cosmological expansion

The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. This expansion involves neither space nor objects in space "moving" in a traditional sense, but rather it is the metric (which governs the size and geometry of spacetime itself) that changes in scale. As the spatial part of the universe's spacetime metric increases in scale, objects become more distant from one another at ever-increasing speeds. To any observer in the universe, it appears that all of space is expanding, and that all but the nearest galaxies (which are bound by gravity) recede at speeds that are proportional to their distance from the observer. While objects within space cannot travel faster than light, this limitation does not apply to the effects of changes in the metric itself.Although anything in a local reference frame cannot accelerate past the speed of light, this limitation does not restrict the expansion of the metric itself. Objects that recede beyond the cosmic event horizon will eventually become unobservable, as no new light from them will be capable of overcoming the universe's expansion, limiting the size of our observable universe.

As an effect of general relativity, the expansion of the universe is different from the expansions and explosions seen in daily life. It is a property of the universe as a whole and occurs throughout the universe, rather than happening just to one part of the universe. Therefore, unlike other expansions and explosions, it cannot be observed from "outside" of it; it is believed that there is no "outside" to observe from.

Metric expansion is a key feature of Big Bang cosmology, is modeled mathematically with the Friedmann–Lemaître–Robertson–Walker metric and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of galaxy clusters and above), because gravity binds matter together strongly enough that metric expansion cannot be observed on a smaller scale at this time. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the length scales associated with the gravitational collapse that are possible in the age of the universe given the matter density and average expansion rate.

According to inflation theory, during the inflationary epoch about 10⁻³² of a second after the Big Bang, the universe suddenly expanded, and its volume increased by a factor of at least 10⁷⁸ (an expansion of distance by a factor of at least 10²⁶ in each of the three dimensions). This would be equivalent to expanding an object 1 nanometer (10⁻⁹ m, about half the width of a molecule of DNA) in length to one approximately 10.6 light years (about 10¹⁷ m or 62 trillion miles) long. A much slower and gradual expansion of space continued after this, until at around 9.8 billion years after the Big Bang (4 billion years ago) it began to gradually expand more quickly, and is still doing so. Physicists have postulated the existence of dark energy, appearing as a cosmological constant in the simplest gravitational models, as a way to explain this late-time acceleration. According to the simplest extrapolation of the currently favored cosmological model, the Lambda-CDM model, this acceleration becomes more dominant into the future. In June 2016, NASA and ESA scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the Hubble Space Telescope.

History

In 1912, Vesto Slipher discovered that light from remote galaxies was redshifted, which was later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used Einstein field equations to provide theoretical evidence that the universe is expanding.

Swedish astronomer Knut Lundmark was the first person to find observational evidence for expansion in 1924. According to Ian Steer of the NASA/IPAC Extragalactic Database of Galaxy Distances, "Lundmark's extragalactic distance estimates were far more accurate than Hubble's, consistent with an expansion rate (Hubble constant) that was within 1% of the best measurements today."

In 1927, Georges Lemaître independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented observational evidence for a linear relationship between distance to galaxies and their recessional velocity. Edwin Hubble observationally confirmed Lundmark's and Lemaître's findings in 1929. Assuming the cosmological principle, these findings would imply that all galaxies are moving away from each other.

Based on large quantities of experimental observation and theoretical work, the scientific consensus is that ''space itself is expanding'', and that it expanded very rapidly within the first fraction of a second after the Big Bang, approximately 13.8 billion years ago. This kind of expansion is known as "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''.

On 13 January 1994, NASA formally announced a completion of its repairs on the main mirror of the Hubble Space Telescope allowing for sharper images and, consequently, more accurate analyses of its observations. Briefly after the repairs were made, Wendy Freedman's 1994 Key Project analyzed the recession velocity of M100 from the core of the Virgo cluster, offering a Hubble constant measurement of 80±17 km s^-1 Mpc^-1 (Mega Parsec). Later the same year, Adam Riess et al utilized an empirical method of visual band light shape curves to more finely estimate the luminosity of Type Ia supernova. This further minimized the systemic measurement errors of the Hubble constant to 67±7 km s^-1 Mpc^-1. Reiss's measurements on the recession velocity of the nearby Virgo cluster more closely agree with subsequent and independent analyses of Cepheid variable calibrations of 1a supernovae, which estimates a Hubble Constant of 73±7km s^-1 Mpc^-1. Within the next decade, in 2003, David Spergel's analysis of the Cosmic microwave background during the first year observations of the ''Wilkinson Microwave Anisotropy Probe'' satellite (WMAP) further agreed with the estimated expansion rates for local galaxies, 72±5 km s^-1 Mpc^-1.

Cosmic inflation

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 as 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. According to Roger Penrose, inflation does not solve the main problem it was supposed to solve, namely the incredibly low entropy (with ''unlikeliness'' of the state on the order of 1/10¹⁰¹²⁸ ⁠) of the early Universe contained in the ''gravitational conformal degrees of freedom'' (in contrast to fields degrees of freedom, such like the cosmic microwave background whose smoothness can be explained by inflation). Thus, he puts forward his scenario of the evolution of the Universe: conformal cyclic cosmology.

No field responsible for 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.

Overview of metrics and comoving coordinates

To understand the metric expansion of the universe, it is helpful to discuss briefly what a metric is, and how metric expansion works.

A metric defines the concept of distance, by stating in mathematical terms how distances between two nearby points in space are measured, in terms of the coordinate system. Coordinate systems locate points in a space (of whatever number of dimensions) by assigning unique positions on a grid, known as coordinates, to each point. Latitude and longitude, and x-y graphs are common examples of coordinates. A metric is a formula that describes how a number known as "distance" is to be measured between two points.

It may seem obvious that distance is measured by a straight line, but in many cases it is not. For example, long haul aircraft travel along a curve known as a "great circle" and not a straight line, because that is a better metric for air travel. (A straight line would go through the earth). Another example is planning a car journey, where one might want the shortest journey in terms of travel time - in that case a straight line is a poor choice of metric because the shortest distance by road is not normally a straight line, and even the path nearest to a straight line will not necessarily be the quickest. A final example is the internet, where even for nearby towns, the quickest route for data can be via major connections that go across the country and back again. In this case the metric used will be the shortest time that data takes to travel between two points on the network.

In cosmology, we cannot use a ruler to measure metric expansion, because our ruler's internal forces easily overcome the extremely slow expansion of space, leaving the ruler intact. Also, any objects on or near earth that we might measure are being held together or pushed apart by several forces that are far larger in their effects. So even if we could measure the tiny expansion that is still happening, we would not notice the change on a small scale or in everyday life. On a large intergalactic scale, we can use other tests of distance and these ''do'' show that space is expanding, even if a ruler on earth could not measure it.

The metric expansion of space is described using the mathematics of metric tensors. The coordinate system we use is called "comoving coordinates", a type of coordinate system that takes account of time as well as space and the speed of light, and allows us to incorporate the effects of both general and special relativity.

Example: "Great Circle" metric for Earth's surface

For example, consider the measurement of distance between two places on the surface of the Earth. This is a simple, familiar example of spherical geometry. Because the surface of the Earth is two-dimensional, points on the surface of the Earth can be specified by two coordinates – for example, the latitude and longitude. Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example latitude and longitude, or X-Y-Z Cartesian coordinates. Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too. On the curved surface of the Earth, we can see this effect in long-haul airline flights where the distance between two points is measured based upon a great circle, rather than the straight line one might plot on a two-dimensional map of the Earth's surface. In general, such shortest-distance paths are called "geodesics". In Euclidean geometry, the geodesic is a straight line, while in non-Euclidean geometry such as on the Earth's surface, this is not the case. Indeed, even the shortest-distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth. The difference between the straight line path and the shortest-distance great circle path is due to the curvature of the Earth's surface. While there is always an effect due to this curvature, at short distances the effect is small enough to be unnoticeable.

On plane maps, great circles of the Earth are mostly not shown as straight lines. Indeed, there is a seldom-used map projection, namely the gnomonic projection, where all great circles are shown as straight lines, but in this projection, the distance scale varies very much in different areas. There is no map projection in which the distance between any two points on Earth, measured along the great circle geodesics, is directly proportional to their distance on the map; such accuracy is possible only with a globe.

Metric tensors

In differential geometry, the backbone mathematics for general relativity, a metric tensor can be defined that precisely characterizes the space being described by explaining the way distances should be measured in every possible direction. General relativity necessarily invokes a metric in four dimensions (one of time, three of space) because, in general, different reference frames will experience different intervals of time and space depending on the inertial frame. This means that the metric tensor in general relativity relates precisely how two events in spacetime are separated.

A metric expansion occurs when the metric tensor changes with time (and, specifically, whenever the spatial part of the metric gets larger as time goes forward). This kind of expansion is different from all kinds of expansions and explosions commonly seen in nature in no small part because times and distances are not the same in all reference frames, but are instead subject to change. A useful visualization is,rather than imagining objects in a fixed "space" moving apart into "emptiness", instead imagine space itself growing between all objects, without any acceleration or movement of the objects themselves. The space between objects shrinks or grows as the various geodesics converge or diverge.

Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound of special relativity. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various cosmological horizons.

Theory and observations suggest that very early in the history of the universe, there was an inflationary phase where the metric changed very rapidly, and that the remaining time-dependence of this metric is what we observe as the so-called Hubble expansion, the moving apart of all gravitationally unbound objects in the universe. The expanding universe is therefore a fundamental feature of the universe we inhabit – a universe fundamentally different from the static universe Albert Einstein first considered when he developed his gravitational theory.

Comoving coordinates

In expanding space, proper distances are dynamical quantities that change with time. An easy way to correct for this is to use comoving coordinates, which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion. In comoving coordinates, the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravity and electromagnetic radiation