The Plasma Era Lecture 4: Matter-Radiation Decoupling and the Cosmic Microwave Background After Nucleosynthesis: charge-neutral plasma. 12 H+ + He++ + 14 e- + 109 photons • Annihilation (with symmetry breaking) Thompson scattering of photons by electrons: – quark soup " e# • • Baryogenesis (quark confinement) 1 e +! ! e +! • e# – neutrons and protons "2 $ "1 • Nucleosynthesis – Plasma of charged nuclei (75% H 25% He) Electrons and photons exchange energy. ! + electrons, photons, neutrinos, traces of Li, Be. Maintains thermal equilibrium and • Recombination coupling (same T) between radiation and matter. – Neutral atoms – Matter and radiation decouple (Universe transparent) • Origin of the Cosmic Microwave Background

The Universe is opaque. Recombination Photons cannot travel far without scattering on electrons. Photons “random walk”. Plasma Like “looking thru fog”.

1. matter-radiation equality ( T ~ 30,000 K t ~ 104 yr ) energy density of photons drops below that of matter Before: 1 1 After: 1 1 T " " T " " Neutral gas R t1/ 2 R t 2 / 3 2. “recombination” ( T ~ 3000 K t ~ 3x105 yr ) electrons + nuclei --> neutral atoms ! !

Recombination Temperature Refined Calculation Energy levels: E = - I / n2. H ionisation potential I = 13.6 eV. n Excitation to n = 1 -->2 needs Photons with h " > I can ionise H. 2 E = E2 - E1 = 13.6 x ( 1 - 1/2 ) = 10.2 eV.

Mean energy of blackbody photons: h 3 k T 13.6 eV N" 9 " = Photon/proton ratio : #10 10.2 eV N ! p Recombination temperature: 3 k T ~ I To get ~ 1 photon (with h$ >10.2 eV) per proton.

-1 N p = N" (h$ > E) # N" exp(%E /k T) I (13.6 eV)(11600! K eV ) T ~ = " 52,000K E & N ) Ionisation from 3 k 3 = ln( " + # ln 109 # 20 k T ( N + ( ) ! 1/k =11,600 K/eV ' p * bound states keeps Too crude, because: 10.2 eV gas ionised until T 9 k T # # 0.5 eV 1) ~10 photons per H atom ln(109) drops further. ! (photons in blackbody tail can ionise H) T # 5700 K 2) H has bound states (excited electrons)

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1 Detailed calculation gives 3000 K. At T < 3000 K, electrons and nuclei form neutral Last Scattering Epoch atoms, not immediately re-ionised by photons. Photons interact strongly with free charges (i.e. mainly free electrons), but not with neutral atoms.

Photons & matter decouple and no longer interact!

Universe becomes transparent. Photons now fly uninterrupted across the Universe. (this is the Cosmic Microwave Background) T > 3000K T < 3000K

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1948. Gamow predicts T ~ 5 K. Redshift of Last Scattering 1965. Penzias & Wilson discover the CMB. T ~ 2.7 K. 1995. COBE measures perfect blackbody spectrum. T = 2.728 K Photons, now free of matter, fly freely in all directions. "T 2004. WMAP resolves the ripples. ~ 1o ~ 10#5 Their temperature decreases as the Universe expands. "# T Today we see these photons from all directions with All-sky maps T = 3000 K / expansion factor = 2.7 K. ! expansion factor = ( 1 + z ) = ( 3000 / 2.7 ) = 1100. COBE : !

WMAP :

CMB CMB Anisotropies Almost isotropic T = 2.728 K COBE "T ~ 10#5 Dipole anisotropy 1994 T V "# "T = = $10%3 c # T Our velocity: ! V ! 400 km/s WMAP ! "# ~ 1o Milky Way sources 2004 "T + anisotropies ~ 10#5 T Snapshot of Universe at z != 1100 Seeds of galaxy formation.

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2 Power Spectrum of CMB anisotropies Recap of key physics

Matter: ! = " c2 ! R"3 Temperature ripple ΔT M M Radiation: c2 T 4 R"4 vs angular scale !R = "R = ! ! o Observations: T 2.7 K 10"31 kg m"3 θ = 180 / l CMB = # !R $ photons N ! $ 10"28 kg m"3 # = ! ~ 109 o M Peak at 1 scale baryons Nb => Flat geometry, Mean energy of blackbody photons: h! = 3kT

Ωtot=1 For <1 photon in the blackbody tail per baryon:

N! (h! > E) $ N! exp("E kT) < Nb E E E # k T < = $ “Acoustic Peaks” arise from sound waves in the plasma era. ln N N 9 20 ( ! b ) ln(10 ) Sound speed is c/√3. Peak when the duration of plasma era matches a multiple of half a sound wave oscillation period. Sets p/n ratio, hence H/He ratio and T=3000K at recombination.

Key stages in the history of our Universe: ~ 1 TeV matter-antimatter annihilation

Radiation era quark soup ~ 1 GeV baryogenesis (quark confinement) neutron proton soup ~ 0.8 MeV neutron – proton freeze-out neutrons decay ~ 0.1 MeV nucleosynthesis H+He+e Thomson scattering plasma Matter era ~ 1 eV Recombination / decoupling neutral atoms + CMB photons

Galaxy Formation ~ 10-3 eV Today Recollapse or Eternal expansion ?

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