Thermal History of the Early Universe
Big Bang Thermodynamics
Hot Dense Initial Conditions
In the early Universe, interaction rates typically exceeded the Hubble expansion rate, keeping species in thermal and chemical equilibrium. As the Universe expanded and cooled, processes froze out when , leaving behind relic abundances that encode particle physics and expansion history.
Key Epochs
| Epoch | Approximate temperature | Physical significance |
|---|---|---|
| Quark-hadron transition | K | Confinement of quarks into hadrons |
| Big-bang nucleosynthesis | K | Light-element synthesis |
| Photon decoupling | K | CMB last scattering |
| Matter-radiation equality | Transition in growth and potential evolution |
Freeze-Out Criterion
A species decouples when its interaction rate drops below the Hubble rate , though precise relic calculations often require solving Boltzmann equations.
What condition typically signals thermal freeze-out?
When interactions become slower than expansion, equilibrium can no longer be maintained and freeze-out begins.
Correct answer:
Entropy Conservation and Temperature Evolution
For adiabatic expansion, comoving entropy is approximately conserved: . During species annihilation, entropy is transferred to the remaining relativistic bath, leading to temperature ratios such as the standard neutrino-to-photon temperature relation after electron-positron annihilation.
Why does photon decoupling matter observationally?
The CMB is our most precise window into the early Universe because photons free-stream after recombination.
Correct answer: It releases the cosmic microwave background, preserving a snapshot of the Universe at last scattering.
Equilibrium vs Freeze-Out
Equilibrium regime
- Interaction rate exceeds expansion rate.
- Distribution functions remain near thermal form.
- Chemical potentials and number densities track plasma conditions.
Freeze-out regime
- Expansion outpaces interactions.
- Relic abundance becomes approximately fixed.
- Residual abundances depend on cross section and expansion history.
Which process primarily determines the CMB last-scattering surface?
The CMB last-scattering surface is set by the epoch when photons decouple from baryons during recombination.
Correct answer: Photon decoupling during recombination
From Microscopic Rates to Relic Abundances
-
1
Write the Boltzmann equation for the species number density.
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2
Approximate equilibrium and out-of-equilibrium regimes.
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3
Compare the relevant reaction rate to the Hubble rate.
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4
Integrate the freeze-out or freeze-in evolution to obtain the relic density.