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