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String Theory and Cosmology

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String Theory and Cosmology The Unity of the Universe Portsmouth UK June 2009 Outline • How current and future observaons in cosmology and experiments in parcle physics have affected and will affect our understanding of `foundaons’ of theorecal physics • String cosmology On chaoc inflaon and B‐modes • Standard model inflaon with and supersymmetry • Recent dramac progress in N=8 four‐dimensional supergravity Quantum Gravity Planck length : B‐modes from inflaon The highway across the desert Gerard ‘t Hoo GUTs Today’s LHC Limit … SUPERSYMMETRY Cosmology, ten‐dimensional superstring theory and effecve four‐dimensional supergravity Kähler potential and the Superpotential Generic potenal of N=1 supergravity depends on a number of complex scalar fields which have geometric meaning of coordinates in Kähler geometry + D-terms String Theory • String theory is the best known candidate for the theory of all interacons, including gravity. • Since 1987 it was known that string theory has many (10500‐101500) soluons defining string theory vacua (Lerche, Lust, Schellekens 1987; Bousso, Polchinsky 2000). This was a source of embarrassment for string theory, aempng to explain our universe in the best tradions of the old paradigm: a dream to explain just one world we live in. • However, all of these vacua were unstable, they had negave energy density, and therefore they could not describe our world. This problem became especially urgent when cosmologists found that the vacuum energy density (the cosmological constant) is posive. • This problem was resolved in 2003 in the KKLT scenario based on many other efforts of string community in this direcon. The volume stabilization problem: A potential of the theory obtained by compactification in string theory of type IIB: X and Y are canonically normalized field corresponding to the dilaton field and to the volume of the compactified space; φ is the field driving inflation The potential with respect to X and Y is very steep, these fields rapidly run down, and the potential energy vanishes. We must stabilize these fields. Dilaton stabilization: Giddings, Kachru, Polchinski 2001 Even now the dilaton was Volume stabilization: KKLT construction not yet stabilized in heterotic string theory Kachru, RK, Linde, Trivedi 2003 Long Term Problem of Moduli Stabilisation And Supersymmetry Breaking 4D Compactifications: String theory is consistent in 10D. One of the moduli is the total volume of extra dimensions, it tend to have a runaway behavior. If this volume becomes infinite, we cannot explain the current cosmological observations which require an effective 4D! Examples of Calabi-Yau 3-folds Other moduli: size of cycles 1) Start with a theory with a typical stringy runaway potential 2) Bend this potential down due to nonperturbative quantum effects 3) Uplift the minimum to the state with a positive vacuum energy by adding a positive energy of a D brane in warped Calabi-Yau geometry Solving the cosmological constant problem Among 10500 vacua one can always find many vacua with vacuum energy smaller than 10‐120. We cannot live in the vacua with vacuum energy much greater than 10‐120. Thus a combinaon of inflaonary theory, string theory and anthropic reasoning can solve the cosmological constant problem. At the moment, we do not have any alternave soluons. Inflation in string theory To produce a reasonable cosmology in string theory it was necessary to stabilize all moduli but the inflaton (or two, for non-gaussianity). In 4d theory such moduli are scalar fields. In string theory and supergravity they often have physical and geometrical meaning as volumes of extra dimensions and various cycles in topologically non- trivial extra dimensions. The inflaton can also be related to a distance between branes. Brane inflation Modular inflation Brane inflation with monodromy KKLMMT brane-anti-brane inflation Two-throat model Dirac-Born-Infeld inflation Hybrid D3/D7 brane inflation (Stringy D-term inflation) Modular Inflaon models Racetrack inflation , Kahler modular inflation Roulette inflation A simple working model of the moduli inflation Blanco-Pilado, Burgess, Cline, Escoda, Gomes-Reino, R.K., Linde, Quevedo Superpotential: Kähler potential: 2003 η-problem ( ) requires fine-tuning of terms After that, the model works and has interesting properties, such as light cosmic strings 2007 Baumann, Dymarsky, Klebanov, Maldacena, McAllister, Murugan, Steinhardt: Stringy corrections do not remove terms as originally expected. With fine-tuning one can find an inflection point and slow-roll inflation. “Delicate inflation.” 2008 Baumann, Dymarsky, Kachru, Klebanov, McAllister Improved understanding of quantum corrections If there are some discrete symmetries, the original KKLMMT scenario with inflaton mass tuned is valid. Haack, RK, Krause, Linde, Lust, Zagermann 2008 Stringy version of the D-term inflation. Naturally flat inflaton direction, string theory corrections under control, eternal inflation regime, a controllably small amount of cosmic strings. Silverstein, Westphal, 2008, McAllister, Silverstein, Westphal 2008 Type IIA string Type IIB, CY Type IIB CY June 2009 MEASUREMENT OF CMB POLARIZATION POWER SPECTRA FROM TWO YEARS OF BICEP DATA B-mode spectrum is consistent with zero Directly from CMB B-mode polarization IMPROVED MEASUREMENTS OF THE TEMPERATURE AND POLARIZATION OF THE CMB FROM QUAD WMAP+ACBAR +QUaD From CMB alone r =0.1 +… Add Where is dark matter and how supersymmetry will affect this conclusion ??? Standard Model + Supersymmetry: impossible with 1 Higgs, minimum 2 Higgs fields Standard model Higgs inflation with non-minimal + supersymmetry 1. It is not possible to simply add to standard supergravity action + fermions 2. Need many new terms in the action proportional to Work in progress Quantum Gravity??? N=8 supergravity in four dimensions during the last 25 years was believed to be UV divergent: all-loop geometric counterterms, candidates for UV divergences, are known RK; Howe, Lindstrom (1981). The onset of divergences was less clear. During the last few years studies of mul‐parcle amplitudes in QCD (N=0) were simplified using N=4 super Yang‐Mills theory. This, in turn, led to significant progress in computaon of QFT amplitudes in N=8 supergravity. Some spectacular cancellaons of UV divergences were discovered at the 3‐loop level in 2007 and at the 4‐loop level in 2009. Is N=8 supergravity UV finite? If the answer is "yes" what would it mean for Quantum Gravity? Bern, Carrasco, Dixon, Johansson, Kosower, Roiban (2007) Bern, Carrasco, Dixon, Johansson, Roiban (2008, 2009) • Major surprise: • The 3‐loop and 4‐loop computaon show much beer UV than expected • Arguments about all‐loop finiteness At 3 loops N=8 supergravity seems to have the same UV behavior as N=4 SYM gauge theory. • Dc = 6 at L=3 same as for N=4 SYM! • Will the same happen at higher loops, so that the formula N=4 SYM continues to be obeyed by N=8 supergravity as well? • If so, N=8 supergravity may represent a perturbatively finite, pointlike theory of quantum gravity Several striking features of the 3‐loop 4‐point amplitude answer • There are no UV log divergent terms of the form log Λ ( R….)4 • There are no terms of the form 1/Λ2 d2( R….)4 • There are no terms of the form 1/Λ4 d4( R….)4 • The first non‐vanishing terms are of the form 1/Λ6 d6( R….)4 + higher derivaves 4‐loop computaon Predicon: if N=8 SG at the 4‐loop level behaves as N=4 SYM they must find 3‐types of cancellaon: log Λ 1/Λ2 Superfiniteness is not a necessary condition for the all- loop UV finiteness in d=4, however, it is extremely unlikely 1/Λ4 to be accidental If the last term is not vanishing, it indicates that D=5 L=4 maximal SG is divergent Howe, Stelle: UV divergent Computation: UV finite terms in 3-loop diagram. There is a reason why this hasn’t been evaluated. This single 5-loop diagram has terms prior to evaluating any integrals. More terms than atoms in the brain! Brute force computations are totally hopeless! Maximal supergravity DeWit, Freedman (1977); Cremmer, Julia, Scherk (1978); Cremmer, Julia (1978,1979); De Wit, Nicolai (1982) • Theory has 28 = 256 massless states. • Multiplicity of states, vs. helicity, from coefficients in 8 binomial expansion of (x+y) – 8th row of Pascal’s triangle SUSY charges Qa, a=1,2,…,8 shift helicity by 1/2 Bern, Dixon, Dunbar and Kosower, 1994 Two-particle cut: Three- particle cut: Generalized unitarity: Apply decomposition of cut amplitudes in terms of product of tree amplitudes. 3 loop N=8 supergravity computation, 2007 4 loop N=8 supergravity computation, May 2009 It continues to be as well behaved as N=4 SYM gauge theory. What is next? Understanding the reason for cancellation of UV divergences, use light-cone superfields, E7(7) symmetry At present we are unaware of any natural way to accommodate in string theory a future detecon of B‐modes and, simultaneously, a possible future experimental idenficaon of the gravino as parcles with mass much smaller than 1013 GeV. Even if B‐modes are not detected, there is sll a tension between string cosmology and light gravino, parcularly if it forms dark maer. New ideas are required. • Supersymmetry? • Is dark energy a cosmological constant? • Non‐gaussianity • More on spectral index • Cosmic strings • B‐modes ? • Mass of gravino ? • Test of superstring theory? We are waiting for LHC and Planck, dark matter and B-mode experiments data .
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