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.
Understanding Cosmology Big Bang to Dark Energy
The Big Bang is not best pictured as an ordinary explosion from one location into empty space. It is a model in which space itself changes scale everywhere. In the early universe, matter and radiation were extremely hot and dense because the scale of space was much smaller.
As expansion continued, the temperature fell. This cooling allowed different physical events to happen in sequence, including the formation of light atomic nuclei, neutral atoms, stars, and galaxies.
The model describes the universe well after its earliest known moments. It does not yet provide a complete tested account of what set the initial conditions or whether an earlier phase existed.
General relativity supplies the framework for cosmic expansion. Its equations relate the changing size of the universe to the total energy content, pressure, and spatial curvature. Pressure matters because, in relativity, it contributes to gravity.
Ordinary matter has very little pressure on cosmic scales, so its gravity slows expansion. Radiation has positive pressure and had a stronger effect when the universe was young. A component with negative pressure can produce accelerated expansion.
Students should separate the expansion rate at one time from the full expansion history. The present rate alone cannot determine the universe's age, since the rate has changed as radiation, matter, and dark energy became important at different times.
Cosmologists test this history by comparing several kinds of evidence. Light from distant galaxies is stretched while it travels through expanding space. Its redshift gives a measure of how much the universe grew during the journey.
Bright exploding stars called type one a supernovae can act as distance indicators after their brightness is calibrated. Their observed brightness revealed that distant supernovae were dimmer than expected in a steadily slowing universe. The cosmic microwave background gives a separate early snapshot.
Small temperature patterns in that background record sound waves in the young plasma. The angular sizes of these patterns constrain the geometry and matter content of the universe. Galaxy clustering adds another test because dark matter provides gravitational wells where ordinary gas can gather and form galaxies.
Dark matter and dark energy are inferred from their effects, not from direct photographs. Dark matter bends light, changes galaxy motions, and helps explain the growth of large structures. It behaves much like slow moving matter during most of cosmic history.
Dark energy is different. It becomes influential only after matter has been diluted by expansion. A cosmological constant is the simplest description, with the same energy density even as the universe grows.
Measurements remain consistent with this simple case, though they do not explain why its value is so small compared with some particle physics estimates. When learning cosmology, pay close attention to which observations constrain distance, expansion, geometry, or structure growth. A model can fit one measurement yet fail when all of them are considered together.