🌠Astrophysics I Unit 14 – Dark Matter and Dark Energy

What's the Big Deal?

• Dark matter and dark energy make up ~95% of the universe's total mass-energy content
• Visible matter accounts for only ~5%, matter we are familiar with (includes protons, neutrons, and electrons)
• Dark matter influences the motion of galaxies and galaxy clusters through its gravitational effects
  • Explains the observed rotational curves of galaxies (Milky Way)
  • Accounts for the gravitational lensing observed around massive galaxy clusters (Bullet Cluster)
• Dark energy drives the accelerating expansion of the universe
  • Responsible for the observed redshift of distant galaxies (Type Ia supernovae)
  • Impacts the geometry and ultimate fate of the universe (flat, open, or closed)
• Understanding dark matter and dark energy is crucial for developing a complete picture of the universe's composition, structure, and evolution

Key Concepts and Definitions

• Dark matter: A hypothetical form of matter that does not interact with electromagnetic radiation (light) but has gravitational effects
  • Contributes to the "missing mass" in galaxies and galaxy clusters
  • Candidates include weakly interacting massive particles (WIMPs), axions, and sterile neutrinos
• Dark energy: A hypothetical form of energy that permeates all of space and drives the accelerating expansion of the universe
  • Behaves like a cosmological constant ($\Lambda$) in Einstein's field equations
  • Can be described by a negative pressure or a positive energy density
• Cosmological constant ($\Lambda$): A term in Einstein's field equations that represents a constant energy density of the vacuum of space
• Weakly interacting massive particles (WIMPs): A class of hypothetical particles that are a prime candidate for dark matter
  • Interact through the weak nuclear force and gravity
  • Have masses ranging from a few GeV to several TeV
• Modified Newtonian dynamics (MOND): An alternative theory to dark matter that proposes a modification to Newton's laws of motion at low accelerations
• Cosmic microwave background (CMB): The leftover radiation from the early universe, providing a snapshot of the universe ~380,000 years after the Big Bang

Historical Background

• 1933: Fritz Zwicky infers the existence of "dark matter" to explain the motion of galaxies in the Coma Cluster
• 1970s: Vera Rubin and Kent Ford measure the rotational curves of galaxies, finding evidence for dark matter
  • Observed that the rotational velocities of stars and gas in galaxies remain constant with increasing distance from the galactic center
  • Contradicts the expected Keplerian decline based on visible matter alone
• 1998: Two independent teams (led by Saul Perlmutter, Brian Schmidt, and Adam Riess) discover the accelerating expansion of the universe using Type Ia supernovae
  • Awarded the 2011 Nobel Prize in Physics for their discovery
• 2006: NASA's Wilkinson Microwave Anisotropy Probe (WMAP) measures the cosmic microwave background, providing evidence for dark matter and dark energy
  • Determines that the universe is composed of ~4.6% ordinary matter, ~24% dark matter, and ~71.4% dark energy
• 2013: The Planck satellite refines the measurements of the cosmic microwave background, updating the composition of the universe
  • ~4.9% ordinary matter, ~26.8% dark matter, and ~68.3% dark energy

Observational Evidence

• Galactic rotation curves: The flat rotation curves of galaxies suggest the presence of a dark matter halo
  • Visible matter alone cannot account for the observed rotational velocities at large distances from the galactic center
  • Dark matter provides the additional gravitational pull needed to explain the flat rotation curves
• Gravitational lensing: Massive objects (galaxies, galaxy clusters) bend the path of light from distant sources, acting as gravitational lenses
  • The amount of lensing observed is greater than that expected from visible matter alone
  • Dark matter's gravitational effects account for the additional lensing (strong lensing arcs, weak lensing distortions)
• Cosmic microwave background (CMB): The CMB power spectrum is sensitive to the amount of dark matter and dark energy in the universe
  • The relative heights of the acoustic peaks in the CMB power spectrum indicate the proportions of ordinary matter, dark matter, and dark energy
  • The CMB provides a snapshot of the universe ~380,000 years after the Big Bang, supporting the existence of dark matter and dark energy
• Baryon acoustic oscillations (BAO): The clustering of galaxies on large scales is influenced by the interplay between dark matter and ordinary matter in the early universe
  • The BAO scale acts as a "standard ruler," allowing the expansion history of the universe to be measured
  • The observed BAO scale is consistent with the presence of dark energy driving the accelerating expansion of the universe

Theoretical Models

• Cold dark matter (CDM): A model in which dark matter consists of non-relativistic, weakly interacting particles
  • CDM particles have low thermal velocities and form hierarchical structures (halos) through gravitational collapse
  • The CDM model successfully explains the large-scale structure of the universe (cosmic web)
• Warm dark matter (WDM): A model in which dark matter consists of particles with higher thermal velocities than CDM
  • WDM particles have larger free-streaming lengths, suppressing the formation of small-scale structures
  • The WDM model may resolve some discrepancies between CDM simulations and observations on small scales (missing satellites problem)
• Modified Newtonian dynamics (MOND): An alternative theory to dark matter that proposes a modification to Newton's laws of motion at low accelerations
  • MOND aims to explain the flat rotation curves of galaxies without invoking dark matter
  • Challenges for MOND include explaining the Bullet Cluster and the CMB power spectrum
• $\Lambda$CDM model: The standard cosmological model that includes cold dark matter (CDM) and a cosmological constant ($\Lambda$) representing dark energy
  • The $\Lambda$CDM model is consistent with a wide range of observational data (CMB, BAO, Type Ia supernovae)
  • The model describes a universe that is flat, homogeneous, and isotropic on large scales

Current Research and Experiments

• Direct detection experiments: Aim to detect dark matter particles through their interactions with ordinary matter
  • Examples include XENON, LUX, and SuperCDMS
  • These experiments search for rare collisions between dark matter particles and atomic nuclei in ultra-sensitive detectors
• Indirect detection experiments: Search for the products of dark matter annihilation or decay
  • Examples include the Fermi Gamma-ray Space Telescope, IceCube, and AMS-02
  • These experiments look for excess gamma rays, neutrinos, or antimatter that could be produced by dark matter interactions
• Particle collider searches: Attempt to produce and detect dark matter particles in high-energy collisions
  • The Large Hadron Collider (LHC) searches for dark matter in proton-proton collisions
  • Dark matter particles would manifest as missing energy in the collision products
• Surveys and telescopes: Map the distribution of dark matter and measure the expansion history of the universe
  • Examples include the Dark Energy Survey (DES), the Hyper Suprime-Cam (HSC) survey, and the Dark Energy Spectroscopic Instrument (DESI)
  • These surveys aim to constrain the properties of dark energy and test modified gravity theories

Implications for the Universe

• Structure formation: Dark matter plays a crucial role in the formation and evolution of cosmic structures
  • Dark matter halos serve as the scaffolding for the formation of galaxies and galaxy clusters
  • The interplay between dark matter and ordinary matter shapes the cosmic web (filaments, voids)
• Cosmic expansion: Dark energy drives the accelerating expansion of the universe
  • The fate of the universe depends on the nature of dark energy (cosmological constant, evolving scalar field)
  • A cosmological constant leads to an eternally expanding universe, while evolving dark energy models can result in different scenarios (Big Rip, Big Freeze)
• Cosmological parameters: The properties of dark matter and dark energy influence key cosmological parameters
  • The matter density parameter ($\Omega_m$) and the dark energy density parameter ($\Omega_\Lambda$) determine the geometry and evolution of the universe
  • Precise measurements of these parameters can constrain the nature of dark matter and dark energy
• Modified gravity: The observed effects attributed to dark matter and dark energy could potentially be explained by modifications to Einstein's theory of general relativity
  • Examples include $f(R)$ gravity, scalar-tensor theories, and brane-world models
  • Modified gravity theories aim to provide a unified description of dark matter and dark energy without invoking new forms of matter or energy

Unanswered Questions and Future Directions

• Nature of dark matter: The particle nature of dark matter remains unknown
  • Is dark matter a single particle species or a combination of different types?
  • What are the properties of dark matter particles (mass, interaction cross-section)?
• Nature of dark energy: The physical origin and properties of dark energy are not well understood
  • Is dark energy a cosmological constant, an evolving scalar field, or a manifestation of modified gravity?
  • How does the equation of state of dark energy evolve with time?
• Small-scale discrepancies: There are tensions between CDM simulations and observations on small scales
  • The missing satellites problem refers to the discrepancy between the predicted and observed number of satellite galaxies around the Milky Way
  • The core-cusp problem relates to the difference between the predicted cuspy dark matter density profiles and the observed cored profiles in dwarf galaxies
• Baryon-dark matter interactions: The possibility of non-gravitational interactions between dark matter and ordinary matter is an active area of research
  • Such interactions could affect the distribution of dark matter in galaxies and galaxy clusters
  • Constraints from observations and experiments can help probe the nature of baryon-dark matter interactions
• Future experiments and observatories: Upcoming projects will provide new insights into dark matter and dark energy
  • The Vera C. Rubin Observatory (LSST) will conduct a deep, wide-field survey of the sky, mapping the distribution of dark matter through gravitational lensing
  • The Euclid mission and the Nancy Grace Roman Space Telescope (WFIRST) will study the expansion history of the universe and the growth of cosmic structures, constraining the properties of dark energy
  • Next-generation direct detection experiments (XENONnT, LUX-ZEPLIN, DARWIN) will push the sensitivity limits for detecting dark matter particles