XIII. The Very Early Universe and Inflation ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 171
Problems with the Big Bang The Flatness Problem The Horizon Problem The Monopole (Relic Particle) Problem ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 172
The Flatness Problem Friedmann Equation: Can rewrite as: 1 Ω(t) = 1 Ω(t) = κc 2 R 0 2 a(t) 2 H(t) 2 κ c 2 R 0 2 a(t) 2 H(t) 2 Assuming a Universe where matter and radiation are more important than curvature or : radiation dominated: a 2 H 2 t 1 1 Ω total t matter dominated: a 2 H 2 t 2 / 3 1 Ω total t 2 / 3 1-Ω increasing with time flat geometry unstable! ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 173
The Flatness Problem II Again, neglecting curvature and, and assuming a radiation-dominated Universe, we can calculate how close Ω tot was to 1 in the early Universe: Decoupling (t~10 13 s): 1 Ω tot 10-5 Matter-Radiation Equality (t~10 12 s): 1 Ω tot 10-6 Nucleosynthesis (t~1 s): 1 Ω tot 10-18 Electro-weak symmetry breaking (t~10-12 s): 1 Ω tot 10-30 Maybe the Universe has Ω tot = 1...but if so, why? ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 174
The Horizon Problem The Universe has a finite age light can only have travelled a finite distance The CMB is almost perfectly isotropic (T =2.725 K), explained if all different parts of the sky have been able to interact and achieve thermal equilibrium However, the CMB radiation from opposite directions in the sky has only just reached us, and couldn t have been in contact with each other A related problem: how did the tiny (1 part in 10 5 ) CMB fluctuations which gave rise to structure arise? ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 175
The Monopole Problem Particle physics is working toward unifying four fundamental forces: gravitational, electromagnetic, weak, strong Electro-weak theory: at energies > ~1 TeV, EM and weak force united (T~10 16 K, t~10-12 s), experimentally supported Grand Unified Theories (GUTs): at energies >~10 12 10 13 TeV (T~10 28 K, t~10-36 s), strong and electroweak forces should be unified Theory of Everything : unifying Grand Unified Force + gravity...? One prediction of most GUTs: Universe went through phase transition as T < T GUT, produced topological defects very massive (10 12 TeV) magnetic monopoles...but not seen ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 176
Cosmological Inflation 1981: Alan Guth proposes inflation as a way to solve the flatness, horizon, and monopole problems simultaneously Hypothesis: early in the Universe, expansion accelerating (ä > 0); can take form of cosmological constant ( ) H 2 = 8πG 3 ρ kc 2 a + Λc 2 2 3 First two terms decrease with expansion, remains constant: H 2 = Λc 2 3 a = Λ 3 c a a(t) = exp Λ 3 ct ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 177
Inflation and the Flatness Problem Friedmann Equation again: 1 Ω(t) = κ c 2 R 0 2 a(t) 2 H(t) 2 Inflation forces Ω tot 1: a > 0 d dt ( a ) > 0 d dt ( ah ) > 0 In the case of perfect exponential expansion, 1 Ω total (t) exp Inflation forces Ω tot so close to 1 that later expansion insufficient to move it away from 1 4Λ 3 ct ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 178
Inflation and the Horizon Problem With inflation, a small region of the Universe small enough to be thermalised before inflation can expand to be larger than the currently observable Universe CMB radiation from opposite directions coming from regions once in equilibrium Inflation expands submicroscopic quantum fluctuations to macroscopic scales inhomogeneities in present Universe The current proper distance to the surface of last scattering is ~14 Gpc; if inflation ended at t f ~10-34 s, that corresponds to a scale factor a f ~ 2 10-27 the portion of the Universe now visible to us was confined to a sphere of proper radius ~0.9m! ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 179
Inflation and the Observable Universe ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 180
Inflation and the Monopole Problem If monopoles created before or during inflation, then their number density is decreased to an undetectably low level If the Universe were expanding exponentially, the number density of monopoles (or other exotic particles) would decrease exponentially, such that the probability of finding one within the last scattering surface could be extremely small ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 181
The Physics of Inflation What triggers inflation at t i and turns it off at t f? If the density of monopoles is reduced to undetectable levels, why isn t the density of photons also reduced to undetectable levels? Why doesn t inflation flatten out the fluctuations in the energy density? Rough idea: scalar field, (r,t), which undergoes a phase transition ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 182
Phase Transitions ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 183
False Vacuum to True Vacuum As field rolls toward true vacuum, it produces exponential expansion ϕ oscillates about minimum in potential V(ϕ), if coupled to other fields oscillations damp more quickly Energy carried away reheats the Universe: if inflation starts around GUT time, and last for ~100 e- foldings, then T(t i )~10 28 K T(t f )~10-15 K (!), need to bring the temperature back up ASTR378 Cosmology : XIII. The Very Early Universe and Inflation 184