Glossary

10.3 Large-Scale Structure Formation and Evolution

3 min read•august 9, 2024

The universe's large-scale structure forms a of , , and . This intricate network emerges through , where smaller structures merge into larger ones over time. Understanding this process is crucial for grasping the universe's evolution.

Scientists use various tools to study large-scale structure. The predicts halo distributions, while correlation functions and power spectra measure clustering. provide a cosmic "ruler," helping us gauge the universe's expansion history and composition.

Large-Scale Structure Formation

Cosmic Web and Dark Matter Halos

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  • Cosmic web forms intricate network of filaments, , and voids spanning universe
  • Dark matter halos act as gravitational wells attracting ordinary matter
  • Halos range in size from dwarf galaxies to massive
  • Filaments connect dark matter halos creating cosmic web structure
  • Voids represent vast empty regions between filaments and sheets
  • Sheets form flattened structures where filaments intersect

Hierarchical Clustering Process

  • Hierarchical clustering describes structure formation from small to large scales
  • Process begins with tiny primordial in early universe
  • Smaller structures form first through
  • Larger structures emerge as smaller ones merge and accrete matter over time
  • Galaxy clusters form at intersections of filaments in cosmic web
  • represent largest known structures in universe

Press-Schechter Formalism

  • Press-Schechter formalism provides mathematical framework for structure formation
  • Formalism predicts mass distribution of collapsed objects in universe
  • Assumes initial density fluctuations follow Gaussian distribution
  • Incorporates critical density threshold for gravitational collapse
  • Predicts number density of dark matter halos as function of mass and redshift
  • Formula: n(M,z)=2πρ0Mδcσ(M,z)∣dln⁡σdln⁡M∣exp⁡(−δc22σ2(M,z))n(M,z) = \sqrt{\frac{2}{\pi}} \frac{\rho_0}{M} \frac{\delta_c}{\sigma(M,z)} \left|\frac{d\ln\sigma}{d\ln M}\right| \exp\left(-\frac{\delta_c^2}{2\sigma^2(M,z)}\right)
  • Helps explain observed abundance of galaxies and clusters at different cosmic epochs

Statistical Measures of Structure

Correlation Function Analysis

  • measures clustering strength of cosmic structures
  • Two-point correlation function quantifies excess probability of finding pairs of objects
  • Function depends on separation distance between objects
  • Stronger correlations indicate more clustered distribution
  • Weaker correlations suggest more uniform distribution
  • Correlation function typically follows power law: ξ(r)=(rr0)−γ\xi(r) = \left(\frac{r}{r_0}\right)^{-\gamma}
  • Correlation length r0r_0 represents scale at which clustering becomes significant

Power Spectrum and Fourier Analysis

  • describes distribution of matter on different scales in Fourier space
  • Fourier transform of correlation function yields power spectrum
  • Power spectrum quantifies amplitude of density fluctuations as function of wavelength
  • Shape of power spectrum reveals information about early universe and structure formation
  • CDM model predicts specific shape for matter power spectrum
  • Observational data from galaxy surveys used to measure power spectrum

Baryon Acoustic Oscillations

  • Baryon acoustic oscillations (BAO) result from sound waves in early universe plasma
  • BAOs create characteristic scale in matter distribution (~150 Mpc)
  • Oscillations leave imprint in and large-scale structure
  • BAO scale serves as "standard ruler" for cosmological distance measurements
  • Detected as subtle peak in galaxy correlation function
  • BAO measurements constrain cosmological parameters (dark energy equation of state)
  • Provide independent method for measuring expansion history of universe

Observational Probes

Redshift Surveys and Galaxy Mapping

  • map three-dimensional distribution of galaxies in universe
  • Measure galaxy positions and redshifts to create 3D maps of large-scale structure
  • Notable surveys include 2dF Galaxy Redshift Survey and Sloan Digital Sky Survey
  • Surveys reveal filamentary structure of cosmic web
  • Allow measurement of galaxy clustering statistics (correlation function, power spectrum)
  • Deeper surveys probe structure formation at earlier cosmic epochs
  • Redshift space distortions in galaxy maps provide information on peculiar velocities

Biased Galaxy Formation and Tracer Populations

  • describes preferential formation of galaxies in dense regions
  • Galaxy bias quantifies relationship between galaxy distribution and underlying dark matter
  • Different types of galaxies exhibit varying degrees of bias
  • Massive galaxies tend to be more strongly biased tracers of dark matter
  • Bias complicates interpretation of galaxy clustering measurements
  • (HOD) models describe how galaxies populate dark matter halos
  • Understanding bias crucial for using galaxies as tracers of large-scale structure
  • Weak lensing surveys provide unbiased probe of total matter distribution

Key Terms to Review (20)

Baryon Acoustic Oscillations: Baryon acoustic oscillations are periodic fluctuations in the density of visible baryonic matter (normal matter) of the universe, which result from sound waves propagating through the hot plasma of the early universe. These oscillations are critical for understanding the large-scale structure of the cosmos, influencing the formation of galaxies and clusters, and providing insights into cosmic evolution and the expansion of the universe.
Biased galaxy formation: Biased galaxy formation refers to the process whereby galaxies form in regions of higher density in the universe, influenced by gravitational effects. This phenomenon occurs because matter is not evenly distributed; rather, it tends to clump together, leading to the formation of structures like galaxies in areas with more mass concentration. This bias impacts the large-scale structure of the universe and helps to explain the distribution and evolution of galaxies over cosmic time.
Correlation function: The correlation function is a statistical tool used to describe how the density of objects, like galaxies or matter, is distributed in relation to one another over a certain distance. It quantifies the degree of clustering by comparing the likelihood of finding pairs of objects separated by a given distance. This concept plays a crucial role in understanding the large-scale structure of the universe and the patterns formed by baryon acoustic oscillations.
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 infant cosmos about 380,000 years after the event. This faint glow of microwave radiation is crucial for understanding the early universe's conditions, the formation of cosmic structures, and the overall evolution of the cosmos.
Cosmic web: The cosmic web is the large-scale structure of the universe, characterized by a vast network of filaments composed of dark matter and galaxies that interconnect and surround enormous voids. This structure illustrates how matter is distributed in the universe, revealing the underlying gravitational forces and cosmic evolution over time.
Dark matter halos: Dark matter halos are vast, roughly spherical regions surrounding galaxies, composed primarily of dark matter that does not emit or absorb light. These halos play a crucial role in the structure and formation of galaxies, as they provide the necessary gravitational influence to hold galaxies together and facilitate their growth over time.
Density fluctuations: Density fluctuations refer to the small variations in the distribution of matter in the universe, which play a crucial role in the formation of cosmic structures like galaxies and galaxy clusters. These fluctuations arise from quantum fluctuations in the early universe, leading to gravitational instabilities that amplify over time, causing matter to clump together and form larger structures. Understanding density fluctuations is key to explaining how the large-scale structure of the universe has evolved.
Filaments: Filaments are elongated structures in the universe that form a part of the cosmic web, connecting galaxies and clusters of galaxies. These structures are crucial in understanding the large-scale distribution of matter in the universe and play a vital role in galaxy formation and evolution, influencing how matter is accumulated and structured on cosmic scales.
Galaxy clusters: Galaxy clusters are large groups of galaxies held together by gravity, consisting of hundreds to thousands of individual galaxies, along with dark matter and hot gas. These clusters serve as important laboratories for studying galaxy formation and evolution, revealing the effects of feedback mechanisms on their development, the role they play in large-scale structure formation, and how they fit into the cosmic web.
Galaxy mapping: Galaxy mapping refers to the process of charting and analyzing the distribution, structure, and characteristics of galaxies within the universe. This technique is essential for understanding the large-scale structure of the cosmos, as it provides insights into how galaxies are organized, how they evolve over time, and their interactions with one another in a gravitationally bound framework.
Gravitational Collapse: Gravitational collapse is the process by which an astronomical object loses its structural integrity due to the gravitational forces overwhelming other forces, causing it to contract under its own gravity. This phenomenon is fundamental in the formation of stars and galaxies, as it leads to the birth of new stellar objects from dense regions of molecular clouds and plays a crucial role in the evolution of large-scale structures in the universe.
Halo Occupation Distribution: Halo occupation distribution refers to the statistical framework that describes how galaxies are distributed within dark matter halos. This concept connects the properties of galaxies to their environment, specifically how likely a halo of a certain mass is to host one or more galaxies. By understanding these distributions, we can gain insights into large-scale structure formation and evolution, revealing how galaxies interact with dark matter and influence cosmic structures over time.
Hierarchical Clustering: Hierarchical clustering is a method of cluster analysis that seeks to build a hierarchy of clusters based on the similarity of their properties. This technique is particularly useful in understanding how different groups, such as galaxy clusters, are structured and how they evolve over time. By organizing data into nested groups, it allows for a better visualization of relationships and the dynamics that govern galaxy formation and interactions.
Power Spectrum: The power spectrum is a representation of the distribution of power or variance of a signal or field across different frequencies or scales. It plays a crucial role in understanding cosmic structures and phenomena, as it helps to quantify the fluctuations in density and temperature within the universe, revealing important insights about its evolution, acoustic oscillations, and background radiation patterns.
Press-Schechter Formalism: The Press-Schechter formalism is a theoretical framework used in cosmology to describe the mass distribution of dark matter halos formed from the gravitational collapse of density fluctuations in the early universe. This approach connects the statistical properties of initial density fields to the distribution of structures, allowing researchers to estimate the number density of halos as a function of mass and redshift, which is crucial for understanding large-scale structure formation and evolution.
Redshift Surveys: Redshift surveys are observational studies that measure the redshift of light from distant galaxies, allowing astronomers to determine their distances and map the large-scale structure of the universe. These surveys help reveal the distribution of galaxies, the evolution of cosmic structures over time, and the overall geometry of the universe, contributing to our understanding of its expansion and the cosmic web.
Sheets: In astrophysics, sheets refer to large, flat structures formed by the gravitational attraction of dark matter and baryonic matter in the universe. These sheets are part of the cosmic web, a vast network of filaments and voids that make up the large-scale structure of the universe. Sheets often contain galaxies and clusters, and their formation is a crucial aspect of understanding how structures evolve over time.
Superclusters: Superclusters are massive groups of galaxies that are bound together by gravity, forming some of the largest known structures in the universe. These enormous cosmic structures consist of numerous clusters and groups of galaxies and can span hundreds of millions of light-years across. Superclusters play a significant role in understanding the large-scale structure and evolution of the universe, as they provide insights into how galaxies and matter are distributed on a grand scale.
Tracer populations: Tracer populations refer to specific groups of astronomical objects used to trace the underlying mass distribution in the universe, particularly in studies of large-scale structure formation and evolution. These populations include galaxies, galaxy clusters, and other celestial objects that help astronomers understand the distribution of dark matter and the overall gravitational influence within cosmic structures. By analyzing the dynamics and distribution of these tracers, researchers can infer the complex interactions that shape the cosmos over time.
Voids: Voids are large, nearly empty regions in the universe that contain very few galaxies and other matter, contrasting with the denser areas filled with galaxy clusters and filaments. These cosmic voids play a crucial role in understanding the large-scale structure of the universe and the distribution of matter, shedding light on cosmic evolution and the formation of high-redshift galaxies.
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