⚛️Particle Physics Unit 12 – Cosmology and Dark Matter

Key Concepts in Cosmology

• Cosmology studies the origin, evolution, and ultimate fate of the universe on the largest scales
• Hubble's law describes the expansion of the universe where galaxies are moving away from each other with velocities proportional to their distances ($v = H_0 d$)
• The cosmological principle states that the universe is homogeneous (uniform density) and isotropic (looks the same in all directions) on large scales
• The cosmic microwave background (CMB) is the leftover radiation from the early universe, providing strong evidence for the Big Bang theory
• Dark matter and dark energy are the dominant components of the universe, with dark matter making up ~27% and dark energy ~68% of the total energy density
  • Baryonic matter (ordinary matter) only accounts for ~5% of the universe's energy density
• The fate of the universe depends on the total energy density and the equation of state of its components (matter, radiation, and dark energy)

The Big Bang Theory

• The Big Bang theory proposes that the universe began as a singularity around 13.8 billion years ago and has been expanding ever since
• The early universe was extremely hot and dense, allowing for the creation of fundamental particles and the formation of light elements (hydrogen, helium, and trace amounts of lithium)
• The universe underwent a rapid exponential expansion called cosmic inflation, which solved several problems in cosmology (horizon problem, flatness problem, and magnetic monopole problem)
• As the universe expanded and cooled, particles combined to form neutral atoms in a process called recombination, which occurred around 380,000 years after the Big Bang
• The cosmic microwave background radiation was emitted during recombination and has been traveling through the universe ever since
• The Big Bang theory is supported by three key observations:
  • Hubble's law and the expansion of the universe
  • The abundance of light elements in the universe
  • The existence and properties of the cosmic microwave background radiation

Evolution of the Universe

• The evolution of the universe can be divided into several distinct eras based on the dominant form of energy or matter
• The Planck era (0 to 10^-43 seconds) is the earliest stage of the universe, where quantum gravity effects were significant, but a complete theory of quantum gravity is still lacking
• The inflationary epoch (10^-36 to 10^-32 seconds) is characterized by the rapid exponential expansion of the universe, driven by a hypothetical scalar field called the inflaton
• The quark epoch (10^-12 to 10^-6 seconds) is when quarks, gluons, and other fundamental particles were created, but the temperature was too high for them to form hadrons
• The hadron epoch (10^-6 to 1 second) is when the universe cooled enough for quarks to combine and form hadrons, including protons and neutrons
• The lepton epoch (1 to 10 seconds) is when leptons (electrons, positrons, neutrinos) dominated the universe's energy density
• The photon epoch (10 seconds to 380,000 years) is when photons were the dominant form of energy, and light elements were formed through Big Bang nucleosynthesis
• The matter-dominated era (380,000 years to ~9.8 billion years) is when matter (both baryonic and dark matter) dominated the energy density of the universe
• The dark energy-dominated era (~ 9.8 billion years to present) is the current era, where dark energy is the dominant component, causing the expansion of the universe to accelerate

Structure Formation

• Structure formation refers to the process by which galaxies, clusters, and large-scale structures in the universe formed from initial density fluctuations
• Quantum fluctuations during the inflationary epoch created tiny density perturbations in the early universe, which served as the seeds for structure formation
• Dark matter played a crucial role in structure formation, as its gravitational effects allowed for the growth of density perturbations
  • Baryonic matter could not form structures on its own due to the high pressure of the photon-baryon fluid in the early universe
• The process of structure formation can be divided into two main stages: linear growth and nonlinear evolution
• During the linear growth stage, density perturbations grow proportionally to the scale factor of the universe, and their evolution can be described using linear perturbation theory
• As density perturbations become larger, they enter the nonlinear regime, where gravitational collapse leads to the formation of dark matter halos
• Baryonic matter falls into the gravitational potential wells created by dark matter halos, leading to the formation of galaxies and clusters
• The large-scale structure of the universe is characterized by a cosmic web, consisting of filaments, walls, and voids
  • Galaxy clusters are found at the intersections of filaments, while voids are large regions with a lower density of galaxies

Dark Matter: Evidence and Observations

• Dark matter is a hypothetical form of matter that does not interact electromagnetically, making it invisible to direct observation
• The existence of dark matter is inferred from its gravitational effects on visible matter, radiation, and the structure of the universe
• Velocity dispersion in galaxies and galaxy clusters: Stars and galaxies move faster than can be explained by the visible matter alone, suggesting the presence of additional unseen mass (dark matter)
• Rotation curves of galaxies: The orbital speeds of stars and gas in galaxies remain constant or increase with distance from the galactic center, contrary to expectations based on visible matter
• Gravitational lensing: Massive objects (such as galaxies and clusters) can bend the path of light from distant sources, creating distortions and multiple images
  • The strength of gravitational lensing depends on the total mass of the object, including both visible and dark matter
• Bullet Cluster: A collision between two galaxy clusters where the hot gas (visible matter) is slowed down, but the dark matter passes through, creating a separation between the two components
• Cosmic microwave background anisotropies: The CMB temperature fluctuations are consistent with a universe composed of ~27% dark matter, which influences the growth of structure
• Large-scale structure formation: Simulations of structure formation in the universe require the presence of dark matter to match observations of the cosmic web and galaxy distribution

Candidates for Dark Matter

• Dark matter candidates are hypothetical particles that could explain the observed gravitational effects while remaining elusive to direct detection
• Weakly Interacting Massive Particles (WIMPs) are a popular class of dark matter candidates that have masses in the GeV to TeV range and interact via the weak force
  • WIMPs naturally arise in theories beyond the Standard Model, such as supersymmetry (SUSY) and extra dimensions
  • Examples of WIMP candidates include the neutralino (the lightest stable SUSY particle) and the Kaluza-Klein photon (from extra dimensions)
• Axions are ultralight particles (mass range: 10^-6 to 10^-3 eV) that were originally proposed to solve the strong CP problem in quantum chromodynamics (QCD)
  • Axions can be produced non-thermally in the early universe and can make up a significant fraction of dark matter
• Sterile neutrinos are hypothetical neutrinos that do not interact via the weak force but mix with the known neutrino flavors (electron, muon, and tau neutrinos)
  • Sterile neutrinos with keV-scale masses could be a viable dark matter candidate, produced through oscillations with active neutrinos in the early universe
• Primordial black holes are black holes that formed in the early universe from density fluctuations or phase transitions
  • Primordial black holes with masses ranging from 10^-8 to 10^5 solar masses could contribute to the dark matter density
• Modified gravity theories propose that the observed gravitational effects attributed to dark matter could be explained by modifying the laws of gravity on large scales
  • Examples include Modified Newtonian Dynamics (MOND) and Tensor-Vector-Scalar gravity (TeVeS)

Detection Methods for Dark Matter

• Direct detection experiments aim to measure the rare interactions between dark matter particles and target nuclei in terrestrial detectors
  • These experiments typically use large, ultra-pure crystals (such as germanium or xenon) cooled to cryogenic temperatures to minimize background noise
  • Examples of direct detection experiments include XENON, LUX, and SuperCDMS
• Indirect detection experiments search for the products of dark matter annihilation or decay, such as gamma rays, neutrinos, and cosmic rays
  • Gamma-ray telescopes (Fermi-LAT, HESS, MAGIC) look for excess gamma-ray emission from regions with high dark matter density, such as the Galactic Center or dwarf spheroidal galaxies
  • Neutrino telescopes (IceCube, ANTARES) search for high-energy neutrinos produced by dark matter annihilation in the Sun or Earth's core
• Collider searches aim to produce dark matter particles in high-energy particle collisions, such as those at the Large Hadron Collider (LHC)
  • Dark matter particles would manifest as missing energy and momentum in the collision products, as they escape the detector without interacting
  • Collider searches can constrain the properties of dark matter particles and their interactions with Standard Model particles
• Astrophysical probes can provide indirect evidence for dark matter and constrain its properties
  • The cosmic microwave background anisotropies are sensitive to the dark matter density and its interaction with baryonic matter in the early universe
  • The Lyman-alpha forest (absorption lines in the spectra of distant quasars) can constrain the small-scale structure of dark matter and its thermal properties
• Complementarity between different detection methods is essential to confirm the existence of dark matter and determine its properties
  • A consistent signal across multiple experiments would provide strong evidence for the discovery of dark matter

Cosmological Models and Dark Matter

• Cosmological models describe the evolution and composition of the universe based on the equations of general relativity and observational data
• The Lambda Cold Dark Matter (ΛCDM) model is the current standard model of cosmology, which includes dark energy (Λ) and cold dark matter (CDM) as its main components
  • Cold dark matter refers to dark matter particles that were non-relativistic (slow-moving) at the time of structure formation, allowing for the efficient growth of density perturbations
• The ΛCDM model successfully explains a wide range of cosmological observations, including:
  • The expansion rate of the universe (Hubble's law)
  • The abundance of light elements (Big Bang nucleosynthesis)
  • The cosmic microwave background anisotropies
  • The large-scale structure of the universe (galaxy distribution and clustering)
• Alternative dark matter models, such as warm dark matter (WDM) and self-interacting dark matter (SIDM), have been proposed to address potential challenges to the ΛCDM model on small scales
  • WDM particles have higher velocities than CDM, which can suppress the formation of small-scale structures and alleviate the "missing satellites" problem
  • SIDM allows for dark matter particles to interact with each other, potentially resolving discrepancies between observations and simulations of dark matter halos (the "cusp-core" problem)
• The nature of dark energy is a major open question in cosmology, with possible explanations including a cosmological constant, a dynamical scalar field (quintessence), or modifications to general relativity
• The equation of state parameter (w) describes the relationship between the pressure and energy density of dark energy, with w = -1 corresponding to a cosmological constant
• Future cosmological observations, such as those from the Euclid mission, the Vera C. Rubin Observatory (LSST), and the James Webb Space Telescope (JWST), will provide more precise measurements of the properties of dark matter and dark energy
  • These observations will help to distinguish between different cosmological models and shed light on the nature of the dark components of the universe