Baryon acoustic oscillations
Encyclopedia
In cosmology
, baryon acoustic oscillations (BAO) refers to an overdensity or clustering of baryonic matter at certain length scales due to acoustic
waves which propagated in the early universe. In the same way that supernova
experiments provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler
" for length scale in cosmology. The length of this standard ruler (~150 Mpc
in today's universe) can be measured by looking at the large scale structure of matter using astronomical surveys
. BAO measurements help cosmologists understand more about the nature of dark energy
(the acceleration of the universe) by constraining cosmological parameters.
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
. 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 recombination happened when the universe was around 400,000 years old, or at a redshift
of z = 1100. Photons rarely interact with neutral matter, therefore at recombination the universe suddenly became transparent to photons, allowing them to decouple from the matter and free-stream through the universe. In other words, 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 400,000 years old.
WMAP indicates (Figure 1) a smooth, homogeneous universe with density anisotropies of one part in 105. However, when we observe the universe today we find large structure and density fluctuations. Galaxies, for instance, are 106 times more dense than the universe's mean density. 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.
. These counteracting forces of gravity and pressure create oscillations, analogous to sound waves created in air by pressure differences.
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
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, 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. 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.
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. This particular configuration of matter occurred at each anisotropy in the early universe, and therefore the universe is not composed of one sound ripple, but many overlapping ripples. As an analogy, imagine dropping many pebbles into a pond and watching the resulting wave patterns in the water. 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.
provides a measurement of this scale to high accuracy. However in the time between recombination and present day, the universe has been expanding. This expansion is well supported by observations
and is one of the foundations of the Big Bang Model
. In the late 90's, observations of supernova
determined that not only is the universe expanding, it is expanding at an increasing rate. Better understanding the 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). Thus BAO provides a measuring stick with which to better understand the nature of the acceleration, completely independent from the supernova technique.
(SDSS) is a 2.5-m wide-angle optical telescope
at Apache Point Observatory
in New Mexico
. The goal of this five-year survey was to take images
and spectra of millions of celestial objects. The result of compiling the Sloan data is a 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. They analyzed the clustering of these galaxies by calculating a two-point correlation function
on the data. The correlation function (
) is a function of comoving
galaxy separation distance (s) and describes the probability that one galaxy will be found within a given distance bin of another (See SDSS Detection Figure). 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 detected by the SDSS team in 2005. SDSS confirmed the WMAP results that the sound horizon is ~150 Mpc
in today's universe.
, the expansion of the universe is parametrized by a scale factor
which is related to redshift:
The Hubble parameter,
, in terms of the scale factor is:
where
is the time-derivative of the scale factor. The Friedmann equations
express the expansion of the universe in terms of Newton's gravitational constant
,
, the mean pressure
,
, the Universe's density 
, the curvature, 
, and the cosmological constant
,
:
Observational evidence of the acceleration of the universe implies that (at present time)
. Therefore the following are possible explanations:
In order to differentiate between these scenarios, precise measurements of the Hubble parameter as a function of redshift
are needed.
, of various components, 
, of the universe can be expressed as ratios of the density of 
to the critical density, 
:
The Friedman equation can be rewritten in terms of the density parameter. For the current prevailing model of the universe, ΛCDM
, this equation is as follows:
where m is matter, r is radiation, k is curvature, Λ is dark energy, and w is the equation of state
. Measurements of the CMB
from WMAP put tight constraints on many of these parameters however it is important to confirm and further constrain them using an independent method with different systematics.
The BAO signal is a standard ruler
such that the length of the sound horizon can be measured as a function of cosmic time
. This measures two cosmological distances: the Hubble parameter,
, and the angular diameter distance, 
, as a function of redshift
. By measuring the subtended angle, 
, of the ruler of length, 
, these parameters are determined as follows:
the redshift interval,
, can be measured from the data and thus determining the Hubble parameter as a function of redshift:
Therefore the BAO technique helps constrain cosmological parameters and provide further insight into the nature of dark energy.
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
, baryon acoustic oscillations (BAO) refers to an overdensity or clustering of baryonic matter at certain length scales due to acoustic
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
waves which propagated in the early universe. In the same way that supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
experiments provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler
Standard ruler
A standard ruler is an astronomical object whose approximate size is known. By measuring its apparent angular diameter in the sky, one can determine its distance from Earth....
" for length scale in cosmology. The length of this standard ruler (~150 Mpc
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....
in today's universe) can be measured by looking at the large scale structure of matter using astronomical surveys
Astronomical surveys
An astronomical survey is a general map or image of a region of the sky which lacks a specific observational target. Alternatively, an astronomical survey may comprise a set of many images of objects which share a common type or feature...
. BAO measurements help cosmologists understand more about the nature of dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
(the acceleration of the universe) by constraining cosmological parameters.
The Early Universe
The early universe consisted of a hot, dense plasmaPlasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
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
Thomson scattering
Thomson scattering is the elastic scattering of electromagnetic radiation by a free charged particle, as described by classical electromagnetism. It is just the low-energy limit of Compton scattering: the particle kinetic energy and photon frequency are the same before and after the scattering...
. 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 recombination happened when the universe was around 400,000 years old, or at a redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
of z = 1100. Photons rarely interact with neutral matter, therefore at recombination the universe suddenly became transparent to photons, allowing them to decouple from the matter and free-stream through the universe. In other words, the mean free path
Mean free path
In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...
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
Wilkinson Microwave Anisotropy Probe
The Wilkinson Microwave Anisotropy Probe — also known as the Microwave Anisotropy Probe , and Explorer 80 — is a spacecraft which measures differences in the temperature of the Big Bang's remnant radiant heat — the Cosmic Microwave Background Radiation — across the full sky. Headed by Professor...
(WMAP) data, we are looking back in time to see an image of the universe when it was only 400,000 years old.
Cosmic Sound
Imagine an overdense region of the primordial plasma. While this overdensity gravitationally attracts matter towards it, the heat of photon-matter interactions creates a large amount of outward pressurePressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
. These counteracting forces of gravity and pressure create oscillations, analogous to sound waves created in air by pressure differences.
Consider a single wave originating from this overdense region in the center of the plasma. This region contains dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
, 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
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
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, 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. 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.
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. This particular configuration of matter occurred at each anisotropy in the early universe, and therefore the universe is not composed of one sound ripple, but many overlapping ripples. As an analogy, imagine dropping many pebbles into a pond and watching the resulting wave patterns in the water. 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.
Standard Ruler
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 recombination. In addition the CMBCMB
CMB can mean:*The IATA airport code for Bandaranaike International Airport, Colombo – Sri Lanka's only international airport*C.M.B., the debut album of American R&B and pop group Color Me Badd...
provides a measurement of this scale to high accuracy. However in the time between recombination and present day, the universe has been expanding. This expansion is well supported by observations
Hubble's law
Hubble's law is the name for the astronomical observation in physical cosmology that: all objects observed in deep space are found to have a doppler shift observable relative velocity to Earth, and to each other; and that this doppler-shift-measured velocity, of various galaxies receding from...
and is one of the foundations of the Big Bang Model
Big Bang
The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...
. In the late 90's, observations of supernova
Supernova
A supernova is a stellar explosion that is more energetic than a nova. It is pronounced with the plural supernovae or supernovas. Supernovae are extremely luminous and cause a burst of radiation that often briefly outshines an entire galaxy, before fading from view over several weeks or months...
determined that not only is the universe expanding, it is expanding at an increasing rate. Better understanding the acceleration of the universe
Accelerating universe
The accelerating universe is the observation that the universe appears to be expanding at an increasing rate, which in formal terms means that the cosmic scale factor a has a positive second derivative, implying that the velocity at which a given galaxy is receding from us should be continually...
, or dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
, 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). Thus BAO provides a measuring stick with which to better understand the nature of the acceleration, completely independent from the supernova technique.
BAO Signal in the Sloan Digital Sky Survey
The Sloan Digital Sky SurveySloan Digital Sky Survey
The Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic redshift survey using a dedicated 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The project was named after the Alfred P...
(SDSS) is a 2.5-m wide-angle optical telescope
Optical telescope
An optical telescope is a telescope which is used to gather and focus light mainly from the visible part of the electromagnetic spectrum for directly viewing a magnified image for making a photograph, or collecting data through electronic image sensors....
at Apache Point Observatory
Apache Point Observatory
The Apache Point Observatory is located in the Sacramento Mountains in Sunspot, New Mexico 18 miles south of Cloudcroft. The observatory consists of the Astrophysical Research Consortium's 3.5-meter telescope, the Sloan Digital Sky Survey 2.5-m telescope with a 20" photometric telescope,...
in New Mexico
New Mexico
New Mexico is a state located in the southwest and western regions of the United States. New Mexico is also usually considered one of the Mountain States. With a population density of 16 per square mile, New Mexico is the sixth-most sparsely inhabited U.S...
. The goal of this five-year survey was to take images
Photometric system
In astronomy, a Photometric system is a set of well-defined passbands , with a known sensitivity to incident radiation. The sensitivity usually depends on the optical system, detectors and filters used. For each photometric system a set of primary standard stars is provided.The first known...
and spectra of millions of celestial objects. The result of compiling the Sloan data is a 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
Light Years
Light Years is the seventh studio album by Australian recording artist Kylie Minogue. It was released on 25 September 2000 by Parlophone and Mushroom Records. The album's style was indicative of her return to "mainstream pop dance tunes"....
in diameter) and out to a redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
of z = 0.47. They analyzed the clustering of these galaxies by calculating a two-point correlation function
Correlation function (astronomy)
In astronomy, a correlation function describes the distribution of galaxies in the universe. By default, correlation function refers to the two-point autocorrelation function. For a given distance, the two-point autocorrelation function is a function of one variable which describes the...
on the data. The correlation function (
) is a function of comovingComoving distance
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects...
galaxy separation distance (s) and describes the probability that one galaxy will be found within a given distance bin of another (See SDSS Detection Figure). 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 detected by the SDSS team in 2005. SDSS confirmed the WMAP results that the sound horizon is ~150 Mpc
Parsec
The parsec is a unit of length used in astronomy. It is about 3.26 light-years, or just under 31 trillion kilometres ....
in today's universe.
General Relativity and Dark Energy
In general relativityGeneral relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the expansion of the universe is parametrized by a scale factor
Scale factor (Universe)
The scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor...
which is related to redshift:The Hubble parameter,
, in terms of the scale factor is:where
is the time-derivative of the scale factor. The Friedmann equationsFriedmann equations
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity...
express the expansion of the universe in terms of Newton's gravitational constant
Gravitational constant
The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitational attraction between objects with mass. It appears in Newton's law of universal gravitation and in Einstein's theory of general relativity. It is also known as the universal...
,
, the mean pressurePressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
,
, the Universe's density , the curvature, , and the cosmological constantCosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
,
:Observational evidence of the acceleration of the universe implies that (at present time)
. Therefore the following are possible explanations:
- The universe is dominated by some field or particle that has negative pressure such that the equation of state:
- There is a non-zero cosmological constant,
. - 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
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
are needed.
Measured Observables of Dark Energy
The density parameter,, of various components, , of the universe can be expressed as ratios of the density of to the critical density, :The Friedman equation can be rewritten in terms of the density parameter. For the current prevailing model of the universe, ΛCDM
Lambda-CDM model
ΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter, which is also known as the cold dark matter model with dark energy...
, this equation is as follows:
where m is matter, r is radiation, k is curvature, Λ is dark energy, and w is the equation of state
Equation of state (cosmology)
In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number \! w, equal to the ratio of its pressure \! p to its energy density \! \rho: \! w=p/\rho...
. Measurements of the CMB
CMB
CMB can mean:*The IATA airport code for Bandaranaike International Airport, Colombo – Sri Lanka's only international airport*C.M.B., the debut album of American R&B and pop group Color Me Badd...
from WMAP put tight constraints on many of these parameters however it is important to confirm and further constrain them using an independent method with different systematics.
The BAO signal is a standard ruler
Standard ruler
A standard ruler is an astronomical object whose approximate size is known. By measuring its apparent angular diameter in the sky, one can determine its distance from Earth....
such that the length of the sound horizon can be measured as a function of cosmic time
Cosmic time
Cosmic time is the time coordinate commonly used in the Big Bang models of physical cosmology. It is defined for homogeneous, expanding universes as follows: Choose a time coordinate so that the universe has the same density everywhere at each moment in time Cosmic time (also known as time since...
. This measures two cosmological distances: the Hubble parameter,
, and the angular diameter distance, , as a function of redshiftRedshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...
. By measuring the subtended angle, , of the ruler of length, , these parameters are determined as follows:the redshift interval,
, can be measured from the data and thus determining the Hubble parameter as a function of redshift:Therefore the BAO technique helps constrain cosmological parameters and provide further insight into the nature of dark energy.