. On 21 March 2013, the European-led research team behind the Planck cosmology probe released the mission's data including a new CMB all-sky map and their determination of the Hubble constant.
These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the ΛCDM model. If the data are fit with more general versions,H0 tends to be smaller and more uncertain: typically around67±4 (km/s)/Mpc although some models allow values near63 (km/s)/Mpc.[148]
This project established the most precise optical determination, consistent with a measurement ofH0 based upon Sunyaev–Zel'dovich effect observations of many galaxy clusters having a similar accuracy.
Determined relationship between luminosity of SN 1a's and their Light Curve Shapes. Riess et al. used this ratio of the light curve of SN 1972E and the Cepheid distance to NGC 5253 to determine the constant.
De Vaucouleurs believed he had improved the accuracy of Hubble's constant from Sandage's because he used 5x more primary indicators, 10× more calibration methods, 2× more secondary indicators, and 3× as many galaxy data points to derive his100±10.
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