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- 1. Inflation, Stringy Landscapeand Anthropic Principle

2. Inflation in String TheoryThe volume stabilization problem:A potential of the theory obtained by compactification instring theory of type IIB:X and Y are canonically normalized field corresponding to the dilaton fieldand to the volume of the compactified space; is the field driving inflationThe potential with respect to X and Y is very steep, these fields rapidly rundown, and the potential energy V vanishes. We must stabilize these fields.Dilaton stabilization: Giddings, Kachru, Polchinski 2001Volume stabilization: KKLT constructionKachru, Kallosh, A.L., Trivedi 2003 3. Basic steps of the KKLT scenario:1) Start with a theory with runaway potential discussed above2) Bend this potential down due to nonperturbative quantumeffects3) Uplift the minimum to the state with a positive vacuumenergy by adding a positive energy of an anti-D3 brane inwarped Calabi-Yau spaceV100 150 200 250 300 350 400s0.5-0.5-1-1.5-2V100 150 200 250 300 350 4001.210.80.60.4AdS minimum Metastable dS minimums0.2 4. It was never easy to discuss anthropicprinciple, even with friendsBut recently the concept of the string theorylandscape came to the rescue 5. String Theory LandscapePerhaps 101000 different minimaLerche, Lust, Schellekens 1987Bousso, Polchinski; Susskind; Douglas, Denef, 6. Two types of string inflflation models:Modular Inflation. The simplest class of models.They use only the fields that are already presentin the KKLT model.Brane inflflation. The inflaton field corresponds tothe distance between branes in Calabi-Yauspace. Historically, this was the first class ofstring inflation models. 7. Inflation in string theoryKKLMMT brane-anti-brane inflationD3/D7 brane inflationRacetrack modular inflationDBI inflation (non-minimal kinetic terms) 8. CMB and InflationBlue and black dots - experimental results (WMAP, ACBAR)Brown line - predictions of inflationary theory 9. Predictions of Inflflation:1) The universe should be homogeneous, isotropic and flat, = 1 + O(10-4) [=/0]Observations: it is homogeneous, isotropic and flat:2) Inflationary perturbations should be gaussian andadiabatic, with flat spectrum, ns = 1+ O(10-1). Spectral indexns slightly differs from 1. (This is an important prediction,similar to asymptotic freedom in QCD.)Observations: perturbations are gaussian and adiabatic,with flat spectrum: 10. Tensor modes:Kallosh, A.L. 2007It does make sense to look for tensor modes even ifnone are found at the level r ~ 0.1 (Planck) 11. STRING COSMOLOGY AND GRAVITINO MASSKallosh, A.L. 2004The height of the KKLT barrier is smaller than |VAdS| =m23/2. Theinflationary potential Vinfl cannot be much higher than the height of thebarrier. Inflationary Hubble constant is given by H2 = Vinfl/3 < m23/2.Constraint on H and r in this class of models:H < m3/2VVAdSModification ofV at large H 12. Tensor Modes and GRAVITINOSuperheavygravitinoA discovery or non-discovery of tensor modeswould be a crucial test for string theory 13. Inflflationary MultiverseFor a long time, people believed in the cosmological principle,which asserted that the universe is everywhere the same.This principle is no longer required. Inflationary universe mayconsist of many parts with different properties depending onthe local values of the scalar fields, compactifications, etc. 14. Example: SUSY landscapeVSupersymmetric SU(5)SU(5) SU(4)xU(1) SU(3)xSU(2)xU(1)Weinberg 1982: Supersymmetry forbids tunneling from SU(5) toSU(3)xSU(2)XU(1). This implied that we cannot break SU(5) symmetry.A.L. 1983: Inflation solves this problem. Inflationary fluctuations bring us toeach of the three minima. Inflation make each of the parts of the universeexponentially big. We can live only in the SU(3)xSU(2)xU(1) minimum. 15. Landscape of eternal inflflation 16. String Theory Multiverse < 0and eternal old inflflation = 0 > 0 17. Discrete and continuous parametersProperties of our world (local part of the universe) dependon 101000 discrete parameters (topological numbers,quantized fluxes, etc.), which describe our vacuum state.Beyond the landscape: Our world may depend ona continuous set of parameters, which took differentvalues during the cosmological evolution far away fromthe vacuum state.EXAMPLES:a) Axion field could take different values during inflation, which shouldaffect the local value of the density of dark matter.b) Affleck-Dine fields could take different values in different parts of theuniverse, thus affecting the local value of the baryon asymmetry of theuniverse. 18. Inflation and Cosmological Constant4 steps in finding the anthropic solution of the CC problem:1) Anthropic solutions of the CC problem using inflation andfluxes of antisymmetric tensor fields (A.L. 1984), multiplicity of KK vacua(Sakharov 1984), and slowly evolving scalar field (Banks 1984, A.L.1986). We considered it obvious that we cannot live in the universe withbut the proof was needed for positive .2) Derivation of the anthropic constraintWeinberg 1987; Martel, Shapiro, Weinberg 1997, 19. Inflation and Cosmological Constant3) String theory landscapeMultiplicity of (unstable) vacua:Lerche, Lust and Schellekens 1987: 101500 vacuum statesDuff, 1986, 1987; Bousso, Polchinski 2000Vacuum stabilization and statistics:KKLT 2003, Susskind 2003, Douglas 2003,perhaps 101000 metastable dS vacuum states - still counting4) Counting probabilities in an eternallyinflating universe (more about it later) 20. Anthropic constraints on Aguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774observed value 21. Dark Energy (Cosmological Constant)is about 74% of the cosmic pieDark Matter constitutes another 22% ofthe pie. Why there is 5 times more darkmatter than ordinary matter? 22. Example: Dark matter in the axion fifieldOld lore: If the axion mass is smaller than 10-5 eV,the amount of dark matter in the axion field contradictsobservations, for a typical initial value of the axion field.Can we give a scientifific defifinition of typical ?Anthropic argument: Inflationary fluctuations make theamount of the axion dark matter a CONTINUOUS RANDOMPARAMETER. We can live only in those parts of theuniverse where the initial value of the axion field wassufficiently small (A.L. 1988).Recently this possibility was analyzed by Aguirre, Rees, Tegmark, andWilczek. 23. Anthropic Constraints on Axion Dark MatterAguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774observed valueThe situation with Dark Matter is even better than with the CC ! 24. What is so special about our world?Problem: Eternal inflflation creates infifinitely many differentparts of the universe, so we must compare infifinities 25. Two different approaches:1. Study events at a given point, ignoring growth of volumeStarobinsky 1986, Garriga, Vilenkin 1998, Bousso 2006, A.L. 2006No problems with infifinities, but the results depend on initial conditions.It is not clear whether these methods are appropriate for description ofeternal inflflation, where the exponential growth of volume is crucial.2. Take into account growth of volumeA.L. 1986; A.L., D.Linde, Mezhlumian, Garcia-Bellido 1994;Garriga, Schwarz-Perlov, Vilenkin, Winitzki 2005; A.L. 2007No dependence on initial conditions, but we are still learning how to doit properly. I will review some recent progress. 26. VBoltzmann Brains are coming!!!BB3 BB1Fortunately, normal brainsare created even faster, dueto eternal inflflation 27. Problems with probabilitiesV35 4 2 1 28. Time can be measured in thenumber of oscillations ( )or in the number of e-foldings ofinflation ( ). The universeexpands asis thegrowth of volumeduring inflationUnfortunately, the result depends on the time parametrization. 29. t21t45t = 0We should compare the trees of bubbles not at the time when the treeswere seeded, but at the time when the bubbles appear 30. A possible solution of this problem:If we want to compare apples to apples, instead of the trunksof the trees, we need to reset the time to the moment whenthe stationary regime of exponential growth begins. In thiscase we obtain the gauge-invariant resultAs expected, the probability is proportional to the rate oftunneling and to the growth of volume during inflation.A.L., arXiv:0705.1160 31. This result agrees with the expectation that theprobability to be born in a part of the universewhich experienced inflation can be very large,because of the exponential growth of volumeduring inflation. 32. Applications: Probabilities and the solution of theCC problem in the BP landscapeClifton, Shenker, Sivanandam, arXiv:0706:3201The main source of volume of new bubbles is the tunneling from thefastest growing dS vacua with large vacuum energy towards theanthropic sphere with .If the tunneling occurs sequentially, between the nearby vacua, theprocess typically moves us to a minor fraction of the anthropic spherewith one of the fluxes being much greater than all others. This allowssharp predictions. One of the predictions - vacuum decay few billionyears from now.However, if the tunneling with large jumps is possible due to nucleationof large stacks of branes (which seems plausible during the tunnelingfrom the high energy dS vacua), then the probability distribution on theanthropic sphere becomes rather uniform, no doomsday. 33. The cosmological constant problem is solved in this scenarioin either case (small or large jumps): the probabilitydistribution for the CC is flat and smooth near the anthropicsphere. It seems that the solution of the CC problem can beachieved with many different probability measures.Predictions of other features of our world, includingstability/instability of our vacuum, depend on the propertiesof the landscape, on the possibility of the nucleation oflarge stacks of branes, on the proper choice of theprobability measure, and on the duration of the slow-rollstage of inflation.Hopefully we will learn many new interestingthings before the next Bie

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