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Physics 224 Spring 2008Origin and Evolution of the UniverseCosmic InflationLecture 16 - Monday Mar 10Joel PrimackUniversity of California, Santa CruzOutline WMAP 5-year Data and Papers ReleasedGrand Unification of ForcesPhase Transitions in the Early UniverseTopological Defects: Strings, MonopolesProblems Solved by Cosmic InflationSimple Models of Cosmic InflationGeneric Predictions of InflationDetails on Some Simple Inflation ModelsNote: I edited much of the material in the Topological Defects slides fromthe website http://www.damtp.cam.ac.uk/user/gr/public/cs_top.html L15L16GUT MonopolesA simple SO(3) GUT illustrates how nonsingular monopoles arise. The Lagragian isThe masses of the resulting charged vector and Higgs bosons after spontaneous symmetry breaking are If the Higgs field Φa happens to rotate about a sphere in SO(3) space as one moves around a sphere about any particular point in x-space, then it must vanish at the particular point. Remarkably, if we identify the massless vector field as the photon, this configuration corresponds to a nonsingular magnetic monopole, as was independently discovered by ‘tHooft and Polyakov. The monopole has magnetic charge twice the minimum Dirac value, g = 2π/e = (4π/e2)(e/2) ≈ 67.5 e. The singular magnetic field is cut off at scale σ, and as a result the GUT monopole has mass Mmonopole ≈ MV/α ≈ MGUT /α ≈ 1018 GeV, which is about 0.5x1016 times the mass of a gold atom!The Kibble mechanism produces ~ one GUT monopole per horizon volume when the GUT phase transition occurs. These GUT monopoles have a number density over entropy nM/s ~ 102 (TGUT/MPl)3 ~ 10-13(compared to nB/s ~ 10-9 for baryons) Their annihilation is inefficient since they are so massive, and as a result they are about as abundant as gold atoms but 1016 times more massive, so they “overclose” the universe. This catastrophe must be avoided! This was Alan Guth’s initial motivation for inventing cosmic inflation.GUT Monopole ProblemInflationI will summarize the key ideas of inflation theory, following my lectures at the Jerusalem Winter School, published as the first chapter in Avishai Dekel & Jeremiah Ostriker, eds., Formation of Structure in the Universe (Cambridge University Press, 1999), and Dierck-Ekkehard Liebscher, Cosmology (Springer, 2005) (available electronically through the UCSC library).Motivations for InflationHorizonsPARTICLE HORIZONSpherical surface that at time t separates worldlines into observed vs. unobservedEVENT HORIZONBackward lightcone that separates events that will someday be observed from those never observedFRWdeSSchwarzschildSee Harrison, Cosmology Rindler, Relativitybackwardlight conesInflation BasicsInflationary FluctuationsManyInflationModelsInflaton Theory in More DetailAction of gravity + scalar inflaton field:The simplest V is just quadratic which just gives the inflaton field a mass m. The model of symmetry breakdown requires a more complicated potentialV [φ]. It must contain degenerate minima that allow ground states with φ = 0. In such a ground state, the mass is defined for small perturbations byThe energy–momentum tensor is given bywhich implies that the energy density and pressure are given byandThus a scalar field with a nearly constant potential V corresponds toSince w = p/ε = -1, this is effectively a cosmological constant. More generally, a scalar field that is not at the minimum of its potential generates generates “dark energy”.The field equation for the inflaton in expanding space isWith a suitably chosen potential V, the inflaton will quickly reach its ground state and inflation will end. The term in parenthesis allows the inflaton to decay into other fields at the end of inflation, thus reheating the universe. This becomes the following equation if the spatial variations of φ(and the last term) can be neglectedThis equation must be solved along with the Einstein equations:The last equation leads towhich allows us to write the Friedmann equation asWhen the inflaton is rolling slowly, the evolution of the inflaton is governed byThen the number N of e-folds of the scale factor a is given byN = lna1a_Inflationary Models in More DetailGenerating the Primordial Density FluctuationsZero-point fluctuations of quantumfields are stretched and frozenEarly phase of exponential expansion(Inflationary epoch)Cosmic density fluctuations arefrozen quantum fluctuationsEternal Inflation(mPlanck = 1/G1/2).Supersymmetric InflationBasic Predictions of Inflation1. Flat universe. This is perhaps the most fundamental prediction of inflation. Through the Friedmann equation it implies that the total energy density is always equal to thecritical energy density; it does not however predict the form (or forms) that the criticaldensity takes on today or at any earlier or later epoch.2. Nearly scale-invariant spectrum of Gaussian density perturbations. Thesedensity perturbations (scalar metric perturbations) arise from quantum-mechanicalfuctuations in the field that drives inflation; they begin on very tiny scales (of theorder of 10-23 cm, and are stretched to astrophysical size by the tremendous growth ofthe scale factor during inflation (factor of e60 or greater). Scale invariant refers to thefact that the fuctuations in the gravitational potential are independent of length scale;or equivalently that the horizon-crossing amplitudes of the density perturbations areindependent of length scale. While the shape of the spectrum of density perturbationsis common to all models, the overall amplitude is model dependent. Achieving density perturbations that are consistent with the observed anisotropy of the CBR andlarge enough to produce the structure seen in the Universe today requires a horizoncrossing amplitude of around 2 ×10-5.3. Nearly scale-invariant spectrum of gravitational waves, from quantum-mechanicalfluctuations in the metric itself . These can be detected as CMB “B-mode” polarization, or using special gravity wave detectors such as LIGO and LISA.generally nonzeroDensity Fluctuations from InflationGravity Waves from InflationGravitational Waves from Early UniverseB. BarishTAUP 03LISA: Science Goals• Beyond Einstein science– determine how and when massive black holes form– investigate whether general relativity correctly describes gravity under extreme conditions– determine how black hole growth is related to galaxy evolution– determine if black holes are correctly described by general


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UCSC ASTRO/PHYSICS 224 - Origin and Evolution of the Universe

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