12.3 Hubble's Law and Expansion of the Universe

Hubble's Law explains how galaxies move away from us faster the farther they are. This key discovery revealed our universe is expanding, challenging old ideas about a static cosmos and supporting the Big Bang theory.

Measuring cosmic expansion helps us understand the universe's age, structure, and future. It's a cornerstone of modern cosmology, shaping our view of space, time, and our place in the cosmos.

Hubble's Law and Cosmic Expansion

Hubble's Law and the Expansion Rate

• Hubble's law describes the relationship between a galaxy's recessional velocity and its distance from Earth expressed mathematically as $v = H₀d$
  • v represents the recessional velocity
  • d represents the distance
  • H₀ represents the Hubble constant
• Hubble constant (H₀) measures the current expansion rate of the universe in kilometers per second per megaparsec (km/s/Mpc)
• Hubble's law implies uniform expansion of the universe in all directions with more distant galaxies moving away faster
• Suggests universe originated from a single point supporting the Big Bang theory (cosmic inflation)
• Allows estimation of the universe's age by extrapolating expansion rate backwards in time
• Breaks down at very large distances due to dark energy effects causing accelerated expansion

Implications for Cosmic History and Structure

• Necessitates a finite age for the universe leading to the concept of cosmic time
• Implies hotter and denser past supporting the hot Big Bang model and its early universe predictions
• Affects future evolution of the universe with different scenarios depending on dark energy nature and space geometry (Big Freeze, Big Rip, Big Crunch)
• Challenges steady-state theory and alternative cosmologies not accounting for observed expansion
• Introduces concept of cosmic inflation rapid expansion period in early universe resolving standard Big Bang model issues (horizon problem, flatness problem)

Redshift and the Expanding Universe

Understanding Redshift in Cosmology

• Redshift increases wavelength (decreases frequency) of electromagnetic radiation from source moving away from observer
• Cosmological redshift caused by expansion of space itself stretching light wavelengths as it travels
• Directly related to recessional velocity of distant galaxies described by Doppler effect for light
• Redshift parameter z defined as fractional change in wavelength $z = \frac{\Delta\lambda}{\lambda}$
• Higher redshift values correspond to greater distances and earlier times in universe history
• Relationship between redshift and distance linear for nearby galaxies non-linear for very distant objects due to changing expansion rate

Redshift as a Cosmic Measurement Tool

• Allows astronomers to study evolution of cosmos through observation of distant objects
• Used to determine distances to galaxies and quasars (Lyman-alpha forest)
• Helps measure large-scale structure of universe (galaxy clusters, cosmic web)
• Enables study of early universe through observation of high-redshift objects (first stars, galaxies)
• Provides information on chemical composition and physical properties of distant celestial bodies
• Crucial for understanding dark energy effects on cosmic expansion (Type Ia supernovae observations)

Evidence for Cosmic Expansion

Observational Evidence Supporting Expansion

• Edwin Hubble's original observations of Cepheid variables in distant galaxies provided first expansion evidence
• Consistent redshift in spectra of distant galaxies with more distant galaxies showing greater redshift
• Discovery and measurement of cosmic microwave background radiation (CMB) supports Big Bang theory and expanding universe model
• Observed abundance of light elements (hydrogen, helium, lithium) matches Big Bang nucleosynthesis predictions in expanding universe
• Large-scale structure observations (galaxy clusters, superclusters) consistent with structure formation models in expanding universe
• Gravitational lensing observations of distant quasars and galaxies provide independent expansion confirmation and cosmological parameter constraints

Additional Supporting Evidence

• Baryon acoustic oscillations (BAO) measurements in galaxy distribution confirm expansion history
• Time dilation effects observed in Type Ia supernovae light curves consistent with cosmic expansion
• Lyman-alpha forest observations in quasar spectra trace expansion history of intergalactic medium
• Integrated Sachs-Wolfe effect detection in CMB-galaxy cross-correlation supports late-time cosmic acceleration
• X-ray observations of galaxy clusters provide independent evidence for expansion through Sunyaev-Zeldovich effect
• Weak gravitational lensing surveys map dark matter distribution consistent with expanding universe models

Implications of an Expanding Universe

Cosmological Model Implications

• Expanding universe model necessitates finite age for universe leading to cosmic time concept
• Expansion affects future evolution of universe with different scenarios (heat death, Big Freeze, Big Rip)
• Discovery of accelerating expansion led to introduction of dark energy in cosmological models
• Challenges alternative cosmologies not accounting for observed expansion (steady-state theory)
• Supports inflationary universe models explaining uniformity and flatness of observed cosmos
• Provides framework for understanding formation and evolution of cosmic structures (galaxies, clusters)

Philosophical and Practical Implications

• Expands our understanding of universe's origin and potential future (Big Bang, cosmic inflation)
• Raises questions about the nature of time and space in an expanding cosmos
• Influences development of new observational techniques and technologies (adaptive optics, space telescopes)
• Impacts our view of humanity's place in the universe (Copernican principle, anthropic principle)
• Drives research into fundamental physics (quantum gravity, unification theories)
• Inspires public interest in astronomy and cosmology fostering scientific literacy and exploration