|
|
| Line 1: |
Line 1: |
| {{cosmology|cTopic=Expanding universe}}
| | I'm Yoshiko Oquendo. Bottle tops gathering is the only pastime his spouse doesn't approve of. His day occupation is a monetary officer but he ideas on altering it. For years she's been residing in Kansas.<br><br>Look into my web page [http://Blogzaa.com/blogs/post/14073 extended auto warranty] |
| The '''metric expansion of space''' is the increase of the [[proper distance|distance]] between two [[observable universe#Size|distant parts of the universe]] with [[cosmological time|time]]. It is an [[intrinsic and extrinsic properties (philosophy)|intrinsic]] expansion whereby ''the scale of space itself changes''. This is different from other examples of [[thermal expansion|expansion]]s and [[explosion]]s in that, as far as [[observational cosmology|observations]] can ascertain, it is a property of the [[Mathematics of general relativity#Local versus global structure|entirety of the universe]] rather than a phenomenon that can be contained and observed from the outside.
| |
| | |
| Metric expansion is a key feature of [[Big Bang cosmology]], is modeled mathematically with the [[Friedmann–Lemaître–Robertson–Walker metric|FLRW 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 cluster]]s and above). At smaller scales matter has [[virial theorem|become bound together]] under the influence of [[gravity|gravitational attraction]] and such things do not expand at the metric expansion rate as the universe ages. 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 [[Jeans length|length scales]] associated with the gravitational collapse that are possible in the [[age of the Universe]] given the [[matter density]] and average expansion rate.
| |
| | |
| At the end of the [[early universe|early universe's]] [[cosmic inflation|inflationary period]], all the matter and energy in the universe was set on an [[inertia|inertial trajectory]] consistent with the [[equivalence principle]] and Einstein's [[theory of general relativity]] and this is when the [[Hubble Law|precise and regular form of the universe's expansion]] had its origin (that is, matter in the universe is separating because it was separating in the past due to the [[inflaton field]]). Additionally, the expansion rate of the universe has been measured to be [[accelerating universe|accelerating]]; to explain this, physicists postulate a repulsive force of [[dark energy]] which appears in the simplest theoretical models as a [[cosmological constant]]. This acceleration of the universe has only recently become measurable. According to such measurements, the universe's expansion rate was ''decelerating'' until about 5 billion years ago due to the gravitational attraction of the matter content of the universe, after which time the expansion [[inflection point|began accelerating]]. According to the simplest extrapolation of the [[Lambda-CDM model|currently-favored cosmological model]] (known as "ΛCDM"), this acceleration becomes more dominant into the future.
| |
| | |
| While [[special relativity]] constrains objects in the universe from moving faster than the speed of light with respect to each other when they are in a local, [[Relativistic dynamics|dynamical]] relationship, it places no theoretical constraint on the relative motion between two objects that are globally separated and out of [[causality|causal contact]]. It is thus possible for two objects to be become separated in space by more than the distance light could have travelled, which means that, if the expansion remains constant, the two objects will never come into causal contact. For example, galaxies that are more than approximately 4.5 [[gigaparsec]]s away from us are expanding away from us faster than the [[speed of light]]. We can still see such objects because the universe in the past was expanding more slowly than it is today, so the ancient light being received from these objects is still able to reach us, though if the expansion continues unabated there will never come a time that we will see the light from such objects being produced ''today'' (on a so-called "[[Space-like|space-like slice of spacetime]]") and vice-versa because space itself is expanding between Earth and the source faster than any light can be exchanged.
| |
| | |
| Because of the changing rate of expansion, it is also possible for a distance to exceed the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.<ref>Tamara M. Davis and Charles H. Lineweaver, ''Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe''. [http://arxiv.org/abs/astro-ph/0310808 astro-ph/0310808]</ref>
| |
| | |
| Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion in the realm of pedagogy and communication of scientific concepts.<ref name=Whiting>{{cite journal |title= The Expansion of Space: Free Particle Motion and the Cosmological Redshift |arxiv=astro-ph/0404095 |year=2004 |journal=ArXiv preprint |author= Alan B. Whiting |bibcode = 2004Obs...124..174W }}</ref><ref name=Hogg>{{cite journal |title=The kinematic origin of the cosmological redshift |author=EF Bunn & DW Hogg |arxiv=0808.1081 |journal=ArXiv preprint |year=2008|bibcode = 2009AmJPh..77..688B |doi = 10.1119/1.3129103 }}</ref><ref name=Baryshev>{{cite journal |title=Expanding Space: The Root of Conceptual Problems of the Cosmological Physics |author=Yu. V. Baryshev |arxiv=0810.0153 |journal=Practical Cosmology |volume=2 |pages=20–30 |year=2008|bibcode = 2008pc2..conf...20B }}</ref><ref name=Peacock>{{cite journal |arxiv=0809.4573 |journal=ArXiv preprint |title=A diatribe on expanding space |author=JA Peacock |year=2008|bibcode = 2008arXiv0809.4573P }}</ref>
| |
| | |
| == Basic concepts and overview ==
| |
| | |
| ===Overview of metrics===
| |
| {{Main|Metric (mathematics)}}
| |
| To understand the metric expansion of the universe, it is helpful to discuss briefly what a metric is, and how metric expansion works.
| |
| | |
| ====Definition of a metric====
| |
| A '''[[Metric (mathematics)|metric]]''' defines how a [[distance]] can be measured between two ''nearby'' points in space, in terms of the [[coordinate system]]. Coordinate systems locate points in a space (of whatever number of [[dimension]]s) by assigning unique positions on a grid, known as [[coordinate]]s, to each point. The metric is then a [[formula]] which describes how displacement through the space of interest can be translated into distances.
| |
| | |
| ====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 coordinate system|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. 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 so small enough to be unnoticeable. In general, such shortest-distance paths are called, "[[geodesic]]s". 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.
| |
| | |
| ====Metric tensor====
| |
| | |
| In [[differential geometry]], the backbone mathematics for [[general relativity]], a [[metric tensor]] can be defined which 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 [[spacetime interval|intervals]] of time and space depending on the [[inertial frame]]. This means that the metric tensor in general relativity relates precisely how two [[event]]s 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 [[Thermal expansion|expansion]]s and [[explosion]]s commonly seen in [[nature]] in no small part because times and [[distance]]s are not the same in all reference frames, but are instead subject to change. A useful visualization is to approach the subject rather than objects in a fixed "space" moving apart into "emptiness", as space itself growing between objects without any [[acceleration]] of the objects themselves. The space between objects grows or shrinks as the various [[geodesic]]s 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]] which is a constraint only on the speed matter can obtain from [[Lorentz transformation|boosts from one reference frame to another]]. Two references frames that are globally separated can be moving apart faster than light without violating special relativity, though 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 horizon]]s.
| |
| | |
| Theory and observations suggest that very early in the history of the universe, there was an "[[cosmic inflation|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 Law|Hubble expansion]], the moving apart of all [[Virial theorem#In astrophysics|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.
| |
| | |
| ===Measuring distances in expanding spaces===
| |
| {{main|comoving coordinates}}
| |
| In expanding space, [[proper distance]]s are dynamical quantities which 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 (physics)|dynamics]] of [[matter]] and [[light]] are determined by the normal [[physics]] of [[gravity]] and [[electromagnetic radiation]]. Any time-evolution however must be accounted for by taking into account the [[Hubble law]] expansion in the appropriate equations in addition to any other effects that may be operating ([[gravity]], [[dark energy]], or [[curvature]], for example). Cosmological simulations that run through significant fractions of the universe's history therefore must include such effects in order to make applicable predictions for [[observational cosmology]].
| |
| | |
| ==Understanding the expansion of the Universe==
| |
| | |
| ===How is the expansion of the universe measured and how does the rate of expansion change?===
| |
| | |
| In principle, the expansion of the universe can 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. In practice, standard rulers are not straightforward to find on cosmological scales and the time-scales for waiting to see a measurable expansion of the universe today are too long to be observable by even generations of humans. Instead, the [[theory of relativity]] predicts and observations show phenomena associated with the expansion of the universe, notably the [[redshift]]-distance relationship known as [[Hubble's Law]], functional forms for [[Distance measures (cosmology)|cosmological distance measurements]] that differ from what would be expected if space were not expanding, and an observable change in the [[Density parameter|matter and energy density]] of the universe seen at different [[lookback time]]s.
| |
| | |
| The first measurement of the expansion of space occurred with the creation of the Hubble diagram. Using [[Cosmic distance ladder|standard candles]] with known intrinsic brightness, the expansion of the universe has been measured using redshift to derive Hubble's Constant: [[Hubble's law|H<sub>0</sub>]] = {{nowrap|67.15 ± 1.2 (km/s)/Mpc}}. For every million [[parsec]]s of distance from the observer, the rate of expansion increases by about 67 kilometers per second.<ref>{{cite web|title=Planck Mission Brings Universe Into Sharp Focus|url=http://www.jpl.nasa.gov/news/news.php?release=2013-109&rn=news.xml&rst=3739|publisher=NASA|accessdate=2013-03-21|date=2013-03-21}}</ref><ref>{{cite web|title=NASA's Hubble Rules Out One Alternative to Dark Energy|url=http://www.nasa.gov/mission_pages/hubble/science/cosmic-expansion.html|publisher=NASA|accessdate=2011-03-27|date=2011-03-14}}</ref><ref name="Riess2011">{{cite journal | title = A 3% solution: determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3 |journal = The Astrophysical Journal | date = 2011-04-01 | first = Adam G. | last = Riess | coauthors = Lucas Macri, Stefano Casertano, Hubert Lampeitl, Henry C. Ferguson, Alexei V. Filippenko, Saurabh W. Jha, Weidong Li, and Ryan Chornock | volume = 730 | issue = 2 | page = 119| id = | accessdate = 2011-05-10 | doi=10.1088/0004-637X/730/2/119 | bibcode=2011ApJ...730..119R|arxiv = 1103.2976 }}</ref> Since distant objects are observed further back in time, there is a one-to-one correspondence between the distance to a distant galaxy and the amount of time that has passed since the light being observed was emitted from that galaxy. Thus, Hubble's Constant can be thought of as an acceleration which in the local universe is equivalent to approximately {{val|7|e=-10|u=m/s<sup>2</sup>}}, though this value is on large-scales dependent on how one defines the distance between two points and how one measures the elapsed time. Cosmologists often adopt [[comoving coordinates]] which remove the expansion altogether.
| |
| | |
| The acceleration of objects moving away from each other in an expanding universe is not the sort of acceleration which can be associated with a force as in [[Newton's second law]] because the expansion is an intrinsic property of the way space and time are measured rather than being due to dynamical interactions. Nevertheless, because the [[Dimensional analysis|dimensional form]] of Hubble's Constant can yield an acceleration this has caused some confusion associated with the so-called "[[accelerating universe]]" which was first discovered and characterized in the late 1990s. In a universe that is undergoing a constant Hubble expansion, the universal Hubble Constant can be conceptualized as a universal acceleration, but Hubble's Constant is not constant through time since there are dynamical forces acting on the particles in the universe which affect the expansion rate. It was expected that the Hubble Constant 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 Hubble's Constant is increasing as time goes on. Since Hubble's Constant can be associated with an acceleration, the change in Hubble's Constant over time can be associated with the time derivative of acceleration, and so some cosmologists have whimsically called the effect associated with the "accelerating universe" the "cosmic [[jerk (physics)|jerk]]".<ref>{{cite news|last=Overbye|first=Dennis|title=A 'Cosmic Jerk' That Reversed the Universe|url=http://www.nytimes.com/2003/10/11/us/a-cosmic-jerk-that-reversed-the-universe.html?pagewanted=all&src=pm|newspaper=New York Times|date=October 11, 2003}}</ref> The 2011 Nobel Prize in Physics was given for the discovery of this phenomenon.<ref>[http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/press.html The Nobel Prize in Physics 2011]</ref>
| |
| | |
| ===How are distances between two points measured if space is expanding?===
| |
| | |
| {{Multiple image|direction=vertical|align=right|image1=Embedded_LambdaCDM_geometry.png|image2=Embedded_LambdaCDM_geometry_(alt_view).png|width=250|caption2=Two views of an [[isometric embedding]] of part of the [[visible universe]] over most of its history, showing how a light ray (red line) can travel an effective distance of 28 billion [[light year]]s (orange line) in just 13 billion years of [[cosmological time]]. Click the images to zoom. ([[:Image:Embedded LambdaCDM geometry.png#Mathematical details|Mathematical details]])}}
| |
| At cosmological scales the present universe is geometrically flat, which is to say that the rules of [[Euclidean geometry]] associated with [[Parallel postulate|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 relativity|general relativistic]]; it cannot be modeled with [[special relativity]] alone, though [[Milne universe|such models]] can be written down, 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 diagram]]s 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 universe|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. 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 [[Integral|integrated]] over a curved surface.
| |
| | |
| ===What space is the universe expanding into?===
| |
| [[File:CMB Timeline300 no WMAP.jpg|right|380px|thumb|A graphical representation of the expansion of the universe with the inflationary epoch represented as the dramatic expansion of the [[metric tensor|metric]] seen on the left. 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.]]
| |
| 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 [[string theory|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.<ref>{{cite book|last=Peebles|first=P. J. E.|title=Principles of Physical Cosmology|year=1993|page=73|publisher=Princeton University Press}}</ref>
| |
| | |
| The ultimate [[topology]] of space is something which in principle must be observed as there are no ''a priori'' constraints on how the space in which we live is [[Simply connected space|connected]] or whether it wraps around on itself as a [[compact space]]. Though certain cosmological models such as [[Gödel metric|Gödel's universe]] even permit bizarre [[worldline]]s 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 [[Shape of the Universe#Detection|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 horizon]]s. The universe could be infinite in extent or it could be finite; but the evidence that leads to the [[cosmic inflation|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.<ref>http://curious.astro.cornell.edu/question.php?number=274</ref>
| |
| | |
| 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.
| |
| | |
| Even if the overall spatial extent is infinite and thus the universe can't 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.
| |
| | |
| ===Is the expansion of the universe felt 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 our [[Local Group]] of galaxies, 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 [[supercluster]]s 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, our 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 metric|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 universe|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 rates of speed and be redshifted out of our range of visibility.
| |
| | |
| === Scale factor ===
| |
| At a fundamental level, the expansion of the universe is a property of spatial measurement on the largest measurable scales of our universe. The distances between cosmologically relevant points increases as time passes leading to observable effects outlined below. This feature of the universe can be characterized by a single parameter that is called the [[Scale factor (cosmology)|scale factor]] which is a [[function (mathematics)|function]] of time and a single value for all of space at any instant (if the scale factor were a function of space, this would violate the [[cosmological principle]]). By convention, the scale factor is set to be unity at the present time and, because the universe is expanding, is smaller in the past and larger in the future. Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero, our current understanding of cosmology sets [[Age of the universe|this time at 13.798 ± 0.037 billion years ago]]. If the universe continues to expand forever, the scale factor will approach infinity in the future. In principle, there is no reason that the expansion of the universe must be [[monotonic function|monotonic]] and there are models that exist where at some time in the future the scale factor decreases with an attendant contraction of space rather than an expansion.
| |
| | |
| ===Other conceptual models of expansion===
| |
| The expansion of space is often illustrated with conceptual models which show only the size of space at a particular time, leaving the dimension of time implicit.
| |
| | |
| In the "[[ant on a rubber rope]] model" one imagines an ant (idealized as pointlike) crawling at a constant speed on a perfectly elastic rope which is constantly stretching. If we stretch the rope in accordance with the ΛCDM scale factor and think of the ant's speed as the speed of light, then this analogy is numerically accurate—the ant's position over time will match the path of the red line on the embedding diagram above.
| |
| | |
| In the "rubber sheet model" one replaces the rope with a flat two-dimensional rubber sheet which expands uniformly in all directions. The addition of a second spatial dimension raises the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet.
| |
| | |
| In the "balloon model" the flat sheet is replaced by a spherical balloon which is inflated from an initial size of zero (representing the big bang). A balloon has positive Gaussian curvature while observations suggest that the real universe is spatially flat, but this inconsistency can be eliminated by making the balloon very large so that it is locally flat to within the limits of observation. This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon. In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time.
| |
| | |
| [[Image:Raisinbread.gif|thumb|200px|Animation of an expanding raisin bread model. As the bread doubles in width (depth and length), the distances between raisins also double.]]
| |
| In the "raisin bread model" one imagines a loaf of raisin bread expanding in the oven. The loaf (space) expands as a whole, but the raisins (gravitationally bound objects) do not expand; they merely grow farther away from each other.
| |
| | |
| All of these models have the conceptual problem of requiring an outside force acting on the "space" at all times to make it expand. Unlike real cosmological matter, sheets of rubber and loaves of bread are bound together electromagnetically and will not continue to expand on their own after an initial tug.
| |
| | |
| ==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 [[galaxy|galaxies]] that are more distant from us are [[recessional velocity|receding]] faster than galaxies that are closer to us ([[Hubble's law]]).
| |
| | |
| ===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 Friedman]] derived a set of equations known as the [[Friedmann equations]], showing that the universe might expand and presenting the expansion speed in this case.<ref>Friedman, A: Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377–386. (English translation in: Gen. Rel. Grav. 31 (1999), 1991–2000.)</ref> 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 is implied by Hubble's 1929 observations, Hubble was concerned with the observational implications of the precise value he measured:
| |
| | |
| {{Quotation|"… 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 principle 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 <ref>[http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1936ApJ....84..517H&db_key=AST&data_type=HTML&format=&high=427d1954a200670]</ref>}}
| |
| | |
| {{Quotation|"[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 <ref>[http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1937MNRAS..97..506H&db_key=AST&data_type=HTML&format=&high=427d1954a200670]</ref>}}
| |
| | |
| In fact, Hubble's skepticism about the universe being too small, dense, and young was justified, though it turned out to be an observational error rather than an error of interpretation. Later investigations showed that Hubble had confused distant [[HII regions]] for [[Cepheid variable]]s 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 [[kilometer|km]]/[[second|s]]/[[Megaparsec|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 [[shape of the universe|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.<ref>http://www.jstor.org/stable/10.1086/316324</ref>
| |
| | |
| ===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 [[inflationary epoch|10<sup>−32</sup> seconds]] of the existence of our universe.<ref>Interview with [[Alan Guth]]; ''THE INFLATIONARY UNIVERSE'', [11.19.02] by [[Edge.org]]. [http://www.edge.org/conversation/the-inflationary-universe-alan-guth]</ref> During inflation, the metric changed [[exponential growth|exponentially]], causing any volume of space that was smaller than an [[atom]] to grow to around 100 million [[light year]]s across in a time scale similar to the time when inflation occurred (10<sup>−32</sup> seconds).
| |
| | |
| [[Image:Universe.svg|thumb|400px|The expansion of the universe proceeds in all directions as determined by the [[Hubble constant]]. 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 [[Density parameter|critical density]] (<math>\Omega_m</math>).]]
| |
| | |
| ===Measuring distance in a metric space===
| |
| {{Main|comoving coordinates}}
| |
| | |
| 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'''. <!--possible usage debate here-->
| |
| | |
| 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 space-time, 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.
| |
| | |
| ==Observational evidence==
| |
| [[File:Expansion of Space (Galaxies).png|thumb|right|175px|A diagram depicting the expansion of the universe and the appearance of galaxies moving away from a single galaxy. The phenomenon is relative to the observer. Object ''t''1 is a smaller expansion than ''t''2. Each section represents the movement of the red galaxies over the white galaxies for comparison. The blue and green galaxies are markers to show which galaxy is the same one (fixed center point) in the subsequent box. ''t'' = time.]]
| |
| | |
| 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 ([[wiktionary:Homogeneous|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 cosmology|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, [[scientist]]s have tested the properties of the universe and observation provides compelling confirmation.<ref>{{cite journal|last=Bennett|first=Charles L.|authorlink=Charles L. Bennett|title=Cosmology from start to finish|journal=Nature|date=27 April 2006|volume=440|issue=7088|pages=1126–1131|doi=10.1038/nature04803|url=http://www.nature.com/nature/journal/v440/n7088/abs/nature04803.html|bibcode = 2006Natur.440.1126B }}</ref> 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.<ref>Hubble, Edwin, "[http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1929PNAS...15..168H&db_key=AST&data_type=HTML&format=&high=42ca922c9c30954 A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae]" (1929) ''Proceedings of the National Academy of Sciences of the United States of America'', Volume 15, Issue 3, pp. 168-173 ([http://www.pnas.org/cgi/reprint/15/3/168 Full article], PDF)</ref> Using the [[redshift]] of their [[electromagnetic spectrum|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 [[wiktionary:Homogeneous|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 survey]]s 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 cluster]]s and [[supercluster]]s 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 burst]]s and [[supernova]]e 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.<ref>Astronomers reported their measurement in a paper published in the December 2000 issue of [[Nature (journal)|Nature]] titled ''[http://adsabs.harvard.edu/cgi-bin/bib_query?astro-ph/0012222 The microwave background temperature at the redshift of 2.33771]'' which can be read here [http://arxiv.org/abs/astro-ph/0012222]. A [http://www.eso.org/outreach/press-rel/pr-2000/pr-27-00.html press release] from the European Southern Observatory explains the findings to the public.</ref> 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. 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 [[Milne Model|early model proposed by Milne]]). Yet before this evidence, many rejected the Milne viewpoint based on the [[mediocrity principle]].
| |
| | |
| The spatial and temporal universality of [[physical law]]s was until very recently taken as a fundamental philosophical assumption that is now tested to the observational limits of time and space.
| |
| | |
| ==Notes==
| |
| {{Reflist}}
| |
| | |
| ==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, "[http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0009F0CA-C523-1213-852383414B7F0147 Misconceptions about the Big Bang]", ''[[Scientific American]]'', March 2005.
| |
| *Mook, Delo E. and Thomas Vargish. ''Inside Relativity''. Princeton University Press, 1991.
| |
| | |
| ==External links==
| |
| *Swenson, Jim [http://www.newton.dep.anl.gov/askasci/phy00/phy00812.htm Answer to a question about the expanding universe]
| |
| *Felder, Gary, "[http://www.ncsu.edu/felder-public/kenny/papers/cosmo.html The Expanding universe]".
| |
| *[[NASA]]'s [[WMAP]] team offers an "[http://map.gsfc.nasa.gov/m_uni/uni_101bbtest1.html Explanation of the universal expansion]" at a very elementary level
| |
| *[http://cmb.physics.wisc.edu/tutorial/hubble.html Hubble Tutorial from the University of Wisconsin Physics Department]
| |
| *[http://theory.uwinnipeg.ca/mod_tech/node216.html Expanding raisin bread] from the University of Winnipeg: an illustration, but no explanation
| |
| *[http://www.ucolick.org/~mountain/AAA/aaa_old/030209.html#expansion "Ant on a balloon" analogy to explain the expanding universe] at "Ask an Astronomer". (The astronomer who provides this explanation is not specified.)
| |
| *[http://www.rahulgladwin.com/docs/the-big-bang.php Researched Essay: "The Big Bang" - Proof that the Universe is Expanding]
| |
| | |
| {{Use dmy dates|date=May 2011}}
| |
| | |
| {{DEFAULTSORT:Metric Expansion Of Space}}
| |
| [[Category:Physical cosmology]]
| |
| [[Category:General relativity]]
| |
| [[Category:Big Bang]]
| |