Physical Cosmology

Physical Cosmology

Universe · Big Bang Age of the universe Timeline of the Big Bang... Ultimate fate of the Universe Image File history File links Download high resolution version (2198x1274, 1278 KB)WMAP map of CMB anisotropy, from NASA.gov File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Physical cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... According to the Big Bang model, the universe emerged from an extremely dense and hot state. ... The age of the universe, according to the Big Bang theory, is the time elapsed between the Big Bang and the present day. ... 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, using the cosmological time parameter of comoving coordinates. ... The ultimate fate of the universe is a topic in physical cosmology. ...

Early universe

Inflation · Nucleosynthesis Cosmic gravitational waves Cosmic microwave background 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. ... In cosmology, the cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR, also referred as relic radiation) is a form of electromagnetic radiation discovered in 1965 that fills the entire universe. ...

Expanding universe

Redshift · Hubble's law Metric expansion of space Friedmann equations · FLRW metric Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared with that of the Sun (left). ... Hubbles law is the statement in physical cosmology that the redshift in light coming from distant galaxies is proportional to their distance. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... 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. ...

Structure formation

Shape of the universe Structure formation Galaxy formation Large-scale structure 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. ...

Components

Lambda-CDM model Dark energy · Dark matter 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. ... In astrophysics and cosmology, dark matter refers to hypothetical matter of unknown composition that does not emit or reflect enough electromagnetic radiation to be observed directly, but whose presence can be inferred from gravitational effects on visible matter. ...

History

Timeline of cosmology... This lists a timeline of cosmological theories and discoveries. ...

Cosmology experiments

Observational cosmology 2dF · SDSS CoBE · BOOMERanG · WMAP 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. ...

Scientists

Einstein · Friedman · Lemaître Hubble · Penzias · Wilson Gamow · Dicke · Zel'dovich Mather · Smoot · others Albert Einstein ( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is best known for his theory of relativity and specifically mass-energy equivalence, . He was awarded the 1921 Nobel Prize in Physics for his services to Theoretical Physics, and especially for his discovery of the... Alexander Alexandrovich Friedman or Friedmann (Александр Александрович Фридман) (June 16, 1888 – September 16, 1925) was a Russian cosmologist and mathematician. ... Father Georges-Henri Lemaître (July 17, 1894 – June 20, 1966) was a Belgian Roman Catholic priest, honorary prelate, professor of physics and astronomer. ... Edwin Powell Hubble (November 29, 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 partial list of persons who have made major contributions to the development of standard mainstream Cosmology. ...

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The shape of the Universe is an informal name for a subject of investigation within physical cosmology. Cosmologists and astronomers describe the geometry of the universe which includes both local geometry and global geometry. It is loosely divided into curvature and topology, even though strictly speaking, it goes beyond both. Physical cosmology, as a branch of astrophysics, is the study of the large-scale structure of the universe and is concerned with fundamental questions about its formation and evolution. ... Calabi-Yau manifold Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ...

Introduction

Considerations of the shape of the universe can be split into two parts; the local geometry relates especially to the curvature of the observable universe, while the global geometry relates especially to the topology of the universe as a whole—which may or may not be within our ability to measure. See universe for a general discussion of the universe. ...

The extrapolation of the local geometry of space to the geometry of the whole universe is not without a specific ontological stance regarding how space and time coexist. Current thinking demands that space and time be considered as two aspects of a single entity 'spacetime'.

Nevertheless it still makes sense to speak about three-dimensional concepts referring to the universe, like the Hubble volume. A Hubble volume refers to a volume of space, usually defined as a cube where each axis is approximately 13. ...

Local geometry (spatial curvature)

The local geometry is the curvature describing any arbitrary point in the observable universe (averaged on a sufficiently large scale). Many astronomical observations, such as those from supernovae and the Cosmic Microwave Background (CMB) radiation, show the observable universe to be very close to homogeneous and isotropic and infer it to be accelerating. In General Relativity, this is modelled by the Friedmann-Lemaître-Robertson-Walker (FLRW) model. This model, which can be represented by the Friedmann equations, provides a curvature (often referred to as geometry) of the universe based on the mathematics of fluid dynamics, i.e. it models the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. Remnant of Keplers Supernova, SN 1604. ... 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. ... General relativity (GR) [also called the general theory of relativity (GTR) and general relativity theory (GRT)] is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... The Friedmann-Lemaître-Robertson-Walker (FLRW) metric describes a homogeneous, isotropic expanding/contracting universe. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ...

Another way of saying this is that if all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies). This assumption is justified by the observations that, while the universe is "weakly" inhomogeneous and anisotropic (see the large-scale structure of the cosmos), it is on average homogeneous and isotropic. The homogeneous and isotropic universe allows for a spatial geometry with a constant curvature. One aspect of local geometry to emerge from General Relativity and the FLRW model is that the density parameter, Omega (Ω), is related to the curvature of space. Omega is the average density of the universe divided by the critical energy density, i.e. that required for the universe to be flat (zero curvature). The curvature of space is a mathematical description of whether or not the Pythagorean theorem is valid for spatial coordinates. In the latter case, it provides an alternative formula for expressing local relationships between distances. 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 physics, homogeneity is the quality of having all properties independent of the position. ... Look up anisotropy in Wiktionary, the free dictionary. ... Astronomy and cosmology examine the universe to understand the large-scale structure of the cosmos. ... 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. ... The Friedmann equations relate various cosmological parameters within the context of general relativity. ... In mathematics, the Pythagorean theorem or Pythagoras theorem is a relation in Euclidean geometry among the three sides of a right triangle. ...

If the curvature is zero, then Ω = 1, and the Pythagorean theorem is correct. If Ω > 1, there is positive curvature, and if Ω < 1 there is negative curvature; in either of these cases, the Pythagorean theorem is invalid (but discrepancies are only detectable in triangles whose sides' lengths are of cosmological scale). If you measure the circumferences of circles of steadily larger diameters and divide the former by the latter, all three geometries give the value π for small enough diameters but the ratio departs from π for larger diameters unless Ω = 1. For Ω > 1 (the sphere, see diagram) the ratio falls below π: indeed, a great circle on a sphere has circumference only twice its diameter. For Ω < 1 the ratio rises above π. There are very few or no other articles that link to this one. ...

Astronomical measurements of both matter-energy density of the universe and spacetime intervals using supernova events constrain the spatial curvature to be very close to zero, although they do not constrain its sign. This means that although the local geometries are generated by the theory of relativity based on spacetime intervals, we can approximate it to the familiar Euclidean geometry. Two-dimensional analogy of space-time curvature described in General Relativity. ... In physics, spacetime is a mathematical model that combines space and time into a single construct called the space-time continuum. ... Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. ...

Local geometries

There are three categories for the possible spatial geometries of constant curvature, depending on the sign of the curvature. If the curvature is exactly zero, then the local geometry is flat; if it is positive, then the local geometry is spherical, and if it is negative than the local geometry is hyperbolic.

The local geometry of the universe is determined by whether Omega is less than, equal to or greater than 1. From top to bottom: a spherical universe, a hyperbolic universe, and a flat universe.

The geometry of the universe is usually represented in the system of comoving coordinates, according to which the expansion of the universe can be ignored. Comoving coordinates form a single frame of reference according to which the universe has a static geometry of three spatial dimensions. Image File history File links End_of_universe. ... Image File history File links End_of_universe. ... 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. ... A frame of reference is a particular perspective from which the universe is observed. ...

Under the assumption that the universe is homogeneous and isotropic, the curvature of the observable universe, or the local geometry, is described by one of the three "primitive" geometries:

• 3-dimensional Euclidean geometry, generally annotated as E³
• 3-dimensional spherical geometry with a small curvature, often annotated as S³
• 3-dimensional hyperbolic geometry with a small curvature, often annotated as H³

Even if the universe is not exactly spatially flat, the spatial curvature is close enough to zero to place the radius at approximately the horizon of the observable universe or beyond. Euclid Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. ... Spherical geometry is the geometry of the two-dimensional surface of a sphere. ... Lines through a given point P and hyperparallel to line l. ... Circle illustration In classical geometry, a radius (plural: radii) of a circle or sphere is any line segment from its center to its boundary. ...

Global geometry

Global geometry covers the geometry, in particular the topology, of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. For a flat spatial geometry, it used to be thought that the scale of any properties of the topology is arbitrary, though recent research suggests that the three spatial dimensions may tend to equalise in length.^[1] The length scale of a flat geometry may or may not be directly detectable. For spherical and hyperbolic spatial geometries, the probability of detection of the topology by direct observation depends on the spatial curvature. Using the radius of curvature or its inverse as a scale, a small curvature of the local geometry, with a corresponding radius of curvature greater than the observable horizon, makes the topology difficult or impossible to detect if the curvature is hyperbolic. A spherical geometry with a small curvature (large radius of curvature) does not make detection difficult. The reciprocal function: y = 1/x. ...

Two strongly overlapping investigations within the study of global geometry are:

• whether the universe is infinite in extent or is a compact space
• whether the universe has a simply or non-simply connected topology

The infinity symbol ∞ in several typefaces. ... In mathematics, a subset of Euclidean space Rn is called compact if it is closed and bounded. ... In topology, a geometrical object or space is called simply connected if it is path-connected and every path between two points can be continuously transformed into every other. ...

Compactness of the global shape

A compact space is a general topological definition that encompasses the more applicable notion of a bounded metric space. In cosmological models, it requires either one or both of: the space has positive curvature (like a sphere), and/or it is "multiply connected", or more strictly non-simply connected. In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. ...

If the 3-manifold of a spatial section of the universe is compact then, as on a sphere, straight lines pointing in certain directions, when extended far enough in the same direction will reach the starting point and the space will have a definable "volume" or "scale". If the geometry of the universe is not compact, then it is infinite in extent with infinite paths of constant direction that, generally do not return and the space has no definable volume, such as the Euclidean plane. On a sphere, the sum of the angles of a triangle is not equal to 180°. A sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. ... In mathematics, a geodesic is a generalization of the notion of a straight line to curved spaces. In presence of a metric, geodesics are defined to be (locally) the shortest path between points on the space. ... In mathematics and astronomy, Euclidean space is a generalization of the 2- and 3-dimensional spaces studied by Euclid. ...

If the spatial geometry is spherical, the topology is compact. Otherwise, for a flat or a hyperbolic spatial geometry, the topology can be either compact or infinite.

Flat universe

In a flat universe, all of the local curvature and local geometry is flat. In general it can be described by Euclidean space, however there are some spatial geometries which are flat and bounded in one or more directions. These include, in two dimensions, the cylinder, the torus, and the Mobius Strip. Similar spaces in three dimensions also exist. Around 300 BC, the Greek mathematician Euclid laid down the rules of what has now come to be called Euclidean geometry, which is the study of the relationships between angles and distances in space. ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... In geometry, a torus (pl. ... The Möbius strip or Möbius band (named after the German mathematician and astronomer August Ferdinand Möbius) is a topological object with only one surface and only one edge. ...

Spherical universe

A positively curved universe is described by spherical geometry, and can be thought of as a three-dimensional hypersphere. Spherical geometry is the geometry of the two-dimensional surface of a sphere. ... Stereographic projection of the hyperspheres parallels (red), meridians (blue) and hypermeridians (green). ...

One of the endeavors in the analysis of data from the Wilkinson Microwave Anisotropy Probe (WMAP) is to detect multiple "back-to-back" images of the distant universe in the cosmic microwave background radiation. Assuming the light has enough time since its origin to travel around a bounded universe, multiple images may be observed. While current results and analysis do not rule out a bounded topology, if the universe is bounded then the spatial curvature is small, just as the spatial curvature of the surface of the Earth is small compared to a horizon of a thousand kilometers or so. 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. ... Adjectives: Terrestrial, Terran, Telluric, Tellurian, Earthly Atmosphere Surface pressure: 101. ... A kilometer (Commonwealth spelling: kilometre), symbol: km is a unit of length in the metric system equal to 1,000 metres (from the Greek words χίλια (khilia) = thousand and μέτρο (metro) = count/measure). ...

Based on analyses of the WMAP data, cosmologists during 2004-2006 focused on the Poincaré dodecahedral space (PDS), but also considered horn topologies to be compatible with the data. shelby was here 2004 (MMIV) was a leap year starting on Thursday of the Gregorian calendar. ... For the Manfred Mann album, see 2006 (album). ... In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1. ...

Hyperbolic universe

A hyperbolic universe (frequently but confusingly called "open") is described by hyperbolic geometry, and can be thought of as something like a three-dimensional equivalent of an infinitely extended saddle shape. For hyperbolic local geometry, many of the possible three-dimensional spaces are informally called horn topologies. Lines through a given point P and hyperparallel to line l. ...

The ultimate fate of an open universe is that it will continue to expand forever, ending in a Heat Death, a Big Freeze or a Big Rip. This topology is consistent with astrophysical measurements made in the late 1990's. See link The ultimate fate of the universe is a topic in physical cosmology. ... The metric expansion of space is a key part of sciences current understanding of the universe, whereby space itself is described by a metric which changes over time. ... The heat death is a possible final state of the universe, in which it has reached maximum entropy. ... The Big Freeze is a scenario in which the universe simply becomes too cold to sustain life due to continued expansion. ... The Big Rip is a cosmological hypothesis about the ultimate fate of the Universe, in which the elements of the universe, from galaxies to atoms, are progressively torn apart by the expansion of the universe. ...

See also

• Theorema Egregium − The "remarkable theorem" discovered by Gauss which showed there is an intrinsic notion of curvature for surfaces. This is used by Riemann to generalize the (intrinsic) notion of curvature to higher dimensional spaces.
• Extra dimensions in String Theory for 6 or 7 extra space-like dimensions all with a compact topology.

The Theorema Egregium (Remarkable Theorem) is an important theorem of Carl Friedrich Gauss concerning the curvature of surfaces. ... Johann Carl Friedrich Gauss or Gauß ( ; Latin: ) (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, magnetism, astronomy, and optics. ... Bernhard Riemann. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point...

External links

• Oct 2003 − Poincaré dodecahedral model − WMAP statistics model predictions for a spherical local geometry
• Feb 2004 − Poincaré dodecahedral model − 11 degree matched circles
• Universe is Finite, "Soccer Ball"-Shaped, Study Hints. Possible wrap-around dodecahedral shape of the universe
• Hyperbolic universes with a Horned Topology and the CMB Anisotropy

1. ^ Roukema, Boudewijn F.; Stanislaw Bajtlik, Marek Biesiada, Agnieszka Szaniewska, Helena Jurkiewicz (8 Dec 2006). "A weak acceleration effect due to residual gravity in a multiply connected universe". Astronomy and Astrophysics. Retrieved on 2006-12-08.