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| | exam2sol |
 | | The two Friedmann equations are linear combinations of the only 2 nontrivial equations that result from Einstein's equations for such a universe (a Friedmann-Robertson-Walker universe). | | | Friedmann's equations are obtained by applying Einstein's equations to the most general spacetime metric | | | State one way in which Friedmann's equations differ from a quasiNewtonian analysis of the Hubble expansion. |
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http://www.emory.edu/PHYSICS/Faculty/Benson/380-04/handouts/exam2sol/exam2sol.html
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| | ASTR 100 Lecture 35 (21 Nov 2003) |
| | The equations of general relativity, after the assumptions of isotropy and homogeneity are applied, turn into what are known as the Friedmann equations. | | | In all of the solutions to the Friedmann equations, the Universe starts out at zero size (what we now think of as the Big Bang) and grows from there. | | | The solutions to the Friedmann equations tell us what the Universe looks like on the largest scales and how it evolves with time. |
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http://www.astro.uiuc.edu/classes/archive/astr100/f03_lect1/lecture35_summary.html
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| | 20 |
| | (which determine what is called a Friedmann-Robertson-Walker universe), we applied Einstein's equations obtain Friedmann's equations for the dynamics of the universe. | | | ) is consistent with Friedmann's equations (it is actually a linear combination of the two). | | | We noted how Friedmann's first equation -- in the case |
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http://www.emory.edu/PHYSICS/Faculty/Benson/380-04/notes/20/20.html
(392 words)
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| | MSN Encarta - Big Bang Theory |
| | After Einstein’s work of 1917, several scientists, including the abbé Georges Lemaître in Belgium, Willem de Sitter in Holland, and Alexander Friedmann in Russia, succeeded in finding solutions to Einstein’s field equations. | | | In 1922 Russian physicist Alexander Friedmann provided a set of solutions to the field equations. | | | In the 1940s George Gamow was joined by his students Ralph Alpher and Robert Herman in working out details of Friedmann’s solutions to Einstein’s theory. |
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http://encarta.msn.com/encnet/refpages/RefArticle.aspx?refid=761570694
(392 words)
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| | index.php?index=1 |
| | The main time dependent function of the Friedmann equations is the so called scale factor, describing the state (expanding, contracting or static) and the fate of the Universe. | | | The scale factor is connected to the curvature, matter density and energy density of the Universe via the Friedmann equations. | | | The main equations of Einsteins theory, the field equations simplify substantially to two independent differential equations (Friedmann 1922). |
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http://www.astro.uni-bonn.de/~mhetter/index.php?index=1
(804 words)
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| | papers |
| | The field equations of the model reduce to a system which is effectively given by the usual Friedmann equations of general relativity, supplied by a correction to the energy density and pressure in form of $\Omega_\psi$, which is related to the non-Riemannian structure of the underlying spacetime. | | | We use two independent data sets to constrain the new density parameter $\Omega_\psi$, which is related to the non-Riemannian structure of the underlying spacetime and supplements the field equations that are very similar to the usual Friedmann equations of general relativity. | | | Our aim is to present the fully nonlinear 1PN equations in a form suitable for implementation in conventional Newtonian hydrodynamic simulations with minimal extensions. |
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http://www.thp.uni-koeln.de/~dp/papers.html
(2480 words)
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| | Is The Universe Static Or Expanding? |
| | Friedmann found that these equations describing the behaviour of the cosmos were capable of an infinite number of solutions if Einstein's model of a static universe was abandoned [Friedmann, 1922, p.377]. | | | If the Friedmann equations are logically followed through, as Sumner did, the observed redshift implies that the very fabric of space must therefore be contracting and not expanding at all. | | | In this current paper, it was pointed out that one of the explanations for the redshift was that, according to the Friedmann equations, the wavelengths of light were being stretched in transit as the fabric of space expanded. |
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http://www.setterfield.org/staticu.html
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| | Projects |
| | The Friedmann equations describe the dynamics of the scale factor in a FRW model-universe. | | | The application of the classical Friedmann equations is limited to the regime where quantum fluctuations of the metric are negligible. | | | When the Friedmann equations have been derived, a brief discussion of the solutions will be given. |
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http://www.astro.ku.dk/~cramer/reports.html
(989 words)
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| | Barmaids |
| | Solving Einstein's equations, Alexander Friedmann found that the Universe was born in a primeval explosion called the big bang. | | | Initially physicists were concerned with the flat spacetime of special relativity, but soon Schrödinger realized that the curved spacetime of general relativity would change the mathematical solutions to the wave equations of quantum mechanics. | | | One mathematical possibility Friedmann explored is that the Universe continued to expand until it reached a maximum size, then reversed its direction and began collapsing back on itself, exactly as a ball thrown straight up reaches a highest point before falling back down on the thrower. |
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http://www.elltel.net/kia/Universe.html
(989 words)
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| | Cosmology Course: General Relativity |
| | The combination of the RW metric and Einstein's field equations led to the Friedmann equations, solutions of which were discussed in detail. | | | In the lecture there was only time for some handwaving arguments as to (i) why the metric has to have a particular form and (ii) the derivation of the Friedmann equations from the Einstein equations. | | | In this lecture the concept of isotropy and homogeneity was discussed in detail and the corresponding metric, the so-called Robertson-Walker (RW) metric was derived. |
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http://t8web.lanl.gov/cosmo-course/kat/lect2.html
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| | Citebase - Braneworld Cosmological Models |
| | A generic equation is given, from which the Friedmann equations of the Randall-Sundrum, induced gravity, Gauss-Bonnet and the combined induced gravity and Gauss-Bonnet cosmological models are obtained. | | | We show that Einstein's equations admit a first integral, analogous to the first Friedmann equation, which governs the evolution of the metric in the brane, whatever the time e... | | | In Randall-Sundrum-type brane-world cosmologies, the dynamical equations on the three-brane differ from the general relativity equations by terms that carry the effects of imbedding and of the free gravitational field in the five-dimensional bulk. |
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http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:gr-qc/0410032
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| | 1.2 Introducing the cosmological constant |
| | ); in that case, Einstein's equations reduce to the two Friedmann equations, | | | The disappearance of the original motivation for introducing the cosmological constant did not change its status as a legitimate addition to the gravitational field equations, or as a parameter to be constrained by observation. | | | To obtain a Robertson-Walker solution to Einstein's equations, the rest frame of the fluid must be that of a comoving observer in the metric (2 |
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http://relativity.livingreviews.org/Articles/lrr-2001-1/node3.html
(562 words)
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| | Friedmann Equation |
| | Friedmann developed it as a relativistic equation in the framework of general relativity, but the description here will be limited to a simplified, non-relativistic version. | | | Alexander Friedmann of Russia is credited with developing a dynamic equation for the expanding universe in the 1920s. | | | The Friedmann equation which models the expanding universe has a parameter k called the curvature parameter which is indicative of the rate of expansion and whether or not that expansion rate is increasing or decreasing. |
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http://hyperphysics.phy-astr.gsu.edu/hbase/astro/fried.html
(562 words)
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| | Brane World Cosmology Comes Down to Earth |
| | In 4D space-time the Friedmann equations describe the evolution of a uniform, homogeneous, and isotropic universe. | | | Our French paper, #4, has become highly cited because it derives the equivalent of the Friedmann equation for a 3-brane in higher dimensional space. | | | They look like the Einstein equations but they have two additional terms, which arise from the fifth dimension. |
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http://www.sciencewatch.com/july-aug2002/sw_july-aug2002_page6.htm
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| | 5 Brane-World Cosmology: Dynamics |
| | A qualitative analysis of the Friedmann equations is given in [48, 47]. | | | is the FRW scale factor, and the junction conditions determine the velocity via the Friedmann equation for | | | Again, the junction conditions determine the Friedmann equation. |
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http://relativity.livingreviews.org/Articles/lrr-2004-7/articlese5.html
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| | Citebase - Brane World Cosmology with Gauss-Bonnet Interaction |
| | It is shown that the usual Friedmann equations are recovered on the brane. | | | The spacelike (timelike) FRW brane equations are considered from the point of view of their representation in the form... | | | In spacetimes of dimension greater than four it is natural to consider higher order (in R) corrections to the Einstein equations. |
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http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:hep-th/0110143
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| | Cardassian Expansion: Dark Energy from Modified Friedmann Equations / Events & Calendar / CITA |
| | Cardassian Expansion: Dark Energy from Modified Friedmann Equations / Events and Calendar / CITA | | | Cardassian Expansion: Dark Energy from Modified Friedmann Equations | | | In the Cardassian model, the current acceleration of the universe is explained by modifications to the Friedmann equation. |
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http://www.cita.utoronto.ca/webpages/temp-ezpub/index.php/events_calendar/cardassian_expansion_dark_energy_from_modified_friedmann_equations
(168 words)
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| | The Uncaused Beginning of the Universe |
| | At first it was thought that the singularity predicted by the Friedmann equations was fictitious, since its prediction depended upon the assumption that the universe is exactly homogeneous and isotropic, whereas in reality it is only approximately so. | | | The idea that the Friedmann equations and the Hawking-Penrose singularity theorems predict an uncaused beginning of the universe is resisted by many philosophers. | | | The field equations show that the metric of space-time is dependent upon the matter present in that space-time. |
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http://www.infidels.org/library/modern/quentin_smith/uncaused.html
(7467 words)
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| | Friedmann equations - Wikipedia, the free encyclopedia |
| | The Friedmann equations relate various cosmological parameters within the context of general relativity. | | | Some cosmologists call the second of these two equations the acceleration equation and reserve the term Friedmann equation for only the first equation. | | | Applied to a fluid with a given equation of state, the Friedman equations yield the time evolution and geometry of the universe as a function of the fluid density. |
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http://en.wikipedia.org/wiki/Friedmann_equations
(7467 words)
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| | Integrating Einstein Field Equations in Observational Coordinates with Cosmological Data Functions: Friedmann-Lemaître-Robertson-Walker case |
| | In this paper we use the integration scheme for the exact spherically symmetric Einstein field equations in observational coordinates recently developed by Araújo and Stoeger, and input data functions for area distance and galaxy number counts that would be obtained if the universe was exactly represented by the Friedmann-Lemaître-Robertson-Walker | | | Integrating Einstein Field Equations in Observational Coordinates with Cosmological Data Functions: Friedmann-Lemaître-Robertson-Walker case | | | The Spherically Symmetric Field Equations in Observational Coordinates |
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http://www.sbf1.if.usp.br/eventos/enfpc/xx/procs/res24/res24.html
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| | Big Bang |
| | It was first implied in Alexander Friedmann's complete solution of Albert Einstein's equations, in 1922. | | | Friedmann, in 1922, and Lemaitre, in 1927, demonstrated that the universe could be in a large scale expansion. | | | The idea of the Big bang and an expanding universe which challenged Einstein's idea of a static and unchanging universe, came primarily from a Russian meteorologist, Alexander Friedmann, and a Belgian cleric and mathematician, Georges Lemaitre. |
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http://www.findaim.com/bigbang.html
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| | Helge Kragh, Modern History of Cosmology, Spring 2001 |
| | Show that the de Sitter model, too, is among the solutions to the Friedmann equations. | | | Friedmann's paper is highly technical, but much of it can be understood without great difficulties. | | | Copied sources include Friedmann's 1922 paper in English translation, and a general introduction by Einstein of 1920, taken from Munitz, Theories of the Universe. |
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http://www.nd.edu/~histast4/exhibits/syllabi/kraghmodhistcosmol.html
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| | Harmonic gauge |
| | With the gauge condition 2.39 the Einstein Equations are wave equations, as in equation: 2.10. | | | For electrodynamics in a Friedmann universe this works, but it does not for linearized gravity in a Friedmann background. | | | the harmonic gauge is then just the same as Coulomb gauge, and the retardation in equation 2.41 becomes irrelevant because of equation 2.37. |
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http://www.mit.edu/~sballmer/physics/dipl/node16.html
(2357 words)
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| | Early Universe I |
| | Work out the Friedmann equations, and the derivation of open, flat and close cosmologies. | | | Friedmann-Robertson-Walker metric: cosmological equations for open, flat and closed Universes. | | | Observational constraints on cosmological parameters: Hubble rate of expansion, age of the Universe, total energy density, dark matter energy density, cosmological constant.... |
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http://astronomy.sussex.ac.uk/~martink/earlyverse1.html
(349 words)
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| | ACGRG Abstract |
| | Most popular cosmological models attempt to be ``predictive'', in the sense that once somea priori equation of state is chosen the Friedmann equations are used to determine the evolution of the FRW scale factor a(t). | | | In contrast, a retrodictive approach might usefully take observational dataconcerning the scale factor, and use the Friedmann equations to infer an observed cosmological equation of state. | | | Taylor expanding the cosmological equation of state around the current epoch is the simplest model one can consider that does not make any a priori restrictions on the nature of the cosmological fluid. |
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http://www.maths.monash.edu.au/~leo/acgrg/acgrg4/html/abstracts/abstract14.html
(134 words)
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| | Chapter 11: Modeling the Universe |
| | The equations that describe the evolution of the universe under the influence of its self-gravity are called the Friedmann equations. | | | If you are running a Java-enabled browser, try Solving the Friedmann Equation. | | | One of the most important consequences of this analysis is the realization that gravity permits three possibilities for the evolution of the universe: it could expand forever; it could stop expanding at infinite time; or it could stop expanding at some finite point in time and recollapse. |
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http://www.astro.virginia.edu/~jh8h/Foundations/chapter11.html
(613 words)
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| | Hubble's law |
| | When this metric was applied to the Einstein equations, the so-called Friedmann equations emerged which characterized the expansion of the universe based on a parameter known today as the scale factor which can be considered a scale invariant form of the proportionality constant of Hubble's Law. | | | However, a few scientists continued to pursue the dynamical universe and discovered that it could be characterized by a metric that came to be known after its discoverers, namely Friedmann, Lemaître, Robertson, and Walker. | | | This idea of an expanding spacetime would eventually lead to the Big Bang and to the Steady State theories. |
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http://www.1bx.com/en/Hubbles_law.htm
(1380 words)
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| | StarChild: Cosmology |
| | Friedmann built on the General Relativity equations to develop models that helped explain the evolution of the Universe. | | | Einstein's theory inspired many other scientists, including Willem de Sitter in Holland and Alexandr Friedmann in Russia. | | | In fact, much of today's cosmology is based on Freedman's solutions to the mathematical equations included in Einstein's Theory. |
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http://starchild.gsfc.nasa.gov/docs/StarChild/universe_level2/cosmology.html
(1362 words)
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| | Scale factor (Universe) - Wikipedia, the free encyclopedia |
| | The evolution of the scale factor is a dynamical question, determined by the equations of general relativity, which are presented in the case of a locally isotropic, locally homogeneous universe by the Friedmann equations. | | | The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model, is a function of time which represents the relative expansion of the universe. | | | The scale factor could, in principle, have units of length or be dimensionless. |
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http://en.wikipedia.org/wiki/Scale_factor_(Universe)
(192 words)
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| | Hubble's law - Wikipedia, the free encyclopedia |
| | When this metric was applied to the Einstein equations, the so-called Friedmann equations emerged which characterized the expansion of the universe based on a parameter known today as the scale factor which can be considered a scale invariant form of the proportionality constant of Hubble's Law. | | | However, a few scientists continued to pursue the dynamical universe and discovered that it could be characterized by a metric that came to be known after its discoverers, namely Friedmann, Lemaître, Robertson, and Walker. | | | However, the best way to calculate the recessional velocity and its associated expansion rate of spacetime is by considering the conformal time associated with the photon traveling from the distant galaxy. |
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http://www.wikipedia.org/wiki/Hubble_Constant
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