The metric expansion of space is a key part of science's current understanding of the universe, whereby spacetime itself is described by a metric which changes over time in such a way that the spatial dimensions grow or stretch as the universe gets older. It explains how the universe expands in the Big Bang model, a feature of our universe supported by all cosmological experiments, astrophysics calculations, and measurements to date. Image File history File links Emblem-important. ... This article is about the physics subject. ... For other uses, see Universe (disambiguation). ... For other uses, see Big Bang (disambiguation). ... This box:      This article is about scientific estimates of the age of the universe. ... A graphical timeline is available here: Graphical timeline of the Big Bang This box:      This timeline of the Big Bang describes the events that have occurred and will occur according to the scientific theory of the Big Bang, using the cosmological time parameter of comoving coordinates. ... This box:      The ultimate fate of the universe is a topic in physical cosmology. ... In cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than H-1, the normal, light hydrogen, during the early phases of the universe, shortly after the Big Bang. ... This article or section is in need of attention from an expert on the subject. ... The Cosmic Neutrino Background (CNB) is the background particle radiation composed of neutrinos. ... CMB redirects here. ... This article is about the physical phenomenon. ... This box:      Hubbles law is a statement in physical cosmology which states that the redshift in light coming from distant galaxies is proportional to their distance. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... // The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of the Einstein field equations of general relativity and which describes a homogeneous, isotropic expanding/contracting universe. ... The shape of the Universe is an informal name for a subject of investigation within physical cosmology. ... It has been suggested that this article or section be merged into Large-scale structure of the cosmos. ... In astrophysics, the questions of galaxy formation and evolution are: How, from a homogeneous universe, did we obtain the very heterogeneous one we live in? How did galaxies form? How do galaxies change over time? A spectacular head-on collision between two galaxies is seen in this NASA Hubble Space... Astronomy and cosmology examine the universe to understand the large-scale structure of the cosmos. ... A pie chart indicating the proportional composition of different energy-density components of the universe. ... In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ... For other uses, see Dark matter (disambiguation). ... This lists a timeline of cosmological theories and discoveries. ... Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. ... In astronomy, the 2dF Galaxy Redshift Survey (Two-degree-Field Galaxy Redshift Gurvey), or 2dFGRS is a redshift survey conducted by the Anglo-Australian Observatory in the 1990s. ... SDSS Logo The Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2. ... The Cosmic Background Explorer (COBE), also referred to as Explorer 66, was the first satellite built dedicated to cosmology. ... The Telescope being readied for launch The BOOMERanG experiment (Balloon Observations Of Millimetric Extragalactic Radiation and Geophysics) measured the cosmic microwave background radiation of a part of the sky during three sub-orbital (high altitude) balloon flights. ... Artist depiction of the WMAP satellite at the L2 point The Wilkinson Microwave Anisotropy Probe (WMAP) is a NASA satellite whose mission is to survey the sky to measure the temperature of the radiant heat left over from the Big Bang. ... “Einstein” redirects here. ... Stephen William Hawking, CH, CBE, FRS, FRSA, (born 8 January 1942) is a British theoretical physicist. ... Alexander Alexandrovich Friedman or Friedmann (Александр Александрович Фридман) (June 16, 1888 – September 16, 1925) was a Russian cosmologist and mathematician. ... Monsignor Georges Lemaître, priest and scientist. ... Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. ... Arno Allan Penzias (born April 26, 1933) is an American physicist and winner of the 1978 Nobel Prize in physics. ... Robert Woodrow Wilson Robert Woodrow Wilson (born January 10, 1936) is an American physicist. ... George Gamow (pronounced GAM-off) (March 4, 1904 – August 19, 1968) , born Georgiy Antonovich Gamov (Георгий Антонович Гамов) was a Ukrainian born physicist and cosmologist. ... Robert Henry Dicke (May 6, 1916 – March 4, 1997) was an American experimental physicist, who made important contributions to the fields of astrophysics, atomic physics, cosmology and gravity. ... Yakov Borisovich Zeldovich (Russian:Яков Борисович Зельдович) (March 8, 1914 – December 2, 1987) was a prolific Soviet physicist. ... John Cromwell Mather (b. ... George Fitzgerald Smoot III (born February 20, 1945) is an American astrophysicist and cosmologist awarded the 2006 Nobel Prize in Physics with John C. Mather for their discovery of the black body form and anisotropy of the cosmic microwave background radiation. This work helped cement the big-bang theory of... This is a list of cosmologists. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... For other uses, see Universe (disambiguation). ... For other uses of this term, see Spacetime (disambiguation). ... In mathematics, in Riemannian geometry, the metric tensor is a tensor of rank 2 that is used to measure distance and angle in a space. ... This article is about the concept of time. ... This article is about the idea of space. ... 2-dimensional renderings (ie. ... For other uses, see Big Bang (disambiguation). ... Model may refer to more than one thing : For models in society, art, fashion, and cosmetics, see; role model model (person) supermodel figure drawing modeling section In science and technology, a model (abstract) is understood as an abstract or theoretical representation of a phenomenon,see; geologic modeling model (economics) model... This article is about the physics subject. ... In the scientific method, an experiment (Latin: ex- periri, of (or from) trying) is a set of observations performed in the context of solving a particular problem or question, to retain or falsify a hypothesis or research concerning phenomena. ... Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature, and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ... Observation basically means watching something and taking note of anything it does. ...

Expansion of space explained

"Metric expansion"

The expansion of space is conceptually different from other kinds of expansions and explosions that are seen in nature. Our understanding of the "fabric of the universe" (spacetime) requires that what we see normally as "space", "time", and "distance" are not absolutes, but are determined by a metric that can change. In the metric expansion of space, rather than objects in a fixed "space" moving apart into "emptiness", it is the space that contains the objects which is itself changing. It is as if without objects themselves moving, space is somehow "growing" in between them. Expansion can have several meanings, including: In physics: Expansion of space In computer hardware: an Expansion card In computer programming: In-line expansion In computer gaming: an expansion pack See also: Wikipedia:Requests for expansion This is a disambiguation page — a navigational aid which lists other pages that might otherwise... This article is about the physical universe. ... For other uses of this term, see Spacetime (disambiguation). ... Distance is a numerical description of how far apart objects are at any given moment in time. ... Look up absolute in Wiktionary, the free dictionary. ... In mathematics, in Riemannian geometry, the metric tensor is a tensor of rank 2 that is used to measure distance and angle in a space. ...

In the language of Riemannian geometry, expansion is an intrinsic effect: the universe is expanding, as measured intrinsically by distances between points, in contrast to the familiar extrinsic notion of an object expanding within an ambient space—there is no need for an ambient space to define expansion. In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i. ...

Superluminal space expansion

Because it is the actual metric that defines distance itself that is changing, rather than objects moving apart within space, this expansion (and the resultant movement apart of objects) is not restricted by the speed of light upper bound that results from special relativity. The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set is an element which is greater than or equal to every element of S. The term lower bound is defined dually. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ...

Inflation and Hubble's law

Theory and observations suggest that very early in the history of the universe, there was an "inflationary" phase where this 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. In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density. ... This box:      Hubbles law is a statement in physical cosmology which states that the redshift in light coming from distant galaxies is proportional to their distance. ... Potential energy (U, or Ep), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. ... Basic description The theory of a static universe is the rival theory to an expanding universe and all of its subvarieties. ... “Einstein” redirects here. ...

Overview of metrics

Main article: Metric (mathematics)

Metric expansion is not something that most humans are aware of, on a day to day basis. It requires that instead of objects moving, it is space itself which is changing. To understand the expansion of the universe, it is helpful to discuss briefly, what a metric is, and how metric expansion works. In mathematics a metric or distance function is a function which defines a distance between elements of a set. ...

Definition of a metric

A metric defines how a distance can be measured between two nearby points in space, in terms of the coordinates of those points. A coordinate system locates points in a space (of whatever number of dimensions) by assigning unique numbers known as coordinates, to each point. The metric is then a formula which converts coordinates of two points into distances. In mathematics a metric or distance function is a function which defines a distance between elements of a set. ... Distance is a numerical description of how far apart objects are at any given moment in time. ... See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ... 2-dimensional renderings (ie. ... See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ... In mathematics and in the sciences, a formula (plural: formulae, formulæ or formulas) is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. ...

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 a non-Euclidean 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 co-ordinates 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, and not along the straight line that passes through the Earth. In theory there is always an effect due to this curvature, even for small distances, but in practice for "nearby" locations, the Earth's curvature is so small as to be almost unnoticeable for all except long distances (for example, travel between continents). Behavior of lines with a common perpendicular in each of the three types of geometry In mathematics, non-Euclidean geometry describes hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... This article is about the geographical term. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... Cartesian means of or relating to the French philosopher and mathematician René Descartes. ... An Airbus A380 of Emirates Airline An airline provides air transport services for passengers or freight. ... For the Brisbane bus routes known collectively as the Great Circle Line (598 & 599), see the following list of Brisbane Transport routes A great circle on a sphere A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the...

Metric for spacetime

Points on the surface of the Earth can be specified by giving two coordinates. Because space-time is four dimensional, we must specify points in space-time by giving four coordinates. The most convenient coordinates to use for cosmology are called comoving coordinates. Because space appears to be Euclidean, on a large scale, one can specify the spatial coordinates in terms of x,y, and z coordinates, though other choices such as spherical coordinates are also commonly used. The fourth required coordinate is time, which is specified in comoving coordinates as cosmological time. Though large-scale space appears to be Euclidean, the same cannot be said for the metric of space-time. The non-Euclidean nature of space-time manifests itself by the fact that the distance between points with constant coordinates grows with time, rather than remaining constant. The comoving distance or conformal distance of two objects in the universe is the distance divided by a time-varying scale factor representing the expansion of the universe. ... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician [[Euclid]] of Alexandria. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... A graphical timeline is available here: Graphical timeline of the Big Bang This timeline of the Big Bang describes the events that have occurred and will occur according to the scientific theory of the Big Bang. ...

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 theoretical explanation provides a clean explanation of the observed Hubble's law which indicates that galaxies that are more distant from us appear to be receding faster than galaxies that are closer to us. The Einstein field equations (EFE) or Einsteins equations are a set of ten equations in Einsteins theory of general relativity in which the fundamental force of gravitation is described as a curved spacetime caused by matter and energy. ... For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... For other uses, see Observation (disambiguation). ... This box:      Hubbles law is a statement in physical cosmology which states that the redshift in light coming from distant galaxies is proportional to their distance. ... For other uses, see Galaxy (disambiguation). ... Recessional Velocity is a term used to describe the rate at which an object is moving away, typically from Earth. ...

In spaces that expand, the metric changes with time in a way that causes distances to appear larger at later times, so in our Big Bang universe, we observe phenomena associated with metric expansion of space. If we lived in a space that contracted (a Big Crunch universe) we would observe phenomena associated with a metric contraction of space instead. For other uses, see Big Bang (disambiguation). ... This article is about the cosmological theory. ...

The cosmological constant and the Friedman 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 Friedman derived the famous Friedmann equations, showing that the universe might expand and presenting the expansion speed in this case.^[1] The observations of Edwin Hubble in 1929 confirmed that distant galaxies were all apparently moving away from us so that scientists accepted that the universe was expanding. In physical cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. ... Year 1922 (MCMXXII) was a common year starting on Sunday (link will display full calendar) of the Gregorian calendar. ... Alexander Alexandrovich Friedman (June 16, 1888 – September 16, Russian cosmologist and mathematician. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. ...

Inflation an explanation for the expansion

Until the theoretical developments in the 1980s no one had an explanation for why this was 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. It is suggested that in this time the metric itself changed exponentially, causing space to change from smaller than an atom to around 100 million light years across. The 1980s refers to the years from 1980 to 1989. ... In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density. ... A vacuum decay region is a large region that allows the Kaons and their decay products to undergo minimal interaction with matter. ... The inflationary epoch is the term used in cosmology to describe the brief time in the very early universe when, according to inflation theory, the universe was expanding exponentially. ... In mathematics, exponential growth (or geometric growth) occurs when the growth rate of a function is always proportional to the functions current size. ... For other uses, see Atom (disambiguation). ... A light-year or lightyear (symbol: ly) is a unit of measurement of length, specifically the distance light travels in vacuum in one year. ...

The expansion of the universe proceeds in all directions as determined by the Hubble constant today. However, the Hubble constant can change in the past and in the future dependent on the observed value of density parameters (Ω). Before the discovery of dark energy, it was believed that the universe was matter dominated and so Ω on this graph corresponds to the ratio of the matter density to the critical density (Ω_m).

Hubbles law is the statement in astronomy that the redshift in light coming from distant galaxies is proportional to their distance. ... In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. ... In cosmology, the Big Crunch is a hypothesis that states the universe will stop expanding and start to collapse upon itself; a counterpart to the Big Bang. ...

Measuring distance in a metric space

Main article: comoving coordinates

In expanding space, distance is a dynamical quantity which changes with time. There are several different ways of defining distance in cosmology, known as distance measures, but the most common is comoving distance. The comoving distance or conformal distance of two objects in the universe is the distance divided by a time-varying scale factor representing the expansion of the universe. ...

The metric only defines the distance between nearby points. In order to define the distance between arbitrarily distant points, one must specify both the points and a specific curve connecting them. The distance between the points can then be found by finding the length of this connecting curve. 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 space-time, such as the Lambda-CDM model. Standard Candles is a compilation of short stories by American science fiction author Jack McDevitt. ... A pie chart indicating the proportional composition of different energy-density components of the universe. ...

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 bourne 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, the properties of the universe which scientists have tested and where observation provides compelling confirmation. Sources of this confidence and confirmation include: The Cosmological Principle is a principle invoked in cosmology that severely restricts the large variety of possible cosmological theories: On large scales, the Universe is homogeneous and isotropic. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... In cosmology, the Copernican principle, named after Nicolaus Copernicus, states [1] More recently, the principle is generalised to the relativistic concept that humans are not privileged observers of the universe. ... Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors. ... A scientist, in the broadest sense, refers to any person that engages in a systematic activity to acquire knowledge or an individual that engages in such practices and traditions that are linked to schools of thought or philosophy. ...

• Edwin Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us ("Hubble's law") as predicted by a universal expansion.^[2] 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 extremely isotropic and homogenous, 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 and superclusters and filaments which were anything but isotropic and homogeneous. This lumpiness disappears into a smooth distribution of galaxies at the largest scales in much the same way a Jackson Pollock painting looks lumpy close-up, but more regular as a whole.
• 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. 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.^[3] Uniform cooling of the cosmic microwave background over billions of years is explainable only if the universe is experiencing a metric expansion.

Taken together, the only theory which coherently explains these phenomena relies on space expanding through a change in metric. Interestingly, 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. Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. ... This box:      Hubbles law is a statement in physical cosmology which states that the redshift in light coming from distant galaxies is proportional to their distance. ... This article is about the physical phenomenon. ... Although some radiations are marked as N for no in the diagram, some waves do in fact penetrate the atmosphere, although extremely minimally compared to the other radiations The electromagnetic (EM) spectrum is the range of all possible electromagnetic radiation. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... Astronomy and cosmology examine the universe to understand the large-scale structure of the cosmos. ... In astronomy, a redshift survey is a survey of a section of the sky to measure the redshift of astronomical objects. ... The End of Greatness is an observational scale discovered at roughly 100 Mpc where the lumpiness seen in the large-scale structure of the universe is homogenized and isotropized as per the Cosmological Principle. ... Galaxy groups and clusters are super-structures in the spread of galaxies of the cosmos. ... Superclusters are large groupings of smaller galaxy groups and clusters, and are among the largest structures of the cosmos. ... Controversy swirls over the alleged sale of No. ... In astronomy, gamma-ray bursts (GRBs) are flashes of gamma rays that last from seconds to hours, the longer ones being followed by several days of X-ray afterglow. ... For other uses, see Supernova (disambiguation). ... WMAP image of the CMB anisotropy,Cosmic microwave background radiation(June 2003) The cosmic microwave background radiation (CMB) is a form of electromagnetic radiation that fills the whole of the universe. ... The European Southern Observatory (ESO) is an international astronomical organisation, composed and supported by ten countries from the European Union plus Switzerland. ... For other uses, see Milky Way (disambiguation). ... Milnes model follows the description from special relativity of an observable universes spacetime diagram containing past and future light cones along with elsewhere in spacetime. ... This article needs additional references or sources for verification. ...

Additionally, scientists are confident that the theories which rely on the metric expansion of space are correct because they have passed the rigorous standards of the scientific method. In particular, when physics calculations are performed based upon the current theories (including metric expansion), they appear to give results and predictions which, in general, agree extremely closely with both astrophysical and particle physics observations. The spatial and temporal universality of physical laws was until very recently taken as a fundamental philosophical assumption that is now tested to the observational limits of time and space. This evidence is taken very seriously because the level of detail and the sheer quantity of measurements which the theories predict can be shown to precisely and accurately match visible reality. The level of precision is difficult to quantify, but is on the order of the precision seen in the physical constants that govern the physics of the universe. Scientific method is a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per nucleon) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... For a list of set rules, see Laws of science. ... A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. ...

Model analogies

Because metric expansion is not seen on the physical scale of humans, the concept may be difficult to grasp; it is a concept in intrinsic Riemannian geometry, which is abstract because all physical objects are extrinsically embedded in space. Three analogies have been developed to aid in conceptual understanding: Spatial scale provides a shorthand form for discussing relative lengths, areas, distances and sizes. ... In differential geometry, Riemannian geometry is the study of smooth manifolds with Riemannian metrics, i. ... Analogy is both the cognitive process of transferring information from a particular subject (the analogue or source) to another particular subject (the target), and a linguistic expression corresponding to such a process. ...

• the ant-on-a-balloon analogy,
• the expanding rubber sheet analogy, and
• the raisin bread analogy.

Each analogy has its conceptual benefits and drawbacks. European sweetbread (strucla) Four loaves French bread has a somewhat rigid crust Breads and Bread Rolls at a bakery Continental Italian Bread Tin Vienna Bread Bread in a traditional oven, in Portugal, with hot coal in front For other uses, see Bread (disambiguation). ...

Ant on a balloon model

The ant on a balloon model is a two-dimensional analog for three-dimensional metric expansion. An ant is imagined to be constrained to move on the surface of a huge balloon which to the ant's understanding is the total extent of space (see article on Flatland for more consequences of a two-dimensional constraint). At an early stage of the balloon-universe, the ant measures distances between separate points on the balloon which serves as a standard by which the scale factor can be measured. The balloon is inflated some more, and then the distance between the same points is measured and determined to be larger by a proportional factor. The surface of the balloon still appears flat, and yet all the points have appeared to recede from the ant, indeed every point on the surface of the balloon is proportionally farther from the ant than earlier in the life of the balloon universe. This explains how an expanding universe can result in all points receding from each other simultaneously. No points are seen to get closer together. A constraint is a limitation of possibilities. ... For various uses of the term Flatlander, see Flatlander (disambiguation) Flatland: A Romance of Many Dimensions is a 1884 novella by Edwin Abbott Abbott, still popular among mathematics and computer science students, and considered useful reading for people studying topics such as the concept of other dimensions. ...

This analog can also be used to illustrate how the ant, by moving at a steady speed and given sufficient time, can reach arbitrarily distant points on the balloon even if the apparent speed at which the ant's destination was initially receding is greater than the speed the ant moves. This explains how light can still reach us from galaxies so distant that their apparent speed away from us is greater than the speed of light.

See also: Ant on a rubber rope

In the limit where the ant is tiny and the balloon is enormous, the ant also cannot detect any curvature associated with the geometry of the surface (which is roughly an elliptical geometry for the outside surface of a curving balloon). To the ant, the balloon appears to be a plane extending out in all directions. This mimics the so-called "flatness" seen in our own observable universe which appears even at the largest scale to follow the geometrical laws associated with flat geometry. Like the ant on an enormous balloon, while we may be unable to detect curvature, on larger, unobservable scales there may be residual curvature. The shape of the universe we observe is driven to be flat no matter what starting conditions the universe had by the same cosmic inflation which caused the universe to begin expanding in the first place. In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. ... For other uses, see Geometry (disambiguation). ... Elliptic geometry (sometimes known as Riemannian geometry) is a non-Euclidean geometry, in which, given a line L and a point p outside L, there exists no line parallel to L passing through p. ... The flatness problem is a cosmological problem with the Big Bang theory, which is solved by hypothesising an inflationary universe. ... See universe for a general discussion of the universe. ... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician [[Euclid]] of Alexandria. ... The shape of the Universe is an informal name for a subject of investigation within physical cosmology. ... In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density. ...

In the analogy, the two dimensions of the balloon do not expand "into" anything since the surface of the balloon admits infinite paths in all directions at all times. There is some possibility for confusion in this analogy since the balloon can be seen by an external observer to be expanding "into" the third dimension (in the radial direction), but this is not a feature of metric expansion, rather it is the result of the arbitrary choice of the balloon which happens to be a manifold embedded in a third dimension. This third dimension is not mathematically necessary for two-dimensional metric expansion to occur, and the ant that is confined to the surface of the balloon has no way of determining whether a third dimension exists or not. It may be useful to visualize a third dimension, but the fact of expansion does not theoretically require such a dimension to exist. This is why the question "what is the universe expanding into?" is poorly phrased. Metric expansion does not have to proceed "into" anything. The universe that we inhabit does expand and distances get larger, but that does not mean that there is a larger space into which it is expanding. In mathematics, a path in a topological space X is a continuous map f from the unit interval I = [0,1] to X f : I → X. The initial point of the path is f(0) and the terminal point is f(1). ... Look up radial in Wiktionary, the free dictionary. ... On a sphere, the sum of the angles of a triangle is not equal to 180° (see spherical trigonometry). ... In physics, hyperspace is a theoretical entity. ...

Expanding rubber sheet model

Similar to the ant on a balloon model, the expanding rubber sheet universe (ERSU) is given as a model that represents the expansion by ignoring the third dimension. Instead of relying on a balloon expanding into three dimensions, the ERSU model describes an infinite rubber sheet that is stretched in both directions. Heavy objects placed on the sheet create dips and dents of local curvature in much the same way massive galaxies curve spacetime in the gravitational wells of our universe. These objects all appear to be receding from each other unless they get caught in each other's gravitational wells (a process called virialization). The infinite rubber sheet stays infinite and two dimensional, but distances between points on the sheet steadily increase with the expansion. This model has the advantage over the balloon model of a macroscopically two-dimensional flat geometry which corresponds well to the measured three-dimensional (lack of) curvature in our observable universe. In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. ... A gravity well is the scientific/science fictional term for the distortion in space-time caused by a massive body such as a planet. ... In mechanics, the virial theorem provides a general equation relating the average total kinetic energy of a system with its average total potential energy , where angle brackets represent the average of the enclosed quantity. ...

Raisin bread model

Animation of an expanding raisin bread model. As the bread doubles in width (depth and length), the distances between raisins also double.

The raisin bread model imagines galaxies as raisins in a raisin bread dough that will "rise" or "expand" when cooked. As the expansion occurs, each of the raisins gets farther from each of the other raisins while the raisins themselves stay the same size. The dough between raisins in this model acts as the space between galaxies while the raisins as "bound objects" are not subject to the expansion. This model is useful for explaining how it is that a standard ruler can be determined for measuring the expansion. In an empty universe, space serves as the only ruler and as rulers expand with space, there would be no way to distinguish between an expanding universe and a static universe. Only in a universe where there are objects which are bound and do not expand so that the rulers are independent of the expansion can the metric expansion be measured. Milnes model follows the description from special relativity of an observable universes spacetime diagram containing past and future light cones along with elsewhere in spacetime. ...

Like the ant on the balloon model, this model also suffers from the problem that the raisin bread is expanding into the pan. To make the analogy to the universe, it is necessary to imagine raisin bread that has no observable edge. Expansion would still occur, but the question "what is the raisin bread expanding into?" would be meaningless.

See also

• World development

Notes

Nature is a prominent scientific journal, first published on 4 November 1869. ...

Printed references

• Eddington, Arthur. The Expanding Universe: Astronomy's 'Great Debate', 1900-1931. Press Syndicate of the University of Cambridge, 1933.
• Liddle, Andrew R. and David H. Lyth. Cosmological Inflation and Large-Scale Structure. Cambridge University Press, 2000.
• Lineweaver, Charles H. and Tamara M. Davis, "Misconceptions about the Big Bang", Scientific American, March 2005.
• Mook, Delo E. and Thomas Vargish. Inside Relativity. Princeton University Press, 1991.

Scientific American is a popular-science magazine, published (first weekly and later monthly) since August 28, 1845, making it the oldest continuously published magazine in the United States. ...

External links

• Video explaning the expansion of the universe by Canadian astrophysicist Doctor P
• Swenson, Jim Answer to a question about the expanding universe
• Felder, Gary, "The Expanding universe".
• NASA's WMAP team offers an "Explanation of the universal expansion" at a very elementary level
• Hubble Tutorial from the University of Wisconsin Physics Department
• Expanding raisin bread from the University of Winnipeg: an illustration, but no explanation
• "Ant on a balloon" analogy to explain the expanding universe at "Ask an Astronomer". (The astronomer who provides this explanation is not specified.)