26.5 The Expanding Universe

The expanding universe revolutionized our cosmic understanding. Hubble's groundbreaking discovery, using the Hooker telescope, revealed a correlation between galaxy distances and redshifts. This led to Hubble's law, now known as the Hubble-Lemaître law, providing evidence for cosmic expansion.

Hubble's law helps calculate galaxy distances and defines the Hubble constant, representing the universe's expansion rate. Different models explain this expansion, from critical density to accelerating expansion. Variations in the Hubble constant arise from measurement techniques, errors, and local variations, shaping our evolving cosmic perspective.

Discovery and Implications of the Expanding Universe

Hubble's universe expansion discovery

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Top images from around the web for Hubble's universe expansion discovery

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• Used 100-inch Hooker telescope at Mount Wilson Observatory observed distant galaxies
  • Measured distances using Cepheid variable stars as standard candles (consistent brightness allows distance calculation)
• Measured redshifts of galaxies by analyzing spectra
  • Redshift is shift of spectral lines towards longer wavelengths due to Doppler effect (similar to pitch change of passing ambulance siren)
• Discovered correlation between distances to galaxies and redshifts
  • More distant galaxies exhibited greater redshifts indicating faster recession velocities (Andromeda galaxy, Triangulum galaxy)
• Relationship known as Hubble's law provided evidence for expansion of universe
  • This relationship is now referred to as the Hubble-Lemaître law, acknowledging Georges Lemaître's earlier work

Application of Hubble's law

• Hubble's law states galaxy's recession velocity proportional to distance
  • $v = H_0 \times d$, where $v$ is recession velocity, $d$ is distance, $H_0$ is Hubble constant
• Hubble constant represents current expansion rate of universe
  • Value approximately 70 km/s/Mpc (kilometers per second per megaparsec) (3.26 million light-years)
• Calculating distance to galaxy using Hubble's law:
  1. Measure galaxy's redshift from spectrum
  2. Convert redshift to recession velocity using Doppler shift formula
  3. Divide recession velocity by Hubble constant to obtain distance
• The observed redshift in this context is known as cosmological redshift, distinct from other types of redshift

Models of expanding universe

• Critical density model:
  • Universe has just enough matter to eventually halt expansion
  • Spatially flat and will expand forever but expansion rate will approach zero (like ball rolled uphill)
• Open model:
  • Universe has less than critical density of matter
  • Spatially open (negatively curved) and will expand forever (like saddle shape)
• Closed model:
  • Universe has more than critical density of matter
  • Spatially closed (positively curved) and will eventually collapse in "Big Crunch" (like surface of sphere)
• Accelerating expansion model:
  • Supported by observations of distant supernovae suggesting accelerating expansion
  • Attributed to dark energy, mysterious form of energy permeating space
  • Implies universe will continue expanding at increasing rate leading to "Big Freeze" (like expanding balloon)

Variations in Hubble constant

• Different measurement techniques:
  • Cepheid variable stars and Type Ia supernovae as standard candles (consistent brightness)
  • Gravitational lensing and cosmic microwave background (CMB) radiation (leftover heat from Big Bang)
• Systematic errors in distance measurements:
  • Calibration uncertainties in cosmic distance ladder (errors compound at large distances)
  • Difficulties accurately determining distances to distant galaxies
• Local variations in expansion rate:
  • Presence of large-scale structures like galaxy clusters can affect local measurements (gravitational attraction)
  • Hubble constant may vary depending on direction and scale of observations
• Differences in assumed cosmological model:
  • Choice of cosmological parameters such as matter density and dark energy can influence derived value of Hubble constant (assumptions built into calculations)

Fundamental concepts in cosmology

• Cosmological principle: The universe is homogeneous and isotropic on large scales
• Friedmann equations: Describe the expansion of space in homogeneous and isotropic models of the universe
• Scale factor: A parameter that represents the relative expansion of the universe
• Cosmic inflation: A theory proposing that the early universe underwent a period of rapid exponential expansion