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| {{Cosmology|cTopic=Baryon Acoustic Oscillations}}
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| {{Technical|date=September 2011}}
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| {{Expert-subject|Physics|date=September 2011}}
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| | |
| In [[cosmology]], '''baryon acoustic oscillations''' (BAO) refers to regular, periodic fluctuations in the density of the visible [[baryonic]] matter of the universe. In the same way that [[supernova]] experiments provide a "[[standard candle]]" for astronomical observations,<ref name="ref:Perlmutter">{{cite journal
| |
| |last=Perlmutter |first=S.
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| |coauthors=''et al.''
| |
| |year=1999
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| |title=Measurements of Ω and Λ from 42 High‐Redshift Supernovae
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| |journal=[[The Astrophysical Journal]]
| |
| |volume=517 |issue=2 |page=565
| |
| |arxiv=astro-ph/9812133
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| |bibcode=1999ApJ...517..565P
| |
| |doi=10.1086/307221
| |
| }}</ref> BAO matter clustering provides a "[[standard ruler]]" for length scale in cosmology.<ref name="ref:EisensteinNAR">
| |
| {{cite journal
| |
| |last=Eisenstein |first=D. J.
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| |year=2005
| |
| |title=Dark energy and cosmic sound
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| |journal=[[New Astronomy Reviews]]
| |
| |volume=49 |issue=7–9|page=360
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| |arxiv=
| |
| |bibcode=2005NewAR..49..360E
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| |doi=10.1016/j.newar.2005.08.005
| |
| }}</ref> The length of this standard ruler (~490 million light years in today's universe<ref name="ref:EisensteinAPJ">
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| {{cite journal
| |
| |last=Eisenstein |first=D. J.
| |
| |coauthors=''et al.''
| |
| |year=2005
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| |title=Detection of the Baryon Acoustic Peak in the Large‐Scale Correlation Function of SDSS Luminous Red Galaxies
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| |journal=[[The Astrophysical Journal]]
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| |volume=633 |issue=2 |page=560
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| |arxiv=astro-ph/0501171
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| |bibcode=2005ApJ...633..560E
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| |doi=10.1086/466512
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| }}</ref>) can be measured by looking at the [[Large-scale structure of the universe|large scale structure]] of matter using [[astronomical surveys]].<ref name="ref:EisensteinAPJ"/> BAO measurements help cosmologists understand more about the nature of [[dark energy]] (which causes the apparent slight acceleration of the expansion of the universe) by constraining [[Lambda-CDM model#Parameters|cosmological parameters]].<ref name="ref:EisensteinNAR"/>
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| | |
| ==The Early Universe==
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| The early universe consisted of a hot, dense [[Plasma (physics)|plasma]] of [[electrons]] and [[baryons]] (protons and neutrons). [[Photons]] (light particles) traveling in this universe were essentially trapped, unable to travel for any considerable distance before interacting with the plasma via [[Thomson scattering]].<ref name="ref:Dodelson">
| |
| {{cite book
| |
| |last=Dodelson |first=S.
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| |year=2003
| |
| |title=Modern Cosmology
| |
| |publisher=[[Academic Press]]
| |
| |isbn=978-0122191411
| |
| }}</ref> As the universe expanded, the plasma cooled to below 3000 K—a low enough energy such that the electrons and protons in the plasma could combine to form neutral [[hydrogen atoms]]. This [[Timeline of the Big Bang#Recombination|recombination]] happened when the universe was around 379,000 years old, or at a [[redshift]] of z = 1089.<ref name="ref:Dodelson"/> Photons interact to a much lesser degree with neutral matter, therefore at recombination the universe suddenly became transparent to photons, allowing them to [[Decoupling (cosmology)|decouple]] from the matter and [[free-stream]] through the universe.<ref name="ref:Dodelson"/> Technically speaking, the [[mean free path]] of the photons became on the order of the size of the universe. The [[cosmic microwave background]] (CMB) radiation is light emitted after recombination which is only now reaching our telescopes. Therefore when we look at [[Wilkinson Microwave Anisotropy Probe]] (WMAP) data, we are looking back in time to see an image of the universe when it was only 379,000 years old.<ref name="ref:Dodelson"/>
| |
| | |
| [[File:Ilc 9yr moll4096.png|thumb|center|350px|Figure 1: Temperature anisotropies of the [[CMB]] based on the nine year [[WMAP]] data (2012).<ref name="Space-20121221">
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| {{cite web
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| |last=Gannon |first=M.
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| |title=New 'Baby Picture' of Universe Unveiled
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| |url=http://www.space.com/19027-universe-baby-picture-wmap.html
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| |date=December 21, 2012
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| |publisher=[[Space.com]]
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| |accessdate=December 21, 2012
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| }}</ref><ref name="arXiv-20121220">
| |
| {{cite arxiv
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| |last=Bennett |first=C. L.
| |
| |coauthors=''et al.''
| |
| |year=2012
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| |title=Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
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| |eprint=1212.5225
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| |class=astro-ph.CO
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| }}</ref><ref name="ref:WMAP">
| |
| {{cite journal
| |
| |last=Hinshaw |first=G.
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| |coauthors=''et al.''
| |
| |year=2009
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| |title=Five-year Wilkinson Microwave Anisotropy Probe observations: Data processing, sky maps, and basic results
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| |url=http://lambda.gsfc.nasa.gov/product/map/dr3/pub_papers/fiveyear/basic_results/wmap5basic_reprint.pdf
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| |journal=[[The Astrophysical Journal Supplement Series]]
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| |volume=180 |issue=2 |page=225
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| |arxiv=0803.0732
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| |bibcode=2009ApJS..180..225H
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| |doi=10.1088/0067-0049/180/2/225
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| }}</ref>
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| ]]
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| | |
| [[WMAP]] indicates (Figure 1) a smooth, homogeneous universe with density [[Anisotropies#Physics|anisotropies]] of 10 parts per million.<ref name="ref:Dodelson"/> However, when we observe the universe today we find large structure and density fluctuations. Galaxies, for instance, are a million times more dense than the universe's mean density.<ref name="ref:EisensteinNAR"/> The current belief is that the universe was built in a bottom-up fashion, meaning that the small anisotropies of the early universe acted as gravitational seeds for the structure we see today. Overdense regions attract more matter, while underdense regions attract less, and thus these small anisotropies we see in the CMB become the large scale structures we observe in the universe today.
| |
| | |
| ==Cosmic Sound==
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| Imagine an overdense region of the [[Structure formation#Primordial plasma|primordial plasma]]. While this overdensity [[gravitationally]] attracts matter towards it, the heat of photon-matter interactions creates a large amount of outward [[pressure]]. These counteracting forces of gravity and pressure create [[oscillations]], analogous to [[sound waves]] created in air by pressure differences.<ref name="ref:EisensteinAPJ"/>
| |
| | |
| Consider a single wave originating from this overdense region in the center of the plasma. This region contains [[dark matter]], [[baryons]] and [[photons]]. The pressure results in a spherical sound wave of both baryons and photons moving with a speed slightly over half the [[speed of light]]<ref name="ref:SunyaevZeldovich">
| |
| {{cite journal
| |
| |last=Sunyaev |first=R.
| |
| |last2=Zeldovich |first2=Ya. B.
| |
| |year=1970
| |
| |title=Small-Scale Fluctuations of Relic Radiation
| |
| |journal=[[Astrophysics and Space Science]]
| |
| |volume=7 |issue=1 |page=3
| |
| |arxiv=
| |
| |bibcode=1970Ap&SS...7....3S
| |
| |doi=10.1007/BF00653471
| |
| }}</ref><ref name="ref:PeeblesYu">
| |
| {{cite journal
| |
| |last=Peebles |first=P. J. E.
| |
| |last2=Yu |first2=J. T.
| |
| |year=1970
| |
| |title=Primeval Adiabatic Perturbation in an Expanding Universe
| |
| |journal=[[The Astrophysical Journal]]
| |
| |volume=162 |issue= |page=815
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| |arxiv=
| |
| |bibcode=1970ApJ...162..815P
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| |doi=10.1086/150713
| |
| }}</ref> outwards from the overdensity. The dark matter only interacts gravitationally and so it stays at the center of the sound wave, the origin of the overdensity. Before [[Decoupling (cosmology)|decoupling]], the photons and baryons move outwards together. After decoupling the photons are no longer interacting with the baryonic matter so they diffuse away. This relieves the pressure on the system, leaving a shell of baryonic matter at a fixed radius. This radius is often referred to as the sound horizon.<ref name="ref:EisensteinAPJ"/> Without the photo-baryon pressure driving the system outwards, the only remaining force on the baryons is gravitational. Therefore, the baryons and dark matter (still at the center of the perturbation) form a configuration which includes overdensities of matter both at the original site of the anisotropy and in a shell at the sound horizon.<ref name="ref:EisensteinAPJ"/>
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| | |
| The ripples in the density of space continue to attract matter and eventually [[galaxies]] formed in a similar pattern, therefore one would expect to see a greater number of galaxies separated by the sound horizon than by nearby length scales.<ref name="ref:EisensteinAPJ"/> This particular configuration of matter occurred at each anisotropy in the early universe, and therefore the universe is not composed of [http://www.cfa.harvard.edu/~deisenst/acousticpeak/anim.gif one sound ripple], but many [http://www.cfa.harvard.edu/~deisenst/acousticpeak/anim_many.gif overlapping ripples]. As an analogy, imagine dropping many pebbles into a pond and watching the resulting wave patterns in the water.<ref name="ref:EisensteinNAR"/> It is not possible to observe this preferred separation of galaxies on the sound horizon scale by eye, but one can measure this signal [[statistically]] by looking at the separations of large numbers of galaxies.
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| | |
| ==Standard Ruler==
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| {{see also|time}}<!--time and expansion of the universe-->
| |
| The physics of the propagation of the baryon waves in the [[early universe]] is fairly simple, so cosmologists can predict the size of the sound horizon at [[Timeline of the Big Bang#Recombination: 240,000–310,000 years|recombination]]. In addition the [[CMB]] provides a measurement of this scale to high accuracy.<ref name="ref:EisensteinAPJ"/> However in the time between recombination and present day, the universe has been [[Expanding universe|expanding]]. This expansion is well supported by [[Hubble's law|observations]] and is one of the foundations of the [[big bang|Big Bang Model]]. In the late 90's, observations of [[supernova]]<ref name="ref:Perlmutter"/> determined that not only is the universe expanding, it is expanding at an increasing rate. Better understanding the [[Accelerating universe|acceleration of the universe]], or [[dark energy]], has become one of the most important questions in cosmology today. In order to understand the nature of the dark energy, it is important to have a variety of ways of measuring this acceleration. BAO can add to the body of knowledge about this acceleration by comparing observations of the sound horizon today (using clustering of galaxies) to the sound horizon at the time of recombination (using the CMB).<ref name="ref:EisensteinAPJ"/> Thus BAO provides a measuring stick with which to better understand the nature of the acceleration, completely independent from the [[Dark energy#Supernovae|supernova technique]]. | |
| | |
| ==BAO Signal in the Sloan Digital Sky Survey==
| |
| <!--[[File:Sloan BAO Slice.jpg|thumb|right|300px|Figure 3: A slice through the SDSS map of the distribution of galaxies. Earth is at the center, and each point in the slice represents a galaxy, the color is the luminosity. This image shows 60,000 galaxies and is 2 billion light-years deep.<ref name="ref:SDSSSlice"> Sloan Digital Sky Survey Press Release, 3D Map of Universe Bolsters Case for Dark Energy and Dark Matter, October 28, 2003. http://www.sdss.org/</ref> {{deletable image-caption}}]]-->
| |
| The [[Sloan Digital Sky Survey]] (SDSS) is a 2.5-metre wide-angle [[optical telescope]] at [[Apache Point Observatory]] in [[New Mexico]]. The goal of this five-year survey was to take [[Photometric system|images]] and [[Spectroscopic astronomy|spectra]] of millions of celestial objects. The result of compiling the Sloan data is a [http://www.sdss.org/includes/sideimages/sdss_pie2.html three-dimensional map] of the objects in the nearby universe. The SDSS catalog provides a picture of the distribution of matter such that one can search for a BAO signal by seeing if there is a larger number of galaxies separated at the sound horizon.
| |
| | |
| The Sloan Team looked at a sample of 46,748 luminous red galaxies (LRGs), over 3816 square-degrees of sky (approximately five billion [[light years]] in diameter) and out to a [[redshift]] of z = 0.47.<ref name="ref:EisensteinAPJ"/> They analyzed the clustering of these galaxies by calculating a [[Correlation function (astronomy)|two-point correlation function]] on the data.<ref name="ref:LandySzalay">
| |
| {{cite journal
| |
| |last=Landy |first=S. D.
| |
| |last2=Szalay |first2=A. S.
| |
| |year=1993
| |
| |title=Bias and variance of angular correlation functions
| |
| |journal=[[The Astrophysical Journal]]
| |
| |volume=412 |issue= |page=64
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| |arxiv=
| |
| |bibcode=1993ApJ...412...64L
| |
| |doi=10.1086/172900
| |
| }}</ref> The correlation function (<math>\xi</math>) is a function of [[Comoving distance|comoving]] galaxy separation distance (s) and describes the probability that one galaxy will be found within a given distance bin of another.<ref name="ref:Peebles">
| |
| {{cite book
| |
| |last=Peebles |first=P. J. E.
| |
| |year=1980
| |
| |title=The large-scale structure of the universe
| |
| |publisher=[[Princeton University Press]]
| |
| |arxiv=
| |
| |bibcode=1980lssu.book.....P
| |
| |isbn=978-0-691-08240-0
| |
| }}</ref> One would expect a high correlation of galaxies at small separation distances (due to the clumpy nature of galaxy formation) and a low correlation at large differences. The BAO signal would show up as a bump in the correlation function at a comoving separation equal to the sound horizon. This signal was [http://www.sdss.org/news/releases/20050111.yardstick.html detected by the SDSS team] in 2005.<ref name="ref:EisensteinAPJ"/> SDSS confirmed the WMAP results that the sound horizon is ~150 [[Parsec|Mpc]] in today's universe.<ref name="ref:EisensteinNAR"/><ref name="ref:EisensteinAPJ"/>
| |
| | |
| ==Detection in other galaxy surveys==
| |
| The 2dFGRS collaboration reported a detection of the BAO signal in the power spectrum at the same time as the SDSS collaboration.<ref name="ref:ColesAPJ">
| |
| {{cite journal
| |
| |last=Cole |first=S.
| |
| |coauthors=''et al.''
| |
| |year=2005
| |
| |title=The 2dF Galaxy Redshift Survey: Power-spectrum analysis of the final data set and cosmological implications
| |
| |journal=[[Monthly Notices of the Royal Astronomical Society]]
| |
| |volume=362 |issue=2 |page=505
| |
| |arxiv=astro-ph/0501174
| |
| |bibcode=2005MNRAS.362..505C
| |
| |doi=10.1111/j.1365-2966.2005.09318.x
| |
| }}</ref> Since then, further detections have been reported in the 6dF Galaxy Survey (6dFGS),<ref name="ref:BeutlerMNRAS">
| |
| {{cite journal
| |
| |last=Beutler |first=F.
| |
| |coauthors=''et al.''
| |
| |year=2011
| |
| |title=The 6dF Galaxy Survey: Baryon acoustic oscillations and the local Hubble constant
| |
| |journal=[[Monthly Notices of the Royal Astronomical Society]]
| |
| |volume=416 |issue=4 |page=3017B
| |
| |arxiv=1106.3366
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| |bibcode=2011MNRAS.416.3017B
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| |doi=10.1111/j.1365-2966.2011.19250.x
| |
| }}</ref> WiggleZ<ref name="ref:BlakeMNRAS">
| |
| {{cite journal
| |
| |last=Blake |first=C.
| |
| |coauthors=''et al.''
| |
| |year=2011
| |
| |title=The WiggleZ Dark Energy Survey: Mapping the distance-redshift relation with baryon acoustic oscillations
| |
| |journal=[[Monthly Notices of the Royal Astronomical Society]]
| |
| |volume=418 |issue=3 |page=1707
| |
| |arxiv=1108.2635
| |
| |bibcode=2011MNRAS.418.1707B
| |
| |doi=10.1111/j.1365-2966.2011.19592.x
| |
| }}</ref> and BOSS.<ref name="ref:AndersonMNRAS">
| |
| {{cite journal
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| |last=Anderson |first=L.
| |
| |coauthors=''et al.''
| |
| |year=2012
| |
| |title=The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon acoustic oscillations in the Data Release 9 spectroscopic galaxy sample
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| |journal=[[Monthly Notices of the Royal Astronomical Society]]
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| |volume=427|issue=4 |page=3435
| |
| |arxiv=1203.6594
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| |bibcode=2012MNRAS.427.3435A
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| |doi=10.1111/j.1365-2966.2012.22066.x
| |
| }}</ref>
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| | |
| ==BAO and Dark Energy Formalism==
| |
| | |
| ===General Relativity and Dark Energy===
| |
| In [[general relativity]], the expansion of the universe is parametrized by a [[Scale factor (Universe)|scale factor]] <math>a(t)</math> which is related to [[Redshift#Expansion of space|redshift]]:<ref name="ref:Dodelson"/>
| |
| | |
| :<math>a(t) \equiv (1+z(t))^{-1}\!</math>
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| | |
| The [[Hubble parameter]], <math>H(z)</math>, in terms of the scale factor is:
| |
| | |
| :<math>H(t) \equiv \frac{\dot a}{a}\!</math>
| |
| | |
| where <math>\dot a</math> is the time-derivative of the scale factor. The [[Friedmann equations]] express the expansion of the universe in terms of Newton's [[gravitational constant]], <math>G_{N}</math>, the mean [[pressure|gauge pressure]], <math>P</math>, the [[Density parameter|Universe's density]] <math>\rho\!</math>, the [[Curvature of the universe|curvature]], <math>k</math>, and the [[cosmological constant]], <math>\Lambda\!</math>:<ref name="ref:Dodelson"/>
| |
| :<math>H^2 = \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G}{3} \rho - \frac{kc^2}{a^2} + \frac{\Lambda c^2}{3}</math>
| |
| :<math>\dot{H} + H^2 = \frac{\ddot{a}}{a} = -\frac{4 \pi G}{3}\left(\rho+\frac{3p}{c^2}\right) + \frac{\Lambda c^2}{3}</math>
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| | |
| Observational evidence of the acceleration of the universe implies that (at present time) <math>\ddot{a} > 0</math>. Therefore the following are possible explanations:<ref name="ref:DETFreport">
| |
| {{cite arxiv
| |
| |last=Albrecht |first=A.
| |
| |coauthors=''et al.''
| |
| |year=2006
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| |title=Report of the Dark Energy Task Force
| |
| |class=astro-ph
| |
| |eprint=astro-ph/0609591
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| }}</ref>
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| * The universe is dominated by some field or particle that has negative pressure such that the equation of state:
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| :<math>w = \frac{P}{\rho} < -1/3\!</math>
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| *There is a non-zero cosmological constant, <math>\Lambda\!</math>.
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| *The Friedmann equations are incorrect since they contain over simplifications in order to make the general relativistic field equations easier to compute.
| |
| | |
| In order to differentiate between these scenarios, precise measurements of the [[Hubble parameter]] as a function of [[redshift]] are needed.
| |
| | |
| ===Measured Observables of Dark Energy===
| |
| The [[density parameter]], <math>\Omega\!</math>, of various components, <math>x</math>, of the universe can be expressed as ratios of the density of <math>x</math> to the [[Friedmann equations#Density parameter|critical density]], <math>\rho_c\!</math>:<ref name="ref:DETFreport"/>
| |
| | |
| :<math>\rho_c = \frac{3 H^2}{8 \pi G}</math>
| |
| :<math>\Omega_x \equiv \frac{\rho_x}{\rho_c} = \frac{8 \pi G\rho_x}{3 H^2}</math>
| |
| | |
| The [[Friedman equation]] can be rewritten in terms of the density parameter. For the current prevailing model of the universe, [[Lambda-CDM model|ΛCDM]], this equation is as follows:<ref name="ref:DETFreport"/>
| |
| :<math>H^2(a) = \left(\frac{\dot{a}}{a}\right)^2 = H_0^2\left [ \Omega_m a^{-3} + \Omega_r a^{-4} + \Omega_k a^{-2} + \Omega_\Lambda a^{-3(1+w)} \right ]</math>
| |
| where m is matter, r is radiation, k is curvature, Λ is dark energy, and w is the [[Equation of state (cosmology)|equation of state]]. Measurements of the [[CMB]] from [[WMAP]] put tight constraints on many of these [[Lambda-CDM model#Parameters|parameters]] however it is important to confirm and further constrain them using an independent method with different systematics.
| |
| | |
| The [http://cmb.as.arizona.edu/~eisenste/acousticpeak/paperfigs/xi_jack.eps.gif BAO signal] is a [[standard ruler]] such that the length of the sound horizon can be measured as a function of [[cosmic time]].<ref name="ref:EisensteinAPJ"/> This measures two cosmological distances: the [[Hubble parameter]], <math>H(z)</math>, and the [[angular diameter distance]], <math>d_A(z)</math>, as a function of [[redshift]] <math>(z)</math>.<ref name="ref:MWhiteSF">
| |
| {{cite web
| |
| |last=White |first=M.
| |
| |year=2007
| |
| |title=The Echo of Einstein's Greatest Blunder
| |
| |work=Santa Fe Cosmology Workshop
| |
| |url=http://mwhite.berkeley.edu/BAO/SantaFe07.pdf
| |
| }}</ref> By measuring the [[subtended angle]], <math>\Delta\theta</math>, of the ruler of length, <math>\Delta\chi</math>, these parameters are determined as follows:<ref name="ref:MWhiteSF"/>
| |
| | |
| :<math>\Delta\theta = \frac{\Delta\chi}{d_A(z)}\!</math>
| |
| | |
| :<math>d_A(z) \propto \int_{0}^{z}\frac{dz'}{H(z')}\!</math>
| |
| | |
| the redshift interval, <math>\Delta z</math>, can be measured from the data and thus determining the Hubble parameter as a function of redshift:
| |
| | |
| :<math>c\Delta z = H(z)\Delta\chi\!</math>
| |
| | |
| Therefore the BAO technique helps constrain cosmological parameters and provide further insight into the nature of dark energy.
| |
| | |
| <!--[[File:Correlation Function for BAO.jpg|thumb|left|300px|Figure 4: Large-scale redshift-space correlation function, $\xi(s)$, from the SDSS LRG sample (black data points). The colored lines represent theoretical models using different cosmologies. The inset shows an expanded view with a linear vertical axis.<ref name="ref:EisensteinAPJ"/>]]-->
| |
| | |
| ==See also==
| |
| * [[Baryon Oscillation Spectroscopic Survey]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| ==External links==
| |
| * [http://astro.berkeley.edu/~mwhite/bao/ Martin White's Baryon Acoustic Oscillations and Dark Energy Web Page]
| |
| * [http://www.cfa.harvard.edu/~deisenst/acousticpeak/ Daniel Eisenstein's Detection of the Baryon Acoustic Peak Web Page]
| |
| * [http://arxiv.org/abs/0910.5224 Review of Baryon Acoustic Oscillations]
| |
| * [http://www.sdss.org/news/releases/20050111.yardstick.html SDSS BAO Press Release]
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| | |
| {{DEFAULTSORT:Baryon Acoustic Oscillations}}
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| [[Category:Physical cosmology]]
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| [[Category:Baryons]]
| |