Cosmology studies the origin, evolution, large-scale structure, and future of the universe. This cheat sheet connects the Big Bang model to modern evidence for cosmic acceleration and dark energy. College students need these ideas to interpret observations such as redshift surveys, supernova distances, and the cosmic microwave background.
The goal is to organize the main concepts, equations, and observational links in one clear reference.
Key Facts
- The scale factor a(t) describes cosmic expansion, and cosmological redshift follows 1 + z = a0 / aem, where a0 is usually set to 1.
- Hubble's law for nearby galaxies is v = H0 d, where H0 is the present-day Hubble constant.
- The Friedmann equation for a homogeneous, isotropic universe is H^2 = (8 pi G / 3) rho - k c^2 / a^2 + Lambda c^2 / 3.
- The critical density is rho_c = 3 H^2 / (8 pi G), and density parameters are defined by Omega_i = rho_i / rho_c.
- Radiation density scales as rho_r proportional to a^-4, matter density scales as rho_m proportional to a^-3, and dark energy from a cosmological constant stays constant.
- The cosmic microwave background formed at recombination, when the universe cooled enough for electrons and protons to form neutral hydrogen at about 380,000 years after the Big Bang.
- Cosmic acceleration occurs when the expansion satisfies a double dot > 0, which requires a component with sufficiently negative pressure such as dark energy.
- For dark energy, the equation of state is w = p / (rho c^2), and a cosmological constant has w = -1.
Vocabulary
- Scale factor
- The scale factor a(t) measures how cosmic distances grow or shrink relative to a chosen reference time.
- Redshift
- Redshift z measures how much light has been stretched by cosmic expansion, with larger z usually meaning earlier cosmic time.
- Friedmann equation
- The Friedmann equation relates the expansion rate of the universe to its energy density, curvature, and cosmological constant.
- Cosmic microwave background
- The cosmic microwave background is the cooled relic radiation from the early hot universe, observed today at about 2.7 K.
- Dark matter
- Dark matter is nonluminous matter inferred from gravity, including galaxy rotation curves, lensing, and structure formation.
- Dark energy
- Dark energy is the unknown component causing the accelerated expansion of the universe, often modeled as a cosmological constant.
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 material flying from a central point.
- Using v = H0 d at all distances is wrong because the simple linear Hubble law is only a low-redshift approximation and must be replaced by cosmological distance relations at high redshift.
- Assuming redshift is only a Doppler effect is wrong because cosmological redshift mainly comes from the stretching of wavelengths as the universe expands.
- Forgetting that radiation scales as a^-4 is wrong because photons lose energy from redshift in addition to being diluted by increasing volume.
- Calling dark matter and dark energy the same thing is wrong because dark matter attracts gravitationally and clusters, while dark energy drives acceleration and is nearly uniform.
Practice Questions
- 1 A galaxy has redshift z = 2. What was the scale factor aem when its observed light was emitted, assuming a0 = 1?
- 2 Using H0 = 70 km/s/Mpc, estimate the recession speed of a nearby galaxy at distance d = 50 Mpc with v = H0 d.
- 3 If the scale factor doubles, by what factors do matter density and radiation density change?
- 4 Explain why the discovery that distant Type Ia supernovae are dimmer than expected supports cosmic acceleration rather than simple constant-speed expansion.