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Pietro Frè University of Torino & Embassy of Italy in Moscow Work in collaboration with

Can Integrable Cosmologies fit into Gauged Supergravity ? . Pietro Frè University of Torino & Embassy of Italy in Moscow Work in collaboration with A. Sagnotti , A. Sorin & M. Trigiante. Dubna July 30 th 2013.

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Pietro Frè University of Torino & Embassy of Italy in Moscow Work in collaboration with

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  1. Can IntegrableCosmologiesfitintoGaugedSupergravity? Pietro Frè Universityof Torino & Embassyof Italy in Moscow Work in collaboration with A. Sagnotti, A. Sorin & M. Trigiante Dubna July 30th 2013

  2. One scalar flatcosmologies Generalizedansatzforspatiallyflatmetric Friedman equations when B(t) = 0

  3. In a recentpaperbyP.F. , Sagnotti & Sorin Ithasbeenderived a BESTIARY ofpotentialsthatleadtointegrablemodelsofcosmology. Therewealsodescribed the explicitintegrationfor the scalar field and the scale factorforeachof the potentials in the list. The questionis: Can anyofthesecosmologiesbeembeddedinto a GaugedSupergravitymodel? Thisis a priori possible and naturalwithin a subclassof the abovementionedBestiary

  4. The integrablepotentials candidatein SUGRA From Friedman equationsto Conversionformulae Effectivedynamicalmodel

  5. There are additional integrable sporadic potentials in the class thatmightbefitintosupergravity

  6. Connection withGauged SUGRA From the gauging procedure the potentialemergesas a polynomialfunctionof the cosetrepresentative and henceas a polynomialfunction in the exponentialsof the Cartanfields hi

  7. The N=2 playingground In N=2 or more extended gauged SUGRA wehave found no integrablesubmodel, so far. The full set ofgaugingshasbeenonstructedonlyfor the STU model p=0 The classificationofothergaugingshastobedone and explored

  8. Some resultsfrom a newpaperbyP.F.,Sagnotti, Sorin & Trigiante(toappear) • Wehaveclassifiedall the gaugingsof the STU model, excludingintegrabletruncations • Wehavefoundtwointegrabletruncationsofgauged N=1 Supergravity. In short suitablesuperpotentialsthatleadtopotentialswithconsistentintegrabletruncations • Analysing in depth the solutionsofoneof the supersymmetricintegrablemodelswehavediscovered some newmechanismswithpotentiallyimportantcosmologicalimplicactions….

  9. N=1 SUGRA potentials N=1 SUGRA coupledto n Wess Zumino multiplets where and Ifonemultiplet, forinstance

  10. Integrable SUGRA model N=1 If in supergravitycoupledtooneWess Zumino multipletspanning the SU(1,1) / U(1) Kaehlermanifold we introduce the followingsuperpotential weobtain a scalar potential where Truncationto zero axion b=0 isconsistent

  11. THIS IS AN INTEGRABLEMODEL

  12. The formof the potential Hyperbolic:  > 0 Runawaypotential Trigonometric < 0 Potentialwith a negative extremum: stableAdSvacuum

  13. The GeneralIntegral in the trigonometric case The scalar fieldtriesto set down at the negative extremumbutitcannotsincethere are no spatialflatsectionsofAdSspace! The resultis a BIG CRUNCH. GeneralMechanismwheneverthereis a negative extremumof the potential

  14. The simplestsolutionY=0

  15. Phaseportraitof the simplestsolution

  16. Y-deformedsolutions An additional zero of the scale factoroccursfor0suchthat Regionof moduli space withoutearly Big Crunch

  17. Whatnewhappensfor Y > Y0 ? Early Big Bang and climbing scalar from -1to + 1

  18. Particle and EventHorizons Radiallight-likegeodesics Particlehorizon: boundaryof the visibleuniverse at time T EventHorizon: Boundaryof the Universe part fromwhich no signalwilleverreachanobserver living at time T

  19. Particle and EventHorizons do not coincide! Y < Y0 Y > Y0

  20. Hyperbolicsolutions We do notwrite the analyticform. Itisalsogiven in termsofhypergeometricfunctionsofexponentials at Big Bang at Big Crunch

  21. FLUX compactifications and anotherintegrablemodel In stringcompactifications on T6 / Z2£ Z2 onearrives at 7 complex moduli fields imposing a global SO(3) symmetryone can reduce the game tothreefields withKahlerpotential Switching on Fluxesintroduces a superpotential W polynomial in S,T,U and breaks SUSY N=4 into N=1

  22. A special case induces a potentialdepending on threedilatons and threeaxions. The axions can beconsistentlytruncated and onehas a potential in threedilatonswithanextremum at h1=h2=h3 = 0 thatis a STABLE dS VACUUM There are two massive and onemasslesseigenstates. The potentialdependsonly on the two massive eigenstates1 and 2

  23. The truncationtoeitheroneof the mass eigenstatesisconsistent oneobtains: THIS MODEL is INTEGRABLE. Number 1) in the list Hencewe can derive exactcosmologicalsolutions in thissupergravity fromfluxcompactifications

  24. Conclusion The studyofintegrablecosmologieswithinsuperstring and supergravityscenarioshas just onlybegun. Integrablecases are rare but do exist and can provide a lotofunexpected information thatilluminatesalso the Physicsbehind the non integrablecases.

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