| Physical cosmology | ||
 | ||
| Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe
| ||
The metric expansion of space is the averaged increase of metric (i. Physical cosmology, as a branch of Astronomy, is the study of the large-scale structure of the Universe and is concerned with fundamental questions about its The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. The age of the Universe is the time elapsed between the theory of the Big Bang and the present day This timeline of the Big Bang describes the events according to the Scientific theory of the Big Bang, using the cosmological time parameter of Comoving coordinates The ultimate fate of the universe is a topic in Physical cosmology. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance The Friedmann equations are a set of Equations in cosmology that govern the expansion of space in homogeneous and isotropic models e. measured) distance between objects in the universe with time. It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space. An intrinsic property is a property that an objected or a thing has of itself independently of other things including its context Metric expansion is a key feature of Big Bang cosmology and is modeled mathematically with the FLRW metric. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. This model is valid in the present era only at relatively large scales (roughly the scale of galactic superclusters and above). Superclusters are large groupings of smaller galaxy groups and clusters, and are among the largest structures of the Cosmos. At smaller scales matter has clumped together under the influence of gravitational attraction and these clumps do not individually expand, though they continue to recede from one another. The expansion is due partly to inertia (that is, the matter in the universe is separating because it was separating in the past) and partly to a repulsive force of unknown nature, which may be a cosmological constant. In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification Inertia dominated the expansion in the early universe, and according to the ΛCDM model the cosmological constant will dominate in the future. &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. In the present era they contribute in roughly equal proportions.
The metric expansion leads naturally to recession speeds which exceed the "speed of light" c and to distances which exceed c times the age of the universe, which is a frequent source of confusion among amateurs and even professional physicists. [1] The speed c has no special significance at cosmological scales.
Contents |
Understanding the expansion of space
.png/250px-Embedded_LambdaCDM_geometry_(alt_view).png)
Spacetime is highly curved at cosmological scales, and as a result the expansion of the universe is inherently general relativistic; it cannot be understood with special relativity alone. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial The images to the right show two views of the large-scale geometry of the universe according to the ΛCDM cosmological model. &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. Two of the dimensions of space are omitted, leaving one dimension of space and one of time. The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the big bang; the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion which eventually dominates in this model. This timeline of the Big Bang describes the events according to the Scientific theory of the Big Bang, using the cosmological time parameter of Comoving coordinates The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The cyan grid lines mark off comoving distance at intervals of one billion light years. In standard cosmology, ' comoving' distance and ' proper distance' are two closely related distance measures used by cosmologists to define distances between Note that the circular curling of the surface is an artifact of the embedding with no physical significance; space does not actually curl around on itself. (A similar effect can be seen in the tubular shape of the pseudosphere. In Geometry, a pseudosphere of radius R is a surface of curvature &minus1/ R 2 (precisely a complete, Simply connected )
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). In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. The yellow line is the worldline of the most distant known quasar. A quasar (contraction of QUASi-stellAR radio source) is an extremely powerful and distant Active galactic nucleus. 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.
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. The equivalence principle In particular, light always travels locally at the speed c; in our diagram, this means 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. 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 in the present era, and the distance between them when the light was emitted. The former distance (shown by the orange line) is about 28 billion light years, much larger than ct. The latter distance is about 4 billion light years, much smaller than ct. Note that the light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away. In fact we can see from the diagram that the light was 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. None of this surprising behavior originates from a special property of metric expansion, but simply from local principles of special relativity integrated over a curved surface.
Note that the universe is not expanding into anything; there is simply more space at later times than at earlier times. Furthermore this notion of "more space" is local, not global; we do not know how much space there is in total. The embedding diagram has been arbitrarily cut off a few billion years past the Earth and the quasar, but it could be extended indefinitely, even infinitely, provided we imagine it as curling into a "spiral of constant radius" rather than a circle. Even if the overall spatial extent is infinite we still say that space is expanding, because locally the characteristic distance between objects is increasing.
Local perturbations
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. In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification For much of the universe's history the expansion has been due mainly to inertia. The vis insita or innate force of matter is a power of resisting by which every body as much as in it lies endeavors to preserve in its present state whether it be of rest or of moving 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 Physical cosmology, cosmic inflation is the idea that the nascent Universe passed through a phase of exponential expansion that In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. These stars and galaxies do not subsequently expand, there being no force compelling them to do so. There is no essential 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. A uniform local "explosion" of matter can be locally described by the FLRW geometry, the same geometry which describes the expansion of the universe as a whole. 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. Albert Einstein 's theory of General relativity predicts that rotating bodies drag Spacetime around themselves in a phenomenon referred to as frame-dragging
This situation changes somewhat with the introduction of a cosmological constant. A cosmological constant has the effect of a repulsive force between objects which is proportional (not inversely proportional) to distance. Unlike inertia it actively "pulls" on objects which have clumped together under the influence of gravity, and even on individual atoms. However this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state which is slightly (undetectably) larger than it would otherwise have been. As the universe expands and the matter in it thins, the gravitational attraction decreases (since it is proportional to the density), while the cosmological repulsion increases; thus the ultimate fate of the ΛCDM universe is a near vacuum expanding at an ever increasing rate under the influence of the cosmological constant. However the only locally visible effect of the accelerating expansion is the disappearance (by runaway redshift) of distant galaxies; gravitationally bound objects like the Milky Way do not expand. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by
Other models of expansion
The expansion of space is often illustrated with 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. Ant on a rubber rope is a Mathematical puzzle with a solution that appears counter-intuitive or paradoxical 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.
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.
Overview of metrics
Metric expansion is not something that most humans are aware of, on a day to day basis. In Mathematics, a metric or distance function is a function which defines a Distance between elements of a set. To understand the 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 defines how a distance can be measured between two nearby points in space, in terms of the coordinates of those points. 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 In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point A coordinate system locates points in a space (of whatever number of dimensions) by assigning unique numbers known as coordinates, to each point. In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point The metric is then a formula which converts coordinates of two points into distances. In Mathematics and in the Sciences a formula (plural formulae, formulæ or formulas) is a concise way of expressing information
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. In mathematics non-Euclidean geometry describes how this all works--> hyperbolic and Elliptic geometry, which are contrasted with 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. Latitude, usually denoted symbolically by the Greek letter phi ( Φ) gives the location of a place on Earth (or other planetary body north or south of the Longitude (ˈlɒndʒɪˌtjuːd or ˈlɒŋgɪˌtjuːd symbolized by the Greek character Lambda (λ is the east-west Geographic coordinate measurement 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. An airline provides air transport services for Passengers or Freight, generally with a recognized operating certificate or license A great circle is a Circle on the surface of a Sphere that has the same circumference as the sphere dividing the sphere into two equal Hemispheres. 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).
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. In standard cosmology, ' comoving' distance and ' proper distance' are two closely related distance measures used by cosmologists to define distances between 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. Euclidean geometry is a mathematical system attributed to the Greek Mathematician Euclid of Alexandria. In Mathematics, the spherical coordinate system is a Coordinate system for representing geometric figures in three dimensions using three coordinates the radial The fourth required coordinate is time, which is specified in comoving coordinates as cosmological time. This timeline of the Big Bang describes the events according to the Scientific theory of the Big Bang, using the cosmological time parameter of Comoving coordinates 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.
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. The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 The Lorentz interval is a Quantity that is used instead of Distance when dealing with Space-time Geometry, because it is the only quantity that 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. Observation is either an activity of a living being (such as a Human) which senses and assimilates the Knowledge of a Phenomenon, or the recording of data Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter 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. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. If we lived in a space that contracted (a Big Crunch universe) we would observe phenomena associated with a metric contraction of space instead. In Physical cosmology, the Big Crunch is one possible scenario for the Ultimate fate of the universe, in which the Metric expansion of space eventually
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. In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification But in 1922 Alexander Friedman derived the famous Friedmann equations, showing that the universe might expand and presenting the expansion speed in this case. Year 1922 ( MCMXXII) was a Common year starting on Sunday of the Gregorian calendar. Alexander Alexandrovich Friedman or Friedmann (Александр Александрович Фридман ( June 16 1888, Saint Petersburg, Imperial The Friedmann equations are a set of Equations in cosmology that govern the expansion of space in homogeneous and isotropic models [2] 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. 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. The 1980s was the decade spanning from January 1 1980 to December 31 1989. In Physical cosmology, cosmic inflation is the idea that the nascent Universe passed through a phase of exponential expansion that In Quantum field theory, a false vacuum is a Metastable sector of Space which appears to be a perturbative vacuum but is unstable to Instanton 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. See also Cosmic inflation In Physical cosmology the inflationary epoch was the period in the evolution of the early universe when according to Inflation 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. Exponential growth (including Exponential decay) occurs when the growth rate of a mathematical function is proportional to the function's current value History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny A light-year or light year (symbol ly) is a unit of Length, equal to just under ten trillion Kilometres As defined by
Measuring distance in a metric space
In expanding space, distance is a dynamical quantity which changes with time. In standard cosmology, ' comoving' distance and ' proper distance' are two closely related distance measures used by cosmologists to define distances between There are several different ways of defining distance in cosmology, known as distance measures, but the most common is comoving distance.
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. A standard candle is an astronomical object that has a known Luminosity. &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter.
Observational evidence
Theoretical cosmologists developing models of the universe have drawn upon a small number of reasonable assumptions in their work. Cosmology (from Greek grc κοσμολογία - grc κόσμος kosmos, "universe" and grc -λογία -logia) is study 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 cosmological principle is an assumption invoked in Cosmology that when applied severely restricts the large variety of possible cosmological theories Isotropy is uniformity in all directions Precise definitions depend on the subject area
- the Copernican Principle which demands that no place in the universe is preferred (that is, the universe has no "starting point"). In Cosmology, the Copernican principle, named after Nicolaus Copernicus, states the Earth is not in a central specially favoured position
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. Observational cosmology is the study of the structure the evolution and the origin of the Universe through Observation, using instruments such as Telescopes 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 Sources of this confidence and confirmation include:
- Edwin Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us ("Hubble's law") as predicted by a universal expansion. Edwin Powell Hubble ( November 20, 1889 – September 28, 1953) was an American astronomer. Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance [3] 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. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by The electromagnetic (EM spectrum is the range of all possible Electromagnetic radiation frequencies Further studies have since shown the expansion to be extremely isotropic and homogeneous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point. Isotropy is uniformity in all directions Precise definitions depend on the subject area
- 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. In Physical cosmology, the term large-scale structure refers to the characterization of observable distributions of Matter and Light In Astronomy, a redshift survey, or galaxy survey, is a survey of a section of the sky to measure the Redshift of astronomical objects In Physical cosmology, the term large-scale structure refers to the characterization of observable distributions of Matter and Light 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. Galaxy groups and clusters are the largest Gravitationally bound objects to have arisen thus far in the process of cosmic structure formation Superclusters are large groupings of smaller galaxy groups and clusters, and are among the largest structures of the Cosmos. 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. Paul Jackson Pollock (January 28 1912 &ndash August 11 1956 was an influential American painter and a major force in the abstract expressionist movement
- The isotropic distribution across the sky of distant gamma-ray bursts and supernovae is another confirmation of the Cosmological Principle. Gamma-ray bursts ( GRB s are the most luminous electromagnetic events occurring in the Universe since the Big Bang. A supernova (plural supernovae or supernovas) is a stellar Explosion.
- 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. [4] 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). The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply The Milne model was a special relativistic cosmological model proposed by Edward Arthur Milne. Yet before this evidence, many rejected the Milne viewpoint based on the Mediocrity principle. The mediocrity principle is the notion in the Philosophy of science that there is nothing special about humans or the Earth
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. Scientific method refers to bodies of Techniques for investigating phenomena 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. Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them 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. A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i 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. A physical Constant is a Physical quantity that is generally believed to be both universal in nature and constant in time
See also
Notes
- ^ Tamara M. Davis and Charles H. Lineweaver, Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe. astro-ph/0310808
- ^ Friedman, A: Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377–386. (English translation in: Gen. Rel. Grav. 31 (1999), 1991–2000. )
- ^ Hubble, Edwin, "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 (Full article, PDF)
- ^ Astronomers reported their measurement in a paper published in the December 2000 issue of Nature titled The microwave background temperature at the redshift of 2.33771 which can be read here. Nature is a prominent Scientific journal, first published on 4 November 1869 A press release from the European Southern Observatory explains the findings to the public.
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. Scientific American is a Popular science magazine, published (first weekly and later monthly since August 28, 1845, making it
- Mook, Delo E. and Thomas Vargish. Inside Relativity. Princeton University Press, 1991.
External links
- Video explaning the expansion of the universe by Canadian astrophysicist Doctor P
- Swenson, Jim Answer to a question about the expanding universe
- The verse in the Noble Quran mentioning the expansion of the 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 National Aeronautics and Space Administration ( NASA, ˈnæsə is an agency of the United States government, responsible for the nation's public space program (The astronomer who provides this explanation is not specified. )
Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic