Baryon acoustic oscillations

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In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter (normal matter) of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way that supernovae provide a "standard candle" for astronomical observations, [1] BAO matter clustering provides a "standard ruler" for length scale in cosmology. [2] The length of this standard ruler is given by the maximum distance the acoustic waves could travel in the primordial plasma before the plasma cooled to the point where it became neutral atoms (the epoch of recombination), which stopped the expansion of the plasma density waves, "freezing" them into place. The length of this standard ruler (≈490 million light years in today's universe [3] ) can be measured by looking at the large scale structure of matter using astronomical surveys. [3] BAO measurements help cosmologists understand more about the nature of dark energy (which causes the accelerating expansion of the universe) by constraining cosmological parameters. [2]

Contents

Early universe

The early universe consisted of a hot, dense plasma of electrons and baryons (which include protons and neutrons). Photons (light particles) travelling in this universe were essentially trapped, unable to travel for any considerable distance before interacting with the plasma via Thomson scattering. [4] The average distance which a photon could travel before interacting with the plasma is known as the mean free path of the photon. 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 379,000 years old, or at a redshift of z = 1089. [4] At this age, the size of BAO bubbles were 450,000 light-years (0.14 Mpc) in radius (490 million light-years today divided by z = 1089). Photons interact to a much lesser degree with neutral matter, and therefore at recombination the universe became transparent to photons, allowing them to decouple from the matter and free-stream through the universe. [4] The cosmic microwave background (CMB) radiation is light that was scattered just before, and emitted by, recombination, now seen with our telescopes as radio waves all over the sky since it is red-shifted. Therefore, when looking at, for example, Wilkinson Microwave Anisotropy Probe (WMAP) data, one is basically looking back in time to see an image of the universe when it was only 379,000 years old. [4]

Figure 1: Temperature anisotropies of the CMB based on the nine year WMAP data (2012). WMAP 2012.png
Figure 1: Temperature anisotropies of the CMB based on the nine year WMAP data (2012).

WMAP indicates (Figure 1) a smooth, homogeneous universe with density anisotropies of 10 parts per million. [4] However, there are large structures and density fluctuations in the present universe. Galaxies, for instance, are a million times more dense than the universe's mean density. [2] 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 observed today. Overdense regions attract more matter, whereas underdense regions attract less, and thus these small anisotropies, seen in the CMB, became the large scale structures in the universe today.

Cosmic sound

Imagine an overdense region of the primordial plasma. While this region of 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 created oscillations, comparable to sound waves created in air by pressure differences. [3]

This overdense region contains dark matter, baryons and photons. The pressure results in spherical sound waves of both baryons and photons moving with a speed slightly over half the speed of light [8] [9] outwards from the overdensity. The dark matter interacts only gravitationally, and so it stays at the center of the sound wave, the origin of the overdensity. Before decoupling, the photons and baryons moved outwards together. After decoupling the photons were no longer interacting with the baryonic matter and they diffused away. That relieved the pressure on the system, leaving behind shells of baryonic matter. Out of all those shells, representing different sound waves wavelengths, the resonant shell corresponds to the first one as it is that shell that travels the same distance for all overdensities before decoupling. This radius is often referred to as the sound horizon. [3]

Without the photo-baryon pressure driving the system outwards, the only remaining force on the baryons was gravitational. Therefore, the baryons and dark matter (left behind at the center of the perturbation) formed a configuration which included overdensities of matter both at the original site of the anisotropy and in the shell at the sound horizon for that anisotropy. [3] Such anisotropies eventually became the ripples in matter density that would form galaxies.

Therefore, one would expect to see a greater number of galaxy pairs separated by the sound horizon distance scale than by other length scales. [3] This particular configuration of matter occurred at each anisotropy in the early universe, and therefore the universe is not composed of one sound ripple, [10] but many overlapping ripples. [11] As an analogy, imagine dropping many pebbles into a pond and watching the resulting wave patterns in the water. [2] It is not possible to observe this preferred separation of galaxies on the sound horizon scale by eye, but one can measure this artifact 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; as a result cosmologists can predict the size of the sound horizon at the time of recombination. In addition the CMB provides a measurement of this scale to high accuracy. [3] 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 1990s, observations of supernovae [1] determined that not only is the universe expanding, it is expanding at an increasing rate. A better understanding of 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 the 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 that of the sound horizon at the time of recombination (using the CMB). [3] 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 Survey (SDSS) is a major multi-spectral imaging and spectroscopic redshift survey using the dedicated 2.5-metre wide-angle SDSS 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 SDSS data is a three-dimensional map of objects in the nearby universe: the SDSS catalog. The SDSS catalog provides a picture of the distribution of matter in a large enough portion of the universe that one can search for a BAO signal by noting whether there is a statistically significant overabundance of galaxies separated by the predicted sound horizon distance.

The SDSS team looked at a sample of 46,748 luminous red galaxies (LRGs), over 3,816 square-degrees of sky (approximately five billion light years in diameter) and out to a redshift of z = 0.47. [3] They analyzed the clustering of these galaxies by calculating a two-point correlation function on the data. [12] The correlation function (ξ) is a function of comoving galaxy separation distance (s) and describes the probability that one galaxy will be found within a given distance of another. [13] 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 separation distances. 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. [3] [14] SDSS confirmed the WMAP results that the sound horizon is ~150  Mpc in today's universe. [2] [3]

In 2023 astronomers using the SDSS catalog as well as the cosmicflow-4 [15] catalog claimed to have found evidence of an individual BAO bubble with a radius containing some of largest structures known – the Boötes supercluster, the Sloan Great Wall, CfA2 Great Wall, and the Hercules–Corona Borealis Great Wall – which they named Ho'oleilana. [16] [17]

Detection in other galaxy surveys

The 2dFGRS collaboration and the SDSS collaboration reported a detection of the BAO signal in the power spectrum at around the same time in 2005. [18] Both teams are credited and recognized for the discovery by the community as evidenced by the 2014 Shaw Prize in Astronomy [19] which was awarded to both groups. Since then, further detections have been reported in the 6dF Galaxy Survey (6dFGS) in 2011, [20] WiggleZ in 2011 [21] and BOSS in 2012. [22]

Dark energy formalism

BAO constraints on dark energy parameters

The BAO in the radial and transverse directions provide measurements of the Hubble parameter and angular diameter distance, respectively. The angular diameter distance and Hubble parameter can include different functions that explain dark energy behavior. [23] [24] These functions have two parameters w0 and w1 and one can constrain them with a chi-square technique. [25]

General relativity and dark energy

In general relativity, the expansion of the universe is parametrized by a scale factor which is related to redshift: [4]

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 gauge pressure, , the Universe's density , the curvature, , and the cosmological constant, : [4]

Observational evidence of the acceleration of the universe implies that (at present time) . Therefore, the following are possible explanations: [26]

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, , of various components, , of the universe can be expressed as ratios of the density of to the critical density, : [26]

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: [26]

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. [3] This measures two cosmological distances: the Hubble parameter, , and the angular diameter distance, , as a function of redshift . [27] By measuring the subtended angle, , of the ruler of length , these parameters are determined as follows: [27]

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.

See also

Related Research Articles

<span class="mw-page-title-main">Cosmic microwave background</span> Trace radiation from the early universe

The cosmic microwave background is microwave radiation that fills all space in the observable universe. It is a remnant that provides an important source of data on the primordial universe. With a standard optical telescope, the background space between stars and galaxies is almost completely dark. However, a sufficiently sensitive radio telescope detects a faint background glow that is almost uniform and is not associated with any star, galaxy, or other object. This glow is strongest in the microwave region of the radio spectrum. The accidental discovery of the CMB in 1965 by American radio astronomers Arno Penzias and Robert Wilson was the culmination of work initiated in the 1940s.

<span class="mw-page-title-main">Redshift</span> Change of wavelength in photons during travel

In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift, or negative redshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.

<span class="mw-page-title-main">Accelerating expansion of the universe</span> Cosmological phenomenon

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are farther away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the farther away that an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.

<span class="mw-page-title-main">Hubble's law</span> Observation in physical cosmology

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible light spectrum. The discovery of Hubble's law is attributed to Edwin Hubble's work published in 1929.

The expansion of the universe is parametrized by a dimensionless scale factor. Also known as the cosmic scale factor or sometimes the Robertson–Walker scale factor, this is a key parameter of the Friedmann equations.

<span class="mw-page-title-main">Lambda-CDM model</span> Model of Big Bang cosmology

The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components:

  1. a cosmological constant, denoted by lambda (Λ), associated with dark energy
  2. the postulated cold dark matter, denoted by CDM
  3. ordinary matter
<span class="mw-page-title-main">Flatness problem</span> Cosmological fine-tuning problem

The flatness problem is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that small deviations from these values would have extreme effects on the appearance of the universe at the current time.

Primordial fluctuations are density variations in the early universe which are considered the seeds of all structure in the universe. Currently, the most widely accepted explanation for their origin is in the context of cosmic inflation. According to the inflationary paradigm, the exponential growth of the scale factor during inflation caused quantum fluctuations of the inflaton field to be stretched to macroscopic scales, and, upon leaving the horizon, to "freeze in". At the later stages of radiation- and matter-domination, these fluctuations re-entered the horizon, and thus set the initial conditions for structure formation.

<span class="mw-page-title-main">Cosmic neutrino background</span> Universes background particle radiation composed of neutrinos

The cosmic neutrino background is the universe's background particle radiation composed of neutrinos. They are sometimes known as relic neutrinos.

In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the Big Bang model. Cosmological perturbation theory may be broken into two categories: Newtonian or general relativistic. Each case uses its governing equations to compute gravitational and pressure forces which cause small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. Both cases apply only to situations where the universe is predominantly homogeneous, such as during cosmic inflation and large parts of the Big Bang. The universe is believed to still be homogeneous enough that the theory is a good approximation on the largest scales, but on smaller scales more involved techniques, such as N-body simulations, must be used. When deciding whether to use general relativity for perturbation theory, note that Newtonian physics is only applicable in some cases such as for scales smaller than the Hubble horizon, where spacetime is sufficiently flat, and for which speeds are non-relativistic.

<span class="mw-page-title-main">Deceleration parameter</span>

The deceleration parameter in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe. It is defined by: where is the scale factor of the universe and the dots indicate derivatives by proper time. The expansion of the universe is said to be "accelerating" if , and in this case the deceleration parameter will be negative. The minus sign and name "deceleration parameter" are historical; at the time of definition was expected to be negative, so a minus sign was inserted in the definition to make positive in that case. Since the evidence for the accelerating universe in the 1998–2003 era, it is now believed that is positive therefore the present-day value is negative. In general varies with cosmic time, except in a few special cosmological models; the present-day value is denoted .

<span class="mw-page-title-main">Lyman-alpha emitter</span>

A Lyman-alpha emitter (LAE) is a type of distant galaxy that emits Lyman-alpha radiation from neutral hydrogen.

<span class="mw-page-title-main">Diffusion damping</span> Physical process in cosmology

In modern cosmological theory, diffusion damping, also called photon diffusion damping, is a physical process which reduced density inequalities (anisotropies) in the early universe, making the universe itself and the cosmic microwave background radiation (CMB) more uniform. Around 300,000 years after the Big Bang, during the epoch of recombination, diffusing photons travelled from hot regions of space to cold ones, equalising the temperatures of these regions. This effect is responsible, along with baryon acoustic oscillations, the Doppler effect, and the effects of gravity on electromagnetic radiation, for the eventual formation of galaxies and galaxy clusters, these being the dominant large scale structures which are observed in the universe. It is a damping by diffusion, not of diffusion.

<span class="mw-page-title-main">Chronology of the universe</span> History and future of the universe

The chronology of the universe describes the history and future of the universe according to Big Bang cosmology.

<span class="mw-page-title-main">Dark energy</span> Energy driving the accelerated expansion of the universe

In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. Assuming that the lambda-CDM model of cosmology is correct, dark energy is the dominant component of the universe, contributing 68% of the total energy in the present-day observable universe while dark matter and ordinary (baryonic) matter contribute 26% and 5%, respectively, and other components such as neutrinos and photons are nearly negligible. Dark energy's density is very low: 7×10−30 g/cm3, much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.

<span class="mw-page-title-main">Recombination (cosmology)</span> Epoch c. 370,000 years after the Big Bang

In cosmology, recombination refers to the epoch during which charged electrons and protons first became bound to form electrically neutral hydrogen atoms. Recombination occurred about 378,000 years after the Big Bang. The word "recombination" is misleading, since the Big Bang theory does not posit that protons and electrons had been combined before, but the name exists for historical reasons since it was named before the Big Bang hypothesis became the primary theory of the birth of the universe.

In astrophysics, the virial mass is the mass of a gravitationally bound astrophysical system, assuming the virial theorem applies. In the context of galaxy formation and dark matter halos, the virial mass is defined as the mass enclosed within the virial radius of a gravitationally bound system, a radius within which the system obeys the virial theorem. The virial radius is determined using a "top-hat" model. A spherical "top hat" density perturbation destined to become a galaxy begins to expand, but the expansion is halted and reversed due to the mass collapsing under gravity until the sphere reaches equilibrium – it is said to be virialized. Within this radius, the sphere obeys the virial theorem which says that the average kinetic energy is equal to minus one half times the average potential energy, , and this radius defines the virial radius.

<span class="mw-page-title-main">Decoupling (cosmology)</span> Type of event in the early universe

In cosmology, decoupling is a period in the development of the universe when different types of particles fall out of thermal equilibrium with each other. This occurs as a result of the expansion of the universe, as their interaction rates decrease up to this critical point. The two verified instances of decoupling since the Big Bang which are most often discussed are photon decoupling and neutrino decoupling, as these led to the cosmic microwave background and cosmic neutrino background, respectively.

In cosmology, the missing baryon problem is an observed discrepancy between the amount of baryonic matter detected from shortly after the Big Bang and from more recent epochs. Observations of the cosmic microwave background and Big Bang nucleosynthesis studies have set constraints on the abundance of baryons in the early universe, finding that baryonic matter accounts for approximately 4.8% of the energy contents of the Universe. At the same time, a census of baryons in the recent observable universe has found that observed baryonic matter accounts for less than half of that amount. This discrepancy is commonly known as the missing baryon problem. The missing baryon problem is different from the dark matter problem, which is non-baryonic in nature.

<span class="mw-page-title-main">Cosmic microwave background spectral distortions</span> Fluctuations in the energy spectrum of the microwave background

CMB spectral distortions are tiny departures of the average cosmic microwave background (CMB) frequency spectrum from the predictions given by a perfect black body. They can be produced by a number of standard and non-standard processes occurring at the early stages of cosmic history, and therefore allow us to probe the standard picture of cosmology. Importantly, the CMB frequency spectrum and its distortions should not be confused with the CMB anisotropy power spectrum, which relates to spatial fluctuations of the CMB temperature in different directions of the sky.

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