When Edwin Hubble was hired to work at Mount Wilson Observatory in 1919 (part of the Observatories of the Carnegie Institution of Washington) as a junior astronomer, the most pressing question of the day concerned the nature of the cloudy patches called nebulae. Most of Hubble’s colleagues at Mount Wilson thought they were all in the Milky Way, but he was not so sure. He succeeded in answering this question by taking the best possible photos of these objects, providing convincing evidence that at least some of them were well beyond the Milky Way. By discovering other galaxies Hubble expanded the known universe 100-fold. But he didn’t stop there. By measuring the distances and motions of the galaxies he surprised everyone, including Einstein, by discovering that the universe is expanding.

Hubble was lucky enough to arrive at Mt. Wilson soon after the 100-inch reflecting telescope was completed. A careful and hard-working observer, Hubble took many photographs of the same set of spiral nebulae (now called galaxies). Multiple images were needed in order to identify changes over time. He observed several novas, or instances in which a dim star became much brighter as it attracted material from a nearby companion star. Then, on October 4, 1923, while comparing a photograph that he had just taken of the Andromeda galaxy with photos taken on previous nights, Hubble identified a Cepheid variable star—the one kind of star that could provide a means of determining the distance to the galaxy. Over the next several months Hubble determined that the star varied in brightness with a period of 31.45 days, which meant it was 7,000 times brighter than the Sun. Comparing its apparent brightness with its actual brightness Hubble determined that it was 900,000 light years away.

Since Harlow Shapley had previously measured the distance across the Milky Way to be about 100,000 light years, the new findings clearly indicated that the Andromeda galaxy was far beyond the Milky Way. Later investigators found that there were two types of Cepheid variable stars, and that Hubble was comparing the bright kind of Cepheid in Andromeda with a dimmer kind of Cepheid in our own galaxy, which meant that Andromeda was actually twice as far away—approximately 2 million light years. In subsequent decades, distances were measured to many other galaxies. Today, galaxies that are billions of light years distant have been observed.

In 1929, Edwin Hubble discovered that light from remote galaxies was redshifted; i.e. the more remote galaxies were, the more shifted was the light coming from them. This observation was quickly interpreted as galaxies receding from earth. If earth is not in some special, privileged, central position in the universe, then it would mean all galaxies are moving apart, and the further away, the faster they are moving away. It is now understood that the universe is expanding, carrying the galaxies with it, and causing this observation. Many other observations agree, and also lead to the same conclusion. However, for many years it was not clear why or how the universe might be expanding, or what it might signify.

Based on a huge amount of experimental observation and theoretical work, it is now believed that the reason for the observation is that space itself is expanding, and that it expanded very rapidly within the first fraction of a second after the Big Bang. This kind of expansion is known as the "metric expansion". In mathematics and physics, a "metric" means a measure of distance, and the term implies that the sense of distance within the universe is itself changing, although at this time it is far too small an effect to see on less than an intergalactic scale.

The modern explanation for the metric expansion of space was proposed by physicist Alan Guth in 1979, while investigating the problem of why no magnetic monopoles are seen today. Guth found in his investigation that if the universe contained a field that has a positive-energy false vacuum state, then according to general relativity it would generate an exponential expansion of space. It was very quickly realized that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does today, the universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation theory largely resolves these problems as well, thus making a universe like ours much more likely in the context of Big Bang theory.

No field responsible for the cosmic inflation has been discovered. However such a field, if found in the future, would be scalar. The first similar scalar field proven to exist was only discovered in 2012 - 2013 and is still being researched. So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered.

The proposed field and its quanta (the subatomic particles related to it) have been named inflaton. If this field did not exist, scientists would have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred, and is still occurring much more slowly today.

But Hubble’s work was not done. He was aware that a decade earlier astronomer Vesto Slipher had measured the Doppler shift of several galaxies, finding a few that were approaching our Milky Way and several that were moving away at very high speeds. Working with his assistant, Milton Humason, Hubble carefully measured the distance and Doppler shift of as many galaxies as possible. In 1929 Hubble published a paper that would lead to the realization that the universe was expanding.

As astronomers’ abilities to measure the distance and Doppler shift of galaxies improved over the years, Hubble’s and Humason’s discovery of the expanding universe was confirmed. Further, it soon became obvious that by measuring the rate of expansion it was possible to determine the age of the universe by calculating when all the galaxies were in one place. This was truly an amazing discovery—that human beings could not only grasp our place within a huge pinwheel of billions of stars, itself one of many such galaxies; but that we could also determine when the universe began. Although Edwin Hubble is credited with these findings he acknowledged that the discoveries were not his alone. They depended on the work many astronomers who had come before, building the knowledge and tools that were needed to reach the summit, and look out across the vast universe and innumerable galaxies to the very beginning of time and space.

Measurement of expansion and change of rate of expansion

In principle, the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again, but in practice, standard rulers are not easy to find on cosmological scales and the timescales over which a measurable expansion would be visible are too great to be observable even by multiple generations of humans. The expansion of space is measured indirectly. The theory of relativity predicts phenomena associated with the expansion, notably the redshift-versus-distance relationship known as Hubble's Law; functional forms for cosmological distance measurements that differ from what would be expected if space were not expanding; and an observable change in the matter and energy density of the universe seen at different lookback times.

The first measurement of the expansion of space occurred with the creation of the Hubble diagram. Using standard candles with known intrinsic brightness, the expansion of the universe has been measured using redshift to derive Hubble's Constant: H₀ = 67.15 ± 1.2 (km/s)/Mpc. For every million parsecs of distance from the observer, the rate of expansion increases by about 67 kilometers per second.

The Hubble parameter is not thought to be constant through time. There are dynamical forces acting on the particles in the universe which affect the expansion rate. It was earlier expected that the Hubble parameter would be decreasing as time went on due to the influence of gravitational interactions in the universe, and thus there is an additional observable quantity in the universe called the deceleration parameter which cosmologists expected to be directly related to the matter density of the universe. Surprisingly, the deceleration parameter was measured by two different groups to be less than zero (actually, consistent with −1) which implied that today the Hubble parameter is converging to a constant value as time goes on. Some cosmologists have whimsically called the effect associated with the "accelerating universe" the "cosmic jerk". The 2011 Nobel Prize in Physics was given for the discovery of this phenomenon.

In October 2018, scientists presented a new third way (two earlier methods, one based on redshifts and another on the cosmic distance ladder, gave results that do not agree), using information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), of determining the Hubble Constant, essential in establishing the rate of expansion of the universe.

Measuring distances in expanding space

At cosmological scales the present universe is geometrically flat, which is to say that the rules of Euclidean geometry associated with Euclid's fifth postulate hold, though in the past spacetime could have been highly curved. In part to accommodate such different geometries, the expansion of the universe is inherently general relativistic; it cannot be modeled with special relativity alone, though such models exist, they are at fundamental odds with the observed interaction between matter and spacetime seen in our universe.

The images to the right show two views of spacetime diagrams that show the large-scale geometry of the universe according to the ΛCDM cosmological model. Two of the dimensions of space are omitted, leaving one dimension of space (the dimension that grows as the cone gets larger) and one of time (the dimension that proceeds "up" the cone's surface). The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the big bang while the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion as a splaying outward of the spacetime, a feature which eventually dominates in this model. The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The cyan grid lines mark off comoving distance at intervals of one billion light years in the present era (less in the past and more in the future). Note that the circular curling of the surface is an artifact of the embedding with no physical significance and is done purely to make the illustration viewable; space does not actually curl around on itself. (A similar effect can be seen in the tubular shape of the pseudosphere.)

The brown line on the diagram is the worldline of the Earth (or, at earlier times, of the matter which condensed to form the Earth). The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years, which is, notably, a larger distance than the age of the universe multiplied by the speed of light: ct.

According to the equivalence principle of general relativity, the rules of special relativity are locally valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed c; in our diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels a distance ct in a time t, as the red worldline illustrates. While it always moves locally at c, its time in transit (about 13 billion years) is not related to the distance traveled in any simple way since the universe expands as the light beam traverses space and time. In fact the distance traveled is inherently ambiguous because of the changing scale of the universe. Nevertheless, we can single out two distances which appear to be physically meaningful: the distance between the Earth and the quasar when the light was emitted, and the distance between them in the present era (taking a slice of the cone along the dimension that we've declared to be the spatial dimension). The former distance is about 4 billion light years, much smaller than ct because the universe expanded as the light traveled the distance, the light had to "run against the treadmill" and therefore went farther than the initial separation between the Earth and the quasar. The latter distance (shown by the orange line) is about 28 billion light years, much larger than ct. If expansion could be instantaneously stopped today, it would take 28 billion years for light to travel between the Earth and the quasar while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.

The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away, and, in fact, the light emitted towards the Earth was actually moving away from the Earth when it was first emitted, in the sense that the metric distance to the Earth increased with cosmological time for the first few billion years of its travel time, and also indicating that the expansion of space between the Earth and the quasar at the early time was faster than the speed of light. None of this surprising behavior originates from a special property of metric expansion, but simply from local principles of special relativity integrated over a curved surface.

Topology of expanding space

Over time, the space that makes up the universe is expanding. The words 'space' and 'universe', sometimes used interchangeably, have distinct meanings in this context. Here 'space' is a mathematical concept that stands for the three-dimensional manifold into which our respective positions are embedded while 'universe' refers to everything that exists including the matter and energy in space, the extra-dimensions that may be wrapped up in various strings, and the time through which various events take place. The expansion of space is in reference to this 3-D manifold only; that is, the description involves no structures such as extra dimensions or an exterior universe.

The ultimate topology of space is a posteriori — something which in principle must be observed — as there are no constraints that can simply be reasoned out (in other words there can not be any a priori constraints) on how the space in which we live is connected or whether it wraps around on itself as a compact space. Though certain cosmological models such as Gödel's universe even permit bizarre worldlines which intersect with themselves, ultimately the question as to whether we are in something like a "Pac-Man universe" where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon (or a planet like the Earth) is an observational question which is constrained as measurable or non-measurable by the universe's global geometry. At present, observations are consistent with the universe being infinite in extent and simply connected, though we are limited in distinguishing between simple and more complicated proposals by cosmological horizons. The universe could be infinite in extent or it could be finite; but the evidence that leads to the inflationary model of the early universe also implies that the "total universe" is much larger than the observable universe, and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe, if they exist, are still allowed. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.

Regardless of the overall shape of the universe, the question of what the universe is expanding into is one which does not require an answer according to the theories which describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse. All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on. This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur. The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" of the expanding universe into which the universe expands.

This diagram can be confusing because the expansion of space looks like it is happening into an empty "nothingness". However, this is a choice made for convenience of visualization: it is not a part of the physical models which describe the expansion.

Even if the overall spatial extent is infinite and thus the universe cannot get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing. As an infinite space grows, it remains infinite.

Density of universe during expansion

Despite being extremely dense when very young and during part of its early expansion - far denser than is usually required to form a black hole - the universe did not re-collapse into a black hole. This is because commonly-used calculations for gravitational collapse are usually based upon objects of relatively constant size, such as stars, and do not apply to rapidly expanding space such as the Big Bang.

Effects of expansion on small scales

The expansion of space is sometimes described as a force which acts to push objects apart. Though this is an accurate description of the effect of the cosmological constant, it is not an accurate picture of the phenomenon of expansion in general. For much of the universe's history the expansion has been due mainly to inertia. The matter in the very early universe was flying apart for unknown reasons (most likely as a result of cosmic inflation) and has simply continued to do so, though at an ever-decreasing rate due to the attractive effect of gravity.

In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so.

There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum; the former is simply a large-scale extrapolation of the latter.

Once objects are bound by gravity, they no longer recede from each other. Thus, the Andromeda galaxy, which is bound to the Milky Way galaxy, is actually falling towards us and is not expanding away. Within the Local Group, the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place. Once one goes beyond the Local Group, the inertial expansion is measurable, though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the "Hubble Flow" and end up as bound, non-expanding objects up to the scales of superclusters of galaxies. We can predict such future events by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled. Currently, the Local Group is being gravitationally pulled towards either the Shapley Supercluster or the "Great Attractor" with which, if dark energy were not acting, we would eventually merge and no longer see expand away from us after such a time.

A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the FLRW geometry, the same geometry which describes the expansion of the universe as a whole and was also the basis for the simpler Milne universe which ignores the effects of gravity. In particular, general relativity predicts that light will move at the speed c with respect to the local motion of the exploding matter, a phenomenon analogous to frame dragging.

The situation changes somewhat with the introduction of dark energy or a cosmological constant. A cosmological constant due to a vacuum energy density has the effect of adding a repulsive force between objects which is proportional (not inversely proportional) to distance. Unlike inertia it actively "pulls" on objects which have clumped together under the influence of gravity, and even on individual atoms. However, this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state which is slightly (undetectably) larger than it would otherwise have been.

As the universe expands and the matter in it thins, the gravitational attraction decreases (since it is proportional to the density), while the cosmological repulsion increases; thus the ultimate fate of the ΛCDM universe is a near vacuum expanding at an ever-increasing rate under the influence of the cosmological constant. However, the only locally visible effect of the accelerating expansion is the disappearance (by runaway redshift) of distant galaxies; gravitationally bound objects like the Milky Way do not expand and the Andromeda galaxy is moving fast enough towards us that it will still merge with the Milky Way in 3 billion years time, and it is also likely that the merged supergalaxy that forms will eventually fall in and merge with the nearby Virgo Cluster. However, galaxies lying farther away from this will recede away at ever-increasing speed and be redshifted out of our range of visibility.

Theoretical basis and first evidence

Hubble's law

Technically, the metric expansion of space is a feature of many solutions to the Einstein field equations of general relativity, and distance is measured using the Lorentz interval. This explains observations which indicate that galaxies that are more distant from us are receding faster than galaxies that are closer to us.

Cosmological constant and the Friedmann equations

The first general relativistic models predicted that a universe which was dynamical and contained ordinary gravitational matter would contract rather than expand. Einstein's first proposal for a solution to this problem involved adding a cosmological constant into his theories to balance out the contraction, in order to obtain a static universe solution. But in 1922 Alexander Friedmann derived a set of equations known as the Friedmann equations, showing that the universe might expand and presenting the expansion speed in this case. The observations of Edwin Hubble in 1929 suggested that distant galaxies were all apparently moving away from us, so that many scientists came to accept that the universe was expanding.

Hubble's concerns over the rate of expansion

While the metric expansion of space appeared to be implied by Hubble's 1929 observations, Hubble disagreed with the expanding-universe interpretation of the data:

[...] if redshift are not primarily due to velocity shift [...] the velocity-distance relation is linear, the distribution of the nebula is uniform, there is no evidence of expansion, no trace of curvature, no restriction of the time scale [...] and we find ourselves in the presence of one of the principles of nature that is still unknown to us today [...] whereas, if redshifts are velocity shifts which measure the rate of expansion, the expanding models are definitely inconsistent with the observations that have been made [...] expanding models are a forced interpretation of the observational results.
— E. Hubble, Ap. J., 84, 517, 1936.

[If the redshifts are a Doppler shift ...] the observations as they stand lead to the anomaly of a closed universe, curiously small and dense, and, it may be added, suspiciously young. On the other hand, if redshifts are not Doppler effects, these anomalies disappear and the region observed appears as a small, homogeneous, but insignificant portion of a universe extended indefinitely both in space and time.
— E. Hubble, Monthly Notices of the Royal Astronomical Society, 97, 506, 1937.

Hubble's skepticism about the universe being too small, dense, and young turned out to be based on an observational error. Later investigations appeared to show that Hubble had confused distant H II regions for Cepheid variables and the Cepheid variables themselves had been inappropriately lumped together with low-luminosity RR Lyrae stars causing calibration errors that led to a value of the Hubble Constant of approximately 500 km/s/Mpc instead of the true value of approximately 70 km/s/Mpc. The higher value meant that an expanding universe would have an age of 2 billion years (younger than the Age of the Earth) and extrapolating the observed number density of galaxies to a rapidly expanding universe implied a mass density that was too high by a similar factor, enough to force the universe into a peculiar closed geometry which also implied an impending Big Crunch that would occur on a similar time-scale. After fixing these errors in the 1950s, the new lower values for the Hubble Constant accorded with the expectations of an older universe and the density parameter was found to be fairly close to a geometrically flat universe.

However, recent measurements of the distances and velocities of faraway galaxies revealed a 9 percent discrepancy in the value of the Hubble constant, implying a universe that seems expanding too fast compared to previous measurements. In 2001, Dr. Wendy Freedman determined space to expand at 72 kilometers per second per megaparsec - roughly 3.3 million light years - meaning that for every 3.3 million light years further away from the earth you are, the matter where you are is moving away from earth 72 kilometers a second faster. In the summer of 2016, another measurement reported a value of 73 for the constant, thereby contradicting 2013 measurements from the European Planck mission of slower expansion value of 67. The discrepancy opened new questions concerning the nature of dark energy, or of neutrinos.

Inflation as an explanation for the expansion

Until the theoretical developments in the 1980s no one had an explanation for why this seemed to be the case, but with the development of models of cosmic inflation, the expansion of the universe became a general feature resulting from vacuum decay. Accordingly, the question "why is the universe expanding?" is now answered by understanding the details of the inflation decay process which occurred in the first 10−32 seconds of the existence of our universe. During inflation, the metric changed exponentially, causing any volume of space that was smaller than an atom to grow to around 100 million light years across in a time scale similar to the time when inflation occurred (10−32 seconds).

Measuring distance in a metric space

In expanding space, distance is a dynamic quantity which changes with time. There are several different ways of defining distance in cosmology, known as distance measures, but a common method used amongst modern astronomers is comoving distance.

The metric only defines the distance between nearby (so-called "local") points. In order to define the distance between arbitrarily distant points, one must specify both the points and a specific curve (known as a "spacetime interval") connecting them. The distance between the points can then be found by finding the length of this connecting curve through the three dimensions of space. Comoving distance defines this connecting curve to be a curve of constant cosmological time. Operationally, comoving distances cannot be directly measured by a single Earth-bound observer. To determine the distance of distant objects, astronomers generally measure luminosity of standard candles, or the redshift factor 'z' of distant galaxies, and then convert these measurements into distances based on some particular model of spacetime, such as the Lambda-CDM model. It is, indeed, by making such observations that it was determined that there is no evidence for any 'slowing down' of the expansion in the current epoch.

When choosing an arbitrary reference point such as the gold galaxy or the red galaxy, the increased distance to other galaxies the further away they are appear the same. This phenomenon of expansion indicates two factors: there is no centralized point in the universe, and that the Milky Way Galaxy is not the center of the universe. The appearance of centrality is due to an observer bias that is equivalent no matter what location an observer sits.

Observational evidence

Theoretical cosmologists developing models of the universe have drawn upon a small number of reasonable assumptions in their work. These workings have led to models in which the metric expansion of space is a likely feature of the universe. Chief among the underlying principles that result in models including metric expansion as a feature are:

• the Cosmological Principle which demands that the universe looks the same way in all directions (isotropic) and has roughly the same smooth mixture of material (homogeneous).
  
• the Copernican Principle which demands that no place in the universe is preferred (that is, the universe has no "starting point").
  

Scientists have tested carefully whether these assumptions are valid and borne out by observation. Observational cosmologists have discovered evidence — very strong in some cases — that supports these assumptions, and as a result, metric expansion of space is considered by cosmologists to be an observed feature on the basis that although we cannot see it directly, scientists have tested the properties of the universe and observation provides compelling confirmation. Sources of this confidence and confirmation include:

• Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us, as predicted by a universal expansion. Using the redshift of their electromagnetic spectra to determine the distance and speed of remote objects in space, he showed that all objects are moving away from us, and that their speed is proportional to their distance, a feature of metric expansion. Further studies have since shown the expansion to be highly isotropic and homogeneous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.
  
• In studies of large-scale structure of the cosmos taken from redshift surveys a so-called "End of Greatness" was discovered at the largest scales of the universe. Until these scales were surveyed, the universe appeared "lumpy" with clumps of galaxy clusters, superclusters and filaments which were anything but isotropic and homogeneous. This lumpiness disappears into a smooth distribution of galaxies at the largest scales.
  
• The isotropic distribution across the sky of distant gamma-ray bursts and supernovae is another confirmation of the Cosmological Principle.
  
• The Copernican Principle was not truly tested on a cosmological scale until measurements of the effects of the cosmic microwave background radiation on the dynamics of distant astrophysical systems were made. A group of astronomers at the European Southern Observatory noticed, by measuring the temperature of a distant intergalactic cloud in thermal equilibrium with the cosmic microwave background, that the radiation from the Big Bang was demonstrably warmer at earlier times. Uniform cooling of the cosmic microwave background over billions of years is strong and direct observational evidence for metric expansion.
  

Taken together, these phenomena overwhelmingly support models that rely on space expanding through a change in metric. It was not until the discovery in the year 2000 of direct observational evidence for the changing temperature of the cosmic microwave background that more bizarre constructions could be ruled out. Until that time, it was based purely on an assumption that the universe did not behave as one with the Milky Way sitting at the middle of a fixed-metric with a universal explosion of galaxies in all directions (as seen in, for example, an early model proposed by Milne). Yet before this evidence, many rejected the Milne viewpoint based on the mediocrity principle.

REFERENCES

Nasa. Available in: https://www.nasa.gov/feature/goddard/2016/nasa-s-hubble-finds-universe-is-expanding-faster-than-expected. Access in: 25/11/2018.

Carnegie Science. Available in: https://cosmology.carnegiescience.edu/timeline/1929. Access in: 25/11/2018.

Space Telescope Science Institute. Available in: http://hubblesite.org/news_release/news/1996-21. Access in: 25/11/2018.

Wikipedia. Available in: https://en.wikipedia.org/wiki/Expansion_of_the_universe. Access in: 25/11/2018.