Cosmology
Cosmology
Cosmology is the study of the origin, structure, and evolution of the universe. Modern cosmology is built on observations of the expanding universe and the cosmic microwave background radiation.
The Doppler Effect for Light
When a light source moves relative to an observer:
- Moving away: light is redshifted (wavelengths increase, shifted toward red)
- Moving toward: light is blueshifted (wavelengths decrease, shifted toward blue)
Redshift, z:
z = Δλ/λ = v/c (for v << c)
where:
- Δλ = change in wavelength
- λ = emitted (rest) wavelength
- v = recession velocity
- c = speed of light
Evidence for the Expanding Universe
In 1929, Edwin Hubble observed that almost all galaxies show redshift in their spectral lines, and the redshift is proportional to their distance. This means galaxies are moving away from us, and the further away they are, the faster they recede.
Hubble's Law
v = H₀d
where:
- v = recession velocity (km s⁻¹)
- H₀ = Hubble constant ≈ 67–73 km s⁻¹ Mpc⁻¹ (current best estimates)
- d = distance to the galaxy (Mpc)
This implies the universe is expanding — space itself is stretching. It is not that galaxies are moving through space, but that the space between galaxies is expanding.
The Age of the Universe
If the expansion has been roughly constant: t ≈ 1/H₀
Using H₀ = 70 km s⁻¹ Mpc⁻¹:
1/H₀ = 1 / (70 × 10³ / 3.09 × 10²²) = 3.09 × 10²² / (70 × 10³) = 4.41 × 10¹⁷ s ≈ 14.0 billion years
This is consistent with the accepted age of ~13.8 billion years.
The Big Bang Theory
The Big Bang model states that the universe began from an extremely hot, dense state approximately 13.8 billion years ago and has been expanding and cooling ever since.
Key evidence:
1. Hubble's observation of galactic redshift (universe is expanding)
2. Cosmic microwave background (CMB) radiation
3. Primordial nucleosynthesis — the observed abundance of hydrogen (~75%) and helium (~25%) matches predictions
Cosmic Microwave Background Radiation
The CMB is thermal radiation filling the universe uniformly from all directions, with a black body spectrum corresponding to a temperature of 2.725 K.
It was emitted about 380,000 years after the Big Bang, when the universe cooled enough for electrons to combine with nuclei ("recombination"), making the universe transparent to radiation for the first time.
The CMB was predicted by Gamow (1948) and discovered accidentally by Penzias and Wilson (1965).
The CMB is almost perfectly uniform but contains tiny fluctuations (~1 part in 100,000) that correspond to density variations in the early universe — the seeds of galaxies and large-scale structure.
Dark Matter
Dark matter is matter that does not emit, absorb, or reflect electromagnetic radiation but exerts gravitational effects.
Evidence for dark matter:
1. Galaxy rotation curves: Stars at the edges of galaxies orbit faster than expected from the visible mass. The flat rotation curve implies a "halo" of invisible mass.
Expected (visible mass only): v ∝ 1/√r at large r
Observed: v ≈ constant at large r → more mass than is visible
2. Gravitational lensing: Light from distant galaxies is bent more than expected by the visible mass of galaxy clusters
3. Galaxy cluster dynamics: Galaxies in clusters move too fast to be gravitationally bound by visible matter alone
4. CMB fluctuation patterns: The power spectrum of CMB anisotropies requires dark matter to fit observations
Dark matter makes up approximately 27% of the total mass-energy of the universe. Its nature is unknown — candidates include WIMPs (Weakly Interacting Massive Particles) and axions.
Dark Energy
In 1998, observations of Type Ia supernovae (standard candles) showed that the expansion of the universe is accelerating, not decelerating as gravity alone would predict.
Dark energy is the name given to whatever causes this acceleration. It constitutes approximately 68% of the total mass-energy of the universe.
Composition of the Universe
| Component | Percentage |
|---|---|
| Dark energy | ~68% |
| Dark matter | ~27% |
| Ordinary (baryonic) matter | ~5% |
The ordinary matter we can see — stars, planets, gas clouds — makes up only about 5% of the universe.
The Fate of the Universe
The ultimate fate depends on the total density compared to the critical density ρ_c:
- ρ < ρ_c (open universe): Expands forever, increasingly fast
- ρ = ρ_c (flat universe): Expansion slows but never stops
- ρ > ρ_c (closed universe): Expansion reverses, leading to a "Big Crunch"
Current observations suggest the universe is very close to flat (ρ ≈ ρ_c) and, with dark energy, will expand forever at an accelerating rate.
Olbers' Paradox
Why is the night sky dark? If the universe were infinite, static, and eternal, every line of sight would eventually reach a star, and the sky should be uniformly bright.
The resolution: The universe has a finite age (~13.8 billion years), so we can only see light from a finite volume. Additionally, the expansion of the universe redshifts light from distant sources out of the visible range.