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Cosmology & The Big Bang Cheat Sheet
A printable reference covering Hubble's law, redshift, cosmic expansion, the Big Bang timeline, CMB, and critical density for grades 10-12.
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Cosmology is the study of the universe as a whole, including its origin, structure, expansion, and possible future. The Big Bang model explains how the universe evolved from an extremely hot, dense early state into the galaxies and large-scale structures seen today. Students need this cheat sheet to connect observations, such as galaxy redshift and the cosmic microwave background, to the scientific model of an expanding universe. The most important ideas are that space itself expands, distant galaxies generally recede faster, and light from the early universe has been stretched over time. Hubble's law, v = H0 d, links recession speed to distance and provides evidence for expansion. Redshift, z = (lambda_obs - lambda_rest) / lambda_rest, measures how much light has been stretched. The Big Bang timeline includes inflation, particle formation, nucleosynthesis, recombination, the cosmic microwave background, star formation, galaxies, and continued expansion.
Key Facts
- Hubble's law is v = H0 d, where v is recession speed, H0 is the Hubble constant, and d is distance.
- For small redshifts, recession speed can be estimated with v = cz, where c is the speed of light and z is redshift.
- Redshift is calculated by z = (lambda_obs - lambda_rest) / lambda_rest, where lambda_obs is observed wavelength and lambda_rest is emitted wavelength.
- Cosmic expansion means the scale of space increases over time, so distant galaxies are not moving through space as much as space between galaxies is stretching.
- The scale factor relation is 1 + z = a_now / a_then, so higher redshift means the light was emitted when the universe was smaller.
- The cosmic microwave background is leftover radiation from about 380,000 years after the Big Bang, when atoms first formed and light could travel freely.
- Critical density is rho_c = 3H0^2 / (8 pi G), and it helps determine whether the universe is flat, open, or closed.
- The approximate age of the universe can be estimated from t approx 1 / H0, but the exact age depends on matter, radiation, dark matter, and dark energy.
Vocabulary
- Cosmology
- The scientific study of the origin, structure, evolution, and large-scale behavior of the universe.
- Big Bang
- The model that the universe began in a hot, dense state and has expanded and cooled over time.
- Redshift
- The stretching of light to longer wavelengths, often showing that a galaxy's light has been stretched by cosmic expansion.
- Hubble Constant
- The current rate of cosmic expansion, usually written as H0 and measured in kilometers per second per megaparsec.
- Cosmic Microwave Background
- Faint microwave radiation left over from the early universe that is observed in nearly every direction in space.
- Dark Energy
- A form of energy associated with the accelerated expansion of the universe.
Common Mistakes to Avoid
- Treating the Big Bang as an explosion into empty space is wrong because the model describes the expansion of space itself, not matter flying outward from a central point.
- Using Hubble's law for nearby objects inside the Milky Way is wrong because local gravity dominates over cosmic expansion at small scales.
- Forgetting units in H0 is wrong because H0 is commonly measured in km/s/Mpc, so distance must be in megaparsecs to get speed in km/s.
- Assuming redshift is always caused only by motion is wrong because cosmological redshift mainly comes from the stretching of space during the light's travel time.
- Thinking the cosmic microwave background comes from stars is wrong because it is ancient radiation from the early universe, released before stars and galaxies formed.
Practice Questions
- 1 A galaxy is 200 Mpc away. Using H0 = 70 km/s/Mpc, calculate its recession speed with v = H0 d.
- 2 A spectral line has a rest wavelength of 500 nm and is observed at 550 nm. Calculate the redshift using z = (lambda_obs - lambda_rest) / lambda_rest.
- 3 Using v approx cz and c = 300,000 km/s, estimate the recession speed of a galaxy with z = 0.03.
- 4 Explain why both galaxy redshift and the cosmic microwave background support the Big Bang model rather than a static universe.