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Cosmic Acceleration in String Theory

Cosmic Acceleration in String Theory. Diederik Roest DRSTP symposium `Trends in Theory 2009’. Size matters!. Why is there any relation at all between cosmology and string theory?. Outline. Modern Cosmology String Theory How to Realise Cosmic Acceleration in String Theory.

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Cosmic Acceleration in String Theory

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  1. Cosmic Acceleration in String Theory Diederik Roest DRSTP symposium `Trends in Theory 2009’

  2. Size matters! Why is there any relation at all between cosmology and string theory?

  3. Outline • Modern Cosmology • String Theory • How to Realise Cosmic Acceleration in String Theory

  4. 1. Modern Cosmology

  5. Cosmological principle Universe is homogeneous and isotropic at large scales. • Space-time described by • scale factor a(t) • curvature k • Matter described by ‘perfect fluids’ with • energy density ρ(t) • equation of state parameter w Fractions of critical energy density: Ω(t) = ρ(t) / ρcrit(t)

  6. Table of content? What are the ingredients of the universe? Dominant components: • w=0 - non-relativistic matter M (attractive - a(t)~t2/3 ) • w=-1 - cosmological constant Λ(repulsive – a(t)~et ) Who ordered Λ? • First introduced by Einstein to counterbalance matter • Overtaken by expansion of universe

  7. Modern cosmology

  8. Supernovae • Explosions of fixed brightness • Standard candles • Luminosity vs. redshift plot • SNe at high redshift (z~0.75) appear dimmer • Sensitive to ΩM- ΩΛ [Riess et al (Supernova Search Team Collaboration) ’98][Perlmutter et al (Supernova Cosmology Project Collaboration) ’98]

  9. Cosmic Microwave Background • Primordial radiation from recombination era • Blackbody spectrum of T=2.7 K • Anisotropies of 1 in 105 • Power spectrum of correlation in δT • Location of first peak is sensitive to ΩM +ΩΛ [Bennett et al (WMAP collaboration) ’03]

  10. Baryon acoustic oscillations • Anisotropies in CMB are the seeds for structure formation. • Acoustic peak also seen in large scale surveys around z=0.35 • Sensitive to ΩM [Eisenstein et al (SDSS collaboration) ’05] [Cole et al (2dFGRS collaboration) ’05]

  11. Putting it all together

  12. Concordance Model Nearly flat Universe, 13.7 billion years old. Present ingredients: • 73% dark energy • 23% dark matter • 4% SM baryons Open questions: • What are dark components made of? • CC unnaturally small: 30 orders below Planck mass! • Fine-tuning mechanism? • Anthropic reasoning? • Cosmic coincidence problem

  13. Inflation • Period of accelerated expansion in very early universe • CMB anisotropies confirm inflation as source of fluctuations • Inflationary properties are now being measured • Planck satellite: • Tensor modes? • Constraints on inflation? … three, two, one, and TAKE-OFF!

  14. 2. String Theory

  15. Strings • Quantum gravity • No point particles, but small strings • Unique theory • Bonus: gauge forces Unification of four forces of Nature?

  16. …and then some! String theory has many implications: How can one extract 4D physics from this?

  17. Compactifications

  18. energy simple comp. with fluxes and branes Scalar field Stable compactifications • Simple compactifications yield massless scalar fields, so-called moduli, in 4D. • Would give rise to a new type of force, in addition to gravity and gauge forces. Has not been observed! • Need to give mass terms to these scalar fields (moduli stabilisation). • Extra ingredients of string theory, such as branes and fluxes, are crucial!

  19. Moduli stabilisation

  20. Flux compactifications • Lots of progress in understanding moduli stabilisation in string theory (2002-…) • Using gauge fluxes one can stabilise the Calabi-Yau moduli • Classic results: • IIB complex structure moduli stabilised by gauge fluxes [1] • IIB Kahler moduli stabilised by non-perturbative effects [2] • All IIA moduli stabilised by gauge fluxes [3] • But: • Vacua are supersymmetric AdS • IIA flux compactifications do not lead to inflation and/or dark energy [4] [1: Giddings, Kachru, Polchinski ’02][2: Kachru, Kallosh, Linde, Trivedi ’03][3: DeWolfe, Giryavets, Kachru, Taylor ’05][4: Hertzberg, Kachru, Taylor, Tegmark ’07]

  21. Going beyond flux compactifications

  22. 3. How to Realise Cosmic Accelerationin String Theory

  23. Cosmic acceleration Cosmic challenges for fundamental physics! • Two periods of accelerated expansion: - inflation in very early universe - present-time acceleration • No microscopic understanding • Modelled by scalar field with non-trivial scalar potential V • Slow-roll parameters: ε = ½ (Mp V’ / V)2 η = Mp2 V’’ / V • Extreme case ε=0 corresponds to positive CC with w=-1 • Leads to De Sitter space-time • Benchmark solution for string theory

  24. Top-down approach • Generically string compactifications lead to Anti-De Sitter space-times • Is it even possible to get De Sitter from string theory? • A number of working models: • Start with IIB moduli stabilisation in AdS using gauge fluxes and non-perturbative effects • Uplift scalar potential using • Anti-D3-branes [1] • D7-brane fluxes [2] • … [1: Kallosh, Kachru, Linde, Trivedi ’03][2: Burgess, Kallosh, Quevedo ’03]

  25. ? Bottom-up approach Analysis of De Sitter in supergravity: • N=4,8: unstable solutions with η= O(1) [1] • N=2: stable solutions [2] • Recent no-go theorems for stable solutions in various N=1,2 theories [3,4] • Requirements for De Sitter similar to those for slow-roll inflation [4] Interplay between supersymmetry and cosmic acceleration! [1: Kallosh, Linde, Prokushkin, Shmakova ’02][2: Fre, Trigiante, Van Proeyen ’02][3: Gomez-Reino, (Louis), Scrucca ’06, ’07, ’08] [4: Covi, Gomez-Reino, Gross, Louis, Palma, Scrucca ’08]

  26. Building a bridge Connecting bottom-up and top-down approaches? How can 4D supergravity results be embedded in string theory? One of the topics of my VIDI project 2008-2013. An example: moduli stabilisation in N=4.

  27. Moduli stabilisation in N=4 • To realise De Sitter in supergravity one needs to stabilise the moduli • In N=4 theories this requires a particular feature of the gauge group and the scalar potential: so-called SU(1,1) angles [1] • Proposed in 1985 in supergravity, their origin in string theory was unclear • Related to orientifold reductions with particular fluxes turned on [2] [1: De Roo, Wagemans ’85][2: DR ’09]

  28. De Sitter in N=4 & N=2? • Previous result leads to Minkowski vacua • Can this be extended such that Minkowski is lifted to De Sitter? • Inclusion of gauge and geometric fluxes [1] • Similar approach to embed stable De Sitter solutions of N=2 in string theory? [1: Dibitetto, Linares, DR - work in progress]

  29. Conclusions • Modern cosmological paradigm involves inflation and dark energy • Link with fundamental physics • Can one stabilise the moduli of string theory in a De Sitter vacuum? • What about inflation? • Many interesting (future) developments!

  30. Thanks for your attention! Diederik Roest DRSTP symposium `Trends in Theory 2009’

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