1Definitions, results, etc.PhysicsGtHtπ8)(3)(ρ2c=)(ρ)(ρ)(tttc=ΩP = wu = wρc2dU = -PdV2cu=ρ0,4,3,RRRorormomΛΑ−−===ρρρρρρMatter:Radiation:Dark energy:r = R(t) ϖdtdRRH1=222ρπ381kcRGdtdRR−=−Per unit mass:K.E. + potential E. = Total EnergyDensities:Temp. of radiation field:Curvature 21ℜ=kCosmological Constant(a.k.a. Dark Energy)+1x 0-1[][]222/)(/)()()(dttdRdttRdtRtq −=**= you should be able to write these down from memory.***********r(t)mHot CoolHigh density Low densityPlanck timeInflationFormationof H, He, LiGalaxy FormationNowThe History of the UniverseCosmic Microwave BackgroundPrimordial Nucleosynthesis(1032K)(109K)(3 K)(3000 K)Time ÎÍ Size of Universe ÎDecoupling of CMB13.72The Planck Time• Dimensional arguments• Planck time• Planck mass• Planck length• Before this, everything fuzzed out by uncertainty principle.= 5 x 10-44s= 2 x 10-8kg= 2 x 10-35m35cGGcmcGtPPP=A=====Time ÆR(t) Æ00Some Problems for Friedmann-Robertson-Walker Universes• Causality and the particle horizon • Flatness• Absence of magnetic monopoles• Absence of “Domain Walls”3The Horizon ProblemFor 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.The Particle Horizon:• Cosmic 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 30.3The Horizon Problem4• Tiny departures from (ρ = ρc) at small t (large z) grow into much larger departures than are observed.• Ω0close to 1 at present time.• But this requires incredible precision at start (t = 0). •Î Ω0exactly = 1R(t)The Flatness ProblemThe solution: Inflation(probably)(maybe)Extremely rapid expansion of universe • due to release of energy in “phase change”.Universe became ~ e100~ 1043times larger within 10-34seconds.5What 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 ~ e100~ 1043times larger within 10-34seconds.Inflation of universe = 1043Milky Way Diskelectron =
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