1Annual Review of Astronomy & Astrophysics 1991• 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 Problem2/1203ρπ8−= kcRGdtdR222ρπ381kcRGdtdRR−=−Empty expanding U. is not flat (k = 0).Flat Î these add up to zero.02Freezing out the forces.[Fig. 30.2]FermilabLHC10321027101510-4410-36–10-3410-11TemperatureAge of UGrand Unified TheoryTheory of EverythingINFLATION?StrongElectromagneticWeakGravityPhase changes and latent heat• Apply heat energy at a steady rate to a fixed quantity of H2O• How does the temperature change?Time ÎTemperature ÎSupercooling3Inflation•At extremely early stage of universe:• t ~ 10-36s• T ~ 1028K• r = ct ~ 3x10-28m• 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 scalar field ÎPotential Energy ÎFrom “Inflation for Dummies”AstronomersInflation•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 scalar field ÎPotential Energy ÎFrom “Inflation for Dummies”Astronomers“So we will drop any pretensions of connecting the generic scalar field which drives inflation to known physics. Making this connection is left as a homework problem for a future Nobel laureate.”from Dodelson, “Modern Cosmology”, 2003.During GUT eraPotential energy due to displacement of field from its minimum“particle” = oscillation in field strength= waveDuring Electroweak era4False Vacuum Î Inflation• Fixed energy density.• Same effect as large value of cosmological constant.• Exponential expansion until universe falls into true lowest energy state.Vacuum Energy = ΛPredict uvac~ 2c7/ hG2= 10114J m-3vs. Observed uΛ= 6 x 10-10J m-310111False vacuum: u = 1098J m-3[CO Fig 30.4]03112222=−=Λ−kcRcdtdRR3)(2)(cttiieRtRΛ−=~0Reheating•Then,reheating.• Vacuum energy density (latent heat) gets converted back to radiation energy.• Current energy density of CMB radiation ( T = 2.725K) :u = aT4= 4×10-14J m-3• GUT epoch ended when T ~ 1028Ku ~ 8×1096J m-3Vacuum Energy = ΛPredict uvac~ 2c7/ hG2= 10114J m-3vs. Observed uΛ= 6 x 10-10J m-310111sameFalse vacuum: u = 1098J m-3[CO Fig 30.4]5Reheating•Then,reheating.• Vacuum energy density (latent heat) gets converted back to radiation energy.[CO Fig 30.4]During GUT eraPotential energy due to displacement of field from its minimum“particle” = oscillation in field strength= waveDuring Electroweak eraImportant note: bottom paragraph on [CO pg. 1241] says regions of zero pressure expand into regions of negative pressure.WRONG!Big-bang Nucleosynthesis 3 minDecoupling 379,000 yrAn expanding, cooling
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