Glossary

7.5 Baryon acoustic oscillations

9 min read•august 20, 2024

(BAO) are remnants of sound waves that propagated through the early universe. These oscillations left an imprint on both the and the of galaxies, providing a powerful tool for cosmologists.

BAO measurements serve as a "standard ruler" for cosmic distances, allowing scientists to probe the expansion history of the universe. By analyzing the BAO signal in galaxy surveys, researchers can constrain key cosmological parameters and test theories of and cosmic acceleration.

Primordial plasma oscillations

  • In the early universe, baryons and photons were tightly coupled in a hot, dense plasma
  • This underwent oscillations driven by the competing forces of gravity and radiation pressure
  • These left an imprint on the cosmic microwave background (CMB) and the large-scale structure of the universe

Photon-baryon fluid interactions

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  • Photons and baryons interacted strongly through Thomson scattering in the early universe
  • acted as a restoring force, while baryon mass provided inertia
  • These interactions created a tightly coupled fluid that behaved like a single entity
  • The fluid underwent compression and rarefaction as it oscillated

Gravity and pressure forces

  • from matter overdensities pulled the photon-baryon fluid inward
  • Radiation pressure from the photons resisted this compression, pushing the fluid back outward
  • The balance between these two forces determined the frequency and amplitude of the oscillations
  • Gravity and pressure created in the primordial plasma

Oscillation frequency and wavelength

  • The was determined by the sound speed in the photon-baryon fluid (approximately c/3c/\sqrt{3})
  • The of the oscillations depended on the size of the sound horizon at the time of decoupling
  • Longer wavelength modes had more time to oscillate before decoupling, while shorter wavelengths were frozen in earlier
  • The characteristic wavelength of the oscillations is around 150 Mpc in today's universe

Cosmic microwave background imprint

  • The primordial plasma oscillations left a distinctive imprint on the cosmic microwave background (CMB) radiation
  • This imprint is visible as small and a series of peaks in the
  • Studying the CMB allows cosmologists to probe the conditions of the early universe and constrain cosmological parameters

Temperature fluctuations

  • The CMB temperature fluctuates on the order of 1 part in 100,000 across the sky
  • These fluctuations correspond to the compression and rarefaction phases of the primordial plasma oscillations
  • Hotter regions represent compressed fluid, while cooler regions represent rarefied fluid
  • The angular size of these fluctuations is determined by the oscillation wavelength at the time of decoupling

Peaks in power spectrum

  • The CMB power spectrum displays a series of peaks and troughs at specific angular scales
  • These peaks correspond to the harmonics of the primordial plasma oscillations
  • The first peak represents the fundamental mode, while subsequent peaks are overtones
  • The relative heights and positions of these peaks provide information about the universe's composition and geometry

Oscillation phases at recombination

  • At the time of recombination (around 380,000 years after the Big Bang), the universe cooled enough for atoms to form
  • This decoupling of photons and baryons effectively froze the plasma oscillations in place
  • The phases of the oscillations at this moment (compression, rarefaction, or in between) determined the initial conditions for
  • Compressed regions formed the seeds for galaxy clusters and filaments, while rarefied regions became voids

Baryon acoustic peak

  • The primordial plasma oscillations also left an imprint on the large-scale structure of the universe
  • This imprint is known as the , a characteristic clustering scale for galaxies
  • The baryon acoustic peak acts as a standard ruler, allowing cosmologists to measure distances and constrain cosmological parameters

Galaxy clustering signature

  • Galaxies are more likely to be separated by the characteristic scale of the baryon acoustic oscillations (BAO)
  • This clustering signature appears as a peak in the galaxy correlation function or a series of wiggles in the power spectrum
  • The BAO signal is a result of the primordial sound waves propagating through the photon-baryon fluid
  • Compressed regions at decoupling formed the initial overdensities that grew into galaxies and clusters

Characteristic scale of 150 Mpc

  • The baryon acoustic peak corresponds to a comoving scale of around 150 megaparsecs (Mpc) in today's universe
  • This scale represents the distance the sound waves traveled before decoupling, known as the sound horizon
  • The sound horizon acts as a standard ruler, as it is a fixed physical scale imprinted on the galaxy distribution
  • Measuring the apparent size of this standard ruler at different redshifts allows cosmologists to trace the expansion history of the universe

Standard ruler for cosmology

  • The baryon acoustic peak serves as a powerful tool for cosmological measurements
  • By comparing the observed BAO scale to the predicted sound horizon, cosmologists can infer the distance to galaxies at various redshifts
  • This distance information can be used to constrain the Hubble constant, the matter density, and the
  • The BAO standard ruler is particularly valuable because it is a robust and model-independent probe of cosmology

Cosmological parameter constraints

  • Baryon acoustic oscillations provide a wealth of information about the fundamental parameters of the universe
  • By measuring the BAO scale at different redshifts and combining this data with other cosmological probes, scientists can place tight constraints on key parameters
  • These constraints help us understand the composition, geometry, and evolution of the universe

Matter and baryon density

  • The matter density (Ωm\Omega_m) and (Ωb\Omega_b) affect the relative heights of the CMB acoustic peaks
  • The second peak is particularly sensitive to the baryon density, as it represents the baryon loading of the photon-baryon fluid
  • BAO measurements can also constrain the matter density, as it influences the growth of structure and the expansion rate
  • Current BAO data, combined with CMB and other probes, suggest a matter density of about 30% and a baryon density of about 5%

Hubble constant measurements

  • The Hubble constant (H0H_0) describes the current expansion rate of the universe
  • BAO measurements can constrain the Hubble constant by providing a standard ruler for distance measurements
  • Comparing the observed BAO scale at different redshifts to the predicted sound horizon allows cosmologists to infer H0H_0
  • BAO measurements have helped to address the tension between local and CMB-based estimates of the Hubble constant

Dark energy equation of state

  • The dark energy equation of state parameter (ww) describes the ratio of pressure to energy density for the mysterious component driving cosmic acceleration
  • BAO measurements can constrain ww by tracing the expansion history of the universe over a wide range of redshifts
  • If dark energy is a cosmological constant (as predicted by the Lambda-CDM model), then ww should be equal to -1
  • Deviations from w=−1w=-1 would suggest a more complex form of dark energy, such as a dynamical scalar field

Galaxy redshift surveys

  • Galaxy play a crucial role in detecting and characterizing baryon acoustic oscillations
  • These surveys map the 3D positions of millions of galaxies by measuring their redshifts and angular positions on the sky
  • Large-scale structure analysis techniques, such as correlation functions and power spectra, are applied to the survey data to extract the BAO signal

Two-point correlation function

  • The measures the excess probability of finding galaxy pairs separated by a given distance, compared to a random distribution
  • The BAO signal appears as a peak in the correlation function at the
  • The position and amplitude of this peak provide information about the expansion history and matter content of the universe
  • Correlation function measurements are particularly useful for visualizing the BAO feature and assessing its statistical significance

Power spectrum analysis

  • The power spectrum quantifies the amplitude of density fluctuations as a function of scale (wavenumber)
  • The BAO signal manifests as a series of wiggles or oscillations in the power spectrum, corresponding to the harmonics of the primordial plasma oscillations
  • is complementary to correlation function measurements, providing a different perspective on the BAO feature
  • The shape and amplitude of the power spectrum can constrain cosmological parameters and test theories of structure formation

Baryon acoustic oscillation detection

  • Detecting the BAO signal requires large galaxy redshift surveys that cover a substantial volume of the universe
  • Surveys such as the Sloan Digital Sky Survey (SDSS), WiggleZ, and the Baryon Oscillation Spectroscopic Survey (BOSS) have successfully measured the BAO feature
  • The significance of the BAO detection increases with survey volume and galaxy density, as this reduces statistical uncertainties
  • Future surveys, such as the Dark Energy Spectroscopic Instrument (DESI) and Euclid, aim to measure the BAO scale with unprecedented precision

Observational challenges

  • Measuring baryon acoustic oscillations with galaxy redshift surveys presents several observational challenges
  • These challenges must be carefully addressed to ensure robust and unbiased BAO measurements
  • Overcoming these challenges requires advanced survey design, data analysis techniques, and theoretical modeling

Survey volume and completeness

  • BAO measurements require surveys that cover a large volume of the universe to reduce statistical uncertainties
  • However, increasing survey volume often comes at the cost of reduced completeness or higher observational costs
  • Incomplete surveys can introduce systematic biases in the BAO measurement, as they may preferentially sample certain regions or galaxy types
  • Careful survey design and completeness corrections are necessary to mitigate these biases

Redshift distortions and bias

  • Peculiar velocities of galaxies can distort their observed redshifts, leading to apparent clustering anisotropies
  • These redshift-space distortions can shift the position of the BAO peak and alter its shape
  • Additionally, galaxies are biased tracers of the underlying matter distribution, which can affect the BAO signal
  • Modeling and correcting for redshift distortions and galaxy bias is crucial for accurate BAO measurements

Nonlinear structure growth effects

  • The BAO feature is a product of linear physics in the early universe, but structure formation becomes nonlinear at late times
  • Nonlinear gravitational evolution can smear out the BAO peak and shift its position
  • These nonlinear effects are scale-dependent and become more significant at smaller scales and lower redshifts
  • Perturbation theory and numerical simulations are used to model and correct for nonlinear structure growth

Concordance cosmology confirmation

  • Baryon acoustic oscillations provide a powerful test of the concordance cosmological model, known as the Lambda Cold Dark Matter (Lambda-CDM) model
  • The Lambda-CDM model posits a flat universe dominated by dark energy and cold dark matter, with a small fraction of baryonic matter
  • BAO measurements, combined with other cosmological probes, have confirmed key predictions of the Lambda-CDM model

Independent distance measure

  • BAO measurements offer an independent way to measure cosmic distances, complementing other methods such as Type Ia supernovae and the CMB
  • The consistency between BAO distances and those derived from other probes strengthens our confidence in the underlying cosmological model
  • Independent distance measures help break degeneracies between cosmological parameters and test the robustness of the Lambda-CDM framework
  • The agreement between BAO and other distance indicators is a major success of the concordance cosmology

Flat geometry and acceleration evidence

  • The Lambda-CDM model predicts a flat spatial geometry for the universe, with the total energy density equal to the critical density
  • BAO measurements, combined with CMB data, provide strong evidence for a flat universe
  • The observed BAO scale at different redshifts is consistent with the expected evolution in a flat Lambda-CDM cosmology
  • BAO data also support the existence of dark energy driving the accelerated expansion of the universe

Consistency with other probes

  • BAO measurements are just one piece of the cosmological puzzle, and they must be consistent with other observational probes
  • The concordance Lambda-CDM model is supported by a wide range of independent observations, including:
    • CMB temperature and polarization anisotropies
    • Type Ia supernova distance measurements
    • Weak gravitational lensing surveys
    • Abundance of galaxy clusters
  • The consistency between BAO and these other probes reinforces the validity of the Lambda-CDM model as the standard cosmological framework

Key Terms to Review (40)

3D mapping of galaxies: 3D mapping of galaxies involves creating a three-dimensional representation of the distribution and properties of galaxies in the universe. This technique provides insights into the large-scale structure of the cosmos, allowing astronomers to understand how galaxies are distributed in space and how they interact with one another over time.
Acoustic Horizon: The acoustic horizon refers to the maximum distance that sound waves can travel in the early universe, specifically during the time of baryon acoustic oscillations. This concept is critical in understanding how fluctuations in density of matter and radiation influenced the formation of cosmic structures. The acoustic horizon defines a boundary beyond which sound waves could not propagate, shaping the large-scale structure of the universe as we observe it today.
Baryon acoustic oscillation detection: Baryon acoustic oscillation detection refers to the observation and measurement of the regular patterns of density fluctuations in the early universe, which are imprinted in the distribution of galaxies and cosmic microwave background radiation. These oscillations arise from the interplay of gravitational forces and pressure waves in the hot plasma of the early universe, creating characteristic scales that serve as a cosmic ruler for understanding the expansion history of the universe.
Baryon Acoustic Oscillations: Baryon acoustic oscillations refer to the periodic fluctuations in the density of visible baryonic matter (normal matter) in the universe, which were produced by sound waves in the early universe. These oscillations are critical as they provide evidence of the distribution of matter and energy in the cosmos, influencing structures like galaxy clusters, superclusters, and voids.
Baryon acoustic peak: The baryon acoustic peak refers to a specific feature observed in the cosmic microwave background radiation and large-scale structure of the universe, resulting from sound waves propagating through the early universe's hot plasma. This phenomenon is crucial for understanding the distribution of matter and energy in the cosmos, as it reveals information about the universe's expansion, density fluctuations, and the nature of dark energy.
Baryon density: Baryon density refers to the number density of baryons, which are particles such as protons and neutrons that make up atomic nuclei. This concept is crucial in cosmology as it influences the formation of structures in the universe, particularly through baryon acoustic oscillations, which are fluctuations in the distribution of baryonic matter due to pressure waves in the early universe.
Characteristic scale of 150 Mpc: The characteristic scale of 150 megaparsecs (Mpc) refers to a specific distance in cosmology, particularly in the study of the large-scale structure of the universe. This scale is significant because it represents the typical distance over which baryon acoustic oscillations, which are fluctuations in density in the early universe, can be observed in the distribution of galaxies. Understanding this scale helps in interpreting the cosmic microwave background radiation and the overall evolution of cosmic structures.
Clustering of galaxies: Clustering of galaxies refers to the tendency of galaxies to group together in specific regions of the universe, forming larger structures such as galaxy clusters and superclusters. This phenomenon is primarily influenced by gravitational attraction, which causes galaxies to be drawn towards one another, ultimately impacting their distribution in the cosmos and leading to the formation of intricate web-like structures known as the cosmic web.
Cmb power spectrum: The CMB power spectrum is a graphical representation of the temperature fluctuations in the Cosmic Microwave Background (CMB) radiation as a function of angular scale. It reveals the distribution of these fluctuations in terms of their strength at different scales, providing vital information about the early universe, including the density variations and the influence of baryon acoustic oscillations.
Concordance Cosmology Confirmation: Concordance cosmology confirmation refers to the agreement among various cosmological observations and theoretical models that describe the universe's structure, composition, and evolution. This concept plays a crucial role in understanding how different phenomena, such as cosmic microwave background radiation, galaxy formation, and large-scale structure align with the predictions of the Lambda Cold Dark Matter ($\Lambda$CDM) model, which serves as the standard framework for modern cosmology.
Consistency with other probes: Consistency with other probes refers to the agreement and validation of measurements and findings across different observational techniques and methods in astrophysics. This concept is crucial when interpreting data from phenomena like baryon acoustic oscillations, as it helps establish the reliability of cosmological models and measurements by comparing results obtained from various sources, such as galaxy surveys and cosmic microwave background radiation observations.
Cosmic Microwave Background: The cosmic microwave background (CMB) is the afterglow radiation from the Big Bang, permeating the universe and providing a snapshot of the early universe when it was just about 380,000 years old. This faint glow, detected in the microwave part of the electromagnetic spectrum, is crucial for understanding the formation and evolution of structures in the universe, linking various aspects of cosmology and astrophysics.
Dark energy: Dark energy is a mysterious form of energy that makes up about 68% of the universe and is responsible for the accelerated expansion of the cosmos. It plays a crucial role in shaping the universe's large-scale structure, influencing phenomena like voids, the cosmological principle, and Hubble's law.
Dark energy equation of state: The dark energy equation of state is a key concept in cosmology that describes the relationship between the pressure and energy density of dark energy, often represented by the parameter \( w \). This equation plays a vital role in understanding the accelerated expansion of the universe and helps distinguish between different models of dark energy, such as a cosmological constant or dynamical dark energy. By examining how dark energy influences cosmic structure formation, scientists gain insights into its properties and effects on the universe's evolution.
David H. Weinberg: David H. Weinberg is a prominent astrophysicist known for his research on the large-scale structure of the universe, particularly in the context of baryon acoustic oscillations. His work has contributed significantly to our understanding of how baryonic matter interacts with dark matter and influences the cosmic web, thereby shedding light on the evolution of galaxies and the expansion of the universe.
Flat geometry and acceleration evidence: Flat geometry refers to a cosmological model in which the universe is spatially flat, meaning that the angles of a triangle sum to 180 degrees, and it follows the rules of Euclidean geometry. In this context, acceleration evidence indicates that the expansion of the universe is not only ongoing but is actually speeding up, suggesting the influence of dark energy.
Friedmann equations: The Friedmann equations are a set of fundamental equations in cosmology that describe the expansion of the universe based on general relativity. They relate the universe's expansion rate to its energy density, pressure, and curvature, forming the basis for understanding cosmic evolution and the dynamics of the universe. These equations connect to essential concepts like the cosmological principle and baryon acoustic oscillations, helping to explain how structures form in the universe over time.
Galaxy clustering signature: The galaxy clustering signature refers to the pattern and distribution of galaxies in the universe, showcasing how they tend to group together in clusters due to gravitational interactions. This signature reveals the underlying structure of the cosmos, influenced by factors such as dark matter, cosmic expansion, and baryon acoustic oscillations, which leave imprints on the spatial distribution of galaxies over time.
Gravitational attraction: Gravitational attraction is the force that pulls two masses toward each other, dictated by their mass and the distance between them. This fundamental force governs the behavior of celestial bodies and influences their formation and evolution in the universe, including the dynamics observed in structures like galaxies and cosmic phenomena.
Hubble Constant Measurements: Hubble constant measurements refer to the determination of the rate of expansion of the universe, expressed as the Hubble constant (H₀), typically given in kilometers per second per megaparsec. This measurement is essential for understanding the scale and dynamics of the universe and plays a key role in determining distances to galaxies and other cosmic structures. Accurate Hubble constant measurements have significant implications for cosmology, affecting theories about dark energy, the age of the universe, and the overall structure of cosmic expansion.
Independent distance measure: An independent distance measure refers to techniques used in astronomy to determine the distances to celestial objects without relying on their intrinsic properties or assumptions about their luminosities. This concept is crucial for understanding the scale of the universe, as it helps astronomers gauge how far away objects like galaxies and clusters are, contributing to our knowledge of cosmic structure and expansion.
Large-scale structure: Large-scale structure refers to the organization and distribution of matter in the universe on scales larger than individual galaxies, encompassing clusters, superclusters, and the cosmic web. This framework helps us understand how galaxies and other cosmic structures form and evolve under the influence of gravitational forces and dark matter.
Linear perturbation theory: Linear perturbation theory is a mathematical framework used to analyze small deviations from a uniform and isotropic universe, allowing for the study of density fluctuations and their growth over time. This theory is essential for understanding how small initial perturbations in the density of matter can lead to the large-scale structure observed in the universe today, including galaxies and clusters of galaxies.
Neil Turok: Neil Turok is a prominent theoretical physicist known for his work in cosmology, particularly in understanding the origins and structure of the universe. He has made significant contributions to models of the universe that suggest a cyclical nature of cosmic events, including the proposal of the cyclic model of the universe, which challenges traditional views on the Big Bang.
Nonlinear structure growth effects: Nonlinear structure growth effects refer to the complex ways in which gravitational forces influence the formation and evolution of cosmic structures, like galaxies and clusters of galaxies, in a way that deviates from linear predictions. These effects become particularly important in the later stages of structure formation, when density fluctuations grow significantly, leading to phenomena like galaxy clustering and the emergence of large-scale structures in the universe. Understanding these effects is essential for interpreting observations of the cosmos and refining cosmological models.
Oscillation frequency: Oscillation frequency refers to the number of complete cycles of oscillation that occur in a given time period, typically measured in Hertz (Hz). This concept is essential in understanding the behavior of sound waves and other oscillatory systems, where it plays a critical role in determining wave properties such as wavelength and amplitude. In the context of cosmology, oscillation frequency helps explain how sound waves propagated through the early universe, influencing the distribution of matter and the formation of large-scale structures.
Photon pressure: Photon pressure refers to the force exerted by electromagnetic radiation, such as light, on a surface. This pressure is the result of photons transferring momentum to the surface they encounter, and it plays a significant role in various astrophysical processes, including the dynamics of the early universe and the behavior of cosmic structures.
Photon-baryon fluid: The photon-baryon fluid refers to the state of matter in the early universe where photons (light particles) and baryons (which include protons and neutrons) were tightly coupled due to frequent interactions. This interaction resulted in a homogeneous and isotropic medium that played a crucial role in the dynamics of the universe's expansion and the formation of structures within it.
Power Spectrum Analysis: Power spectrum analysis is a technique used to understand the distribution of power across different frequencies in a signal, allowing researchers to identify the underlying structures and patterns within data. This method is particularly important for analyzing the cosmic microwave background radiation and large-scale structures in the universe, revealing insights about phenomena like baryon acoustic oscillations and galaxy clustering.
Primordial plasma oscillations: Primordial plasma oscillations refer to the oscillatory motion of charged particles in the early universe's hot, dense plasma state, occurring shortly after the Big Bang. These oscillations played a crucial role in shaping the density fluctuations that later evolved into the large-scale structure of the universe. They are directly linked to baryon acoustic oscillations, which left an imprint on the cosmic microwave background radiation and influenced the distribution of galaxies.
Redshift distortions and bias: Redshift distortions and bias refer to the systematic effects in the observed redshift of galaxies due to their peculiar velocities and the large-scale structure of the universe. These distortions can impact our understanding of cosmic structures, influencing how we interpret the distribution and dynamics of galaxies, particularly in relation to baryon acoustic oscillations.
Redshift surveys: Redshift surveys are astronomical studies that measure the redshift of light from galaxies to determine their distance and velocity relative to Earth. By analyzing how light stretches to longer wavelengths as galaxies move away, these surveys help map the large-scale structure of the universe, providing insights into galaxy clusters, voids, baryon acoustic oscillations, and the overall cosmic web.
Sound waves in plasma: Sound waves in plasma are pressure waves that propagate through ionized gases, characterized by their interaction with charged particles. These waves are essential for understanding various astrophysical processes and phenomena, as they provide insights into the behavior of matter under extreme conditions, such as those found in stars and interstellar mediums.
Standard ruler for cosmology: A standard ruler for cosmology is an object of known physical size that can be used to measure cosmic distances by observing the angular size it subtends in the sky. This concept plays a critical role in determining the expansion rate of the universe and helps to understand the underlying geometry of space on cosmic scales.
Standing sound waves: Standing sound waves are a pattern of oscillation that occurs when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. This phenomenon creates fixed points of no displacement, known as nodes, and points of maximum displacement, known as antinodes, resulting in a stationary wave pattern. In the context of baryon acoustic oscillations, standing sound waves play a crucial role in understanding how matter and radiation interacted in the early universe.
Structure Formation: Structure formation refers to the process by which matter in the universe organizes itself into larger structures like galaxies, clusters, and superclusters over time. This process is influenced by the interplay of dark matter, gravity, and baryonic matter, leading to a complex web of cosmic structures we observe today.
Survey volume and completeness: Survey volume refers to the total spatial region from which data about celestial objects is collected, while completeness indicates the extent to which this survey captures all relevant objects within that volume. Together, they play a crucial role in understanding the large-scale structure of the universe and the distribution of galaxies, particularly in relation to baryon acoustic oscillations, which reflect the sound waves from the early universe.
Temperature fluctuations: Temperature fluctuations refer to the small variations in temperature that occur in the universe, particularly during its early stages. These fluctuations can provide insights into the density and distribution of matter, influencing cosmic structures and the formation of galaxies. They are significant in understanding phenomena like baryon acoustic oscillations and the cosmic microwave background radiation.
Two-point correlation function: The two-point correlation function is a statistical tool used in cosmology to quantify the degree of clustering of objects, such as galaxies, in the universe. It measures the probability of finding a pair of objects separated by a specific distance compared to a random distribution, helping to understand the large-scale structure of the universe and the influence of baryon acoustic oscillations.
Wavelength: Wavelength is the distance between successive peaks (or troughs) of a wave, commonly measured in meters. This concept is crucial in understanding various types of waves, including electromagnetic waves, which include visible light, radio waves, and gamma rays. Wavelength plays a significant role in the behavior and properties of these waves, impacting how they interact with matter and are perceived by observers.
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