CMB anisotropies are tiny temperature differences in the cosmic microwave background, the oldest light we can observe from the early universe. This cheat sheet helps students connect those patterns to the universe's age, composition, expansion rate, and geometry. It is useful because the CMB is one of the strongest pieces of evidence for the Big Bang model and modern cosmology.
Key Facts
- The average CMB temperature is about 2.725 K, and typical anisotropies are only about 1 part in 100,000.
- Redshift is calculated by z = (observed wavelength - emitted wavelength) / emitted wavelength.
- The scale factor and redshift are related by a = 1 / (1 + z), where a = 1 today.
- The CMB was released at recombination, about 380,000 years after the Big Bang, when the universe cooled enough for neutral atoms to form.
- The angular power spectrum C_l shows how strongly CMB temperature variations appear at different angular scales.
- The first acoustic peak near l = 220 indicates that the universe is very close to spatially flat.
- The density parameters satisfy Omega_total = Omega_m + Omega_r + Omega_Lambda + Omega_k.
- The Hubble law for nearby galaxies is v = H0 d, where H0 is the Hubble constant, d is distance, and v is recession speed.
Vocabulary
- Cosmic microwave background
- The CMB is leftover radiation from the early universe that now appears as microwave light in every direction.
- Anisotropy
- An anisotropy is a small difference in a measured quantity, such as CMB temperature, depending on direction in the sky.
- Angular power spectrum
- The angular power spectrum is a graph showing the strength of CMB temperature variations at different angular sizes.
- Acoustic peak
- An acoustic peak is a high point in the CMB power spectrum caused by sound-like waves in the early hot plasma.
- Density parameter
- A density parameter, written Omega, compares a component's density to the critical density needed for a flat universe.
- Hubble constant
- The Hubble constant, H0, describes the present-day expansion rate of the universe.
Common Mistakes to Avoid
- Confusing CMB temperature with ordinary star temperature is wrong because the CMB is diffuse background radiation from the early universe, not light from stars.
- Treating anisotropies as large hot and cold regions is wrong because CMB temperature variations are extremely tiny, usually about 0.00001 of the average temperature.
- Assuming redshift only means an object is moving through space is wrong because cosmological redshift mainly comes from the expansion of space itself.
- Reading one acoustic peak as one physical object is wrong because peaks describe statistical patterns across the whole sky, not individual structures.
- Ignoring units for H0 is wrong because the Hubble constant is usually measured in km/s/Mpc, which links speed to distance.
Practice Questions
- 1 If a galaxy has observed wavelength 750 nm for a spectral line emitted at 500 nm, calculate its redshift z.
- 2 Using v = H0 d with H0 = 70 km/s/Mpc, find the recession speed of a galaxy 120 Mpc away.
- 3 If the scale factor was a = 0.25, calculate the redshift using a = 1 / (1 + z).
- 4 Explain why tiny CMB anisotropies are important evidence for the later formation of galaxies and galaxy clusters.