1The actual agenda:•Inflation--------------• Present-day structure• The case for dark matter• Gravitational lenses• The nature of dark matter• The growth of structure• Galactic evolutionThe Syllabus:Homework for next Wed. Nov. 14:CO 30.4, 27.10, 27.12(= 28.10, 25.10, 25.12 1sted.)In 30.4, use Tend of GUT epoch= 1028KDue Friday Nov. 160611001081014---10711074RedshiftoKAge of U.Event19950 million yrsGalaxy Formation103210-43secPlanck time; Gravity separated out102910-38secStrong nuclear force separated out3000300,000 yrsDecoupling of CMB2.7313.7 billion yrsNow1091 sec - 3 minNucleosynthesis of H, He, Li101510-12secElectromagentic, Weak nuclear forces---10-36secInflationhotcoollow densityhigh density2Freezing out the forces.Grand Unified TheoryTheory of EverythingFig. 30.2The Planck Time• Dimensional arguments• Planck time• Planck mass• Planck length• Before this, everything fuzzed out by uncertainty principle.5 x 10-44s2 x 10-8kg2 x 10-35m3Three Problems for Friedmann-Robertson-Walker Universes1. Causality and the particle horizon 2. Flatness3. Matter-antimatter asymmetry3. Absence of magnetic monopolesThe Particle HorizonFor k = 0, Λ = 0, Ω = 1 example:• Radiation era: R(t) ~ t1/2dh(t) = 2ct ϖh(t) = dh(t)/R(t) ~ t1/2• Matter Era: R(t) ~ t2/3 dh(t) = 3ct ϖh(t) = dh(t)/R(t) ~ t1/3As time passes, we can see larger and larger fraction of universe.Fig. 29.22 Proper distance from Earth to particle horizon as function of time, including Λ.Î causally connected fraction of universe is constantly growing.4Cosmic Microwave Background is smooth to about 1 part in 105• Yet regions in causal contact at time of decoupling should subtend only ~2oon sky.• How do regions 180oapart know about each other? ..Blue = 0oKRed = 4oKBlue = 2.724oKRed = 2.732oKDipole Anistropy~ 1 part in 300After removing dipoleRed – blue = 0.0002oK~ 1 part in 105Fig 30.3All Universes ~ “flat” (ρ ~ ρc) at early times.• Homework problem 29.9 will show:(29.194)• In terms of redshift, for large z :• Tiny departures from (ρ = ρc) at small t (large z) grow into much larger departures than are observed.(29.43)R(t)for all values of k.dR/dt →∞as t → 0The Flatness Problem:Ω0close to 1 at present time.• But this requires incredible precision at start (t = 0). • Î Ω0exactly = 15The solution: Inflation(probably)(maybe)Extremely rapid expansion of universe • due to release of energy in “phase change” .• like ice to water.Universe became 1043times larger within 10-32seconds.What does inflation predict for geometry of present universe?• Predicts a flat universe• Ω0= 1.000000….• As far out as we can see • red circle = horizon = most distant place from which light has had time to travel.• Solves flatness and horizon problems.BeforeInflationAfterInflationUniverse became 1043times larger within 10-32seconds.Ball Î Earth= 107= 10,000,000 times bigger.Inflation of universe= 1043 = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000 times bigger.6Annual Review of Astronomy & Astrophysics 1991Freezing out the forces.INFLATIONGrand Unified TheoryTheory of EverythingFig. 30.27Phase changes and latent heat• Apply heat energy at a steady rate to a fixed quantity of H2O• How does the temperature change?Time ÎTemperature ÎSupercoolingInflation•At extremely early stage of universe:• t ~ 10-34s• T ~ 1032K• r = ct ~ 3x10-26m• No baryons yet• Gravity is a separate force, but E&M, strong, weak forces still joined (GUT)• Expansion Î cooling Î “false vacuum”• Quasi-stable energy state above true ground stateStrength of Higgs field ÎPotential Energy ÎFrom “Inflation for Dummies”Astronomers8False Vacuum Î Inflation• Fixed energy density.• Same effect as large value of cosmological constant.• Exponential expansion until universe falls into true lowest energy state.•Then, reheating.• Vacuum energy density (latent heat) gets converted back to radiation energy.Vacuum Energy = ΛPredict uvac~ 2c7/ hG2= 10114J m-3vs. Observed uΛ= 6 x 10-10J m-310111False vacuum: u = 1098J m-3Effects of inflation• Amount of expansion• Inflation ends when strong nuclear force separates off.• Duration: ~10-32s• Size increase: A ~ e100~ 3x1043 • [ Narlikar, Liddle & Lyth give e70 = 1030] • Effect on curvature9• Effect on particle horizon• Co-moving coordinate distance to last scattering surface:• Co-moving coordinate distance from last scattering surface to particle horizon seen from that surface:• Ratio of these distances:• Dilution of monopole density by factor A-3~ 10-130[10-90]• (Effects on growth of structure)Example for flat Λ = 0 case.ϖϖϖϖϖiϖϖϖLSS=ϖi=ϖLSSϖf= Aϖiinflation~ 0~ AϖSize of Today’s Observable UniverseNow 4x1026mtLSS4x1023mtf4