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.
Understanding Cosmology & The Big Bang
Astronomers measure expansion by comparing known spectral lines with the same lines in light from faraway galaxies. Every chemical element absorbs or emits particular wavelengths, making a pattern like a barcode. In a laboratory, hydrogen produces its pattern at fixed wavelengths.
If the pattern from a galaxy appears at longer wavelengths, the source has been redshifted. This measurement is more reliable than judging a galaxy by its color alone.
Dust, temperature, and star populations can change color, while spectral lines give a precise reference. Measurements from many galaxies reveal a consistent relation between distance and redshift.
Distance is one of the hard parts of cosmology. A galaxy can look faint because it is distant, but it can also be faint because it contains fewer bright stars. Astronomers build a distance ladder using objects with known brightness.
Cepheid variable stars change brightness in a predictable way, so they help measure nearby galaxies. Type Ia supernovae have a similar peak brightness, so they can be used much farther away.
Comparing their expected brightness with their observed brightness gives an estimate of distance. These methods helped show that expansion is speeding up, which points to the influence of dark energy.
Looking farther into space means looking farther into the past. Light takes time to travel, so a very distant galaxy is seen as it was billions of years ago. Its redshift tells students more than its speed in a simple approximation.
It tells how much the universe has changed in size while the light was traveling. Very high redshift objects show young galaxies that were smaller, more irregular, and still forming many stars.
The earliest period cannot be observed directly with ordinary light because the early universe was opaque. The microwave background is the oldest light that can travel freely to us.
The microwave background is not perfectly smooth. It has tiny temperature differences across the sky. These small differences mark slightly denser and less dense regions in the early universe.
Gravity pulled more matter toward the denser regions over a long time. This process produced the web-like pattern of galaxy clusters, filaments, and large empty regions seen today.
The size and pattern of the microwave background variations allow scientists to estimate the amounts of ordinary matter, dark matter, and dark energy. This is why a weak microwave signal contains major evidence about the universe.
When learning this topic, separate observations from the models used to explain them. Redshift, galaxy brightness, supernova measurements, and microwave background maps are observations. Expansion history, dark matter, dark energy, and the overall geometry are conclusions built from evidence.
Be careful with the word velocity. For nearby galaxies, speed can be estimated from redshift, but at enormous distances expansion is more complicated than an object flying away through static space.
Critical density is a useful comparison value, not the total amount of matter alone. The universe can be close to geometrically flat while its future is strongly shaped by dark energy and continued accelerated expansion.