1. Modern cosmology: a challenge for fundamental physics Diederik Roest (University of Groningen, The Netherlands) November 6, 2009 – UAM, Ciudad de México

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

4. Outline 1. Modern Cosmology 2. Fundamental Physics 3. How to Realise Cosmic Acceleration in String Theory

5. 1. Modern Cosmology

6. Cosmological principle Universe has no structure at large scales: stars -> galaxies -> clusters -> superclusters -> … No preferred points or directions: homogeneous and isotropic.

7. Cosmological principle General Relativity simplifies to:  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) / ρ crit (t)

8. Table of content? What are the ingredients of the universe? Dominant components: w=0 - non-relativistic matter M (attractive) w=0 - non-relativistic matter M (attractive) w=-1 - cosmological constant Λ (repulsive) w=-1 - cosmological constant Λ (repulsive)

9. History of CC Who ordered Λ ? First introduced by Einstein First introduced by Einstein to counterbalance matter Overtaken by expansion Overtaken by expansion of universe Convoluted history through the 20th century.

10. Modern cosmology Supernovae (SNe) Cosmic Microwave Background (CMB) Baryon Acoustic Oscillations (BAO)

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

12. Cosmic Microwave Background Primordial radiation from recombination era Primordial radiation from recombination era Blackbody spectrum of T=2.7 K Blackbody spectrum of T=2.7 K Anisotropies of 1 in 10 5 Anisotropies of 1 in 10 5 Power spectrum of Power spectrum of correlation in δT Location of first peak Location of first peak is sensitive to Ω M + Ω Λ [Bennett et al (WMAP collaboration) ’03]

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

14. Putting it all together

15. Concordance Model Nearly flat Universe, 13.7 billion years old. Present ingredients: 73% dark energy 73% dark energy 23% dark matter 23% dark matter 4% SM baryons 4% SM baryons

16. Concordance Model Open questions: What are dark components made of? What are dark components made of? CC unnaturally small: 30 orders below Planck mass! CC unnaturally small: 30 orders below Planck mass!  Fine-tuning mechanism?  Anthropic reasoning? Cosmic coincidence problem Cosmic coincidence problem

17. Inflation Period of accelerated expansion in very early universe (~10 -36 sec) to explain: Cosmological principle Cosmological principle Why universe is flat Why universe is flat Absence of magnetic monopoles Absence of magnetic monopoles Bonus: quantum fluctuations during inflation can become source for structure formation ( CMB). Probes physics of very high energies (GUT scale ~ 10 16 GeV).

18. The future is bright! Many models of inflation are possible Many models of inflation are possible Inflationary properties are now being measured Inflationary properties are now being measured Planck satellite: Planck satellite: –Tensor modes? –Constraints on inflation? … three, two, one, and TAKE-OFF! [May 14, 2009]

19. 2. Fundamental Physics

20. Elementary particle physics Matter consists of fermions: three generattions of quarks and leptons. Forces are mediated by bosons: belonging to SU(3) x SU(2) x U(1). Standard Model (1970 - ) Standard Model (1970 - ) Unprecedented experimental verification!

21. Any questions? Where is Higgs particle? Why three generations? Include gravity? Effective description of fundamental theory?

22. Experimental input?

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

24. …and then some! Extra dimensions Many vacua ( ~10 500 )? Branes & fluxes Dualities Super- symmetry String theory has many implications: How can one extract 4D physics from this?

25. Compactifications

26. Stable compactifications Simple compactifications yield massless scalar fields, so-called moduli, in 4D. 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! 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). Need to give mass terms to these scalar fields (moduli stabilisation). Extra ingredients of string theory, such as branes and fluxes, are crucial! Extra ingredients of string theory, such as branes and fluxes, are crucial! energy Scalar field with fluxes and branes simple comp.

27. 3. How to Realise Cosmic Acceleration in String Theory

28. Cosmic challenges for fundamental physics! Cosmic acceleration Two periods of accelerated expansion: inflation in very early universe inflation in very early universe present-time acceleration present-time acceleration No microscopic understanding

29. Cosmic acceleration Modelled by scalar field with non-trivial scalar potential V Slow-roll parameters: ² = 1 2 M 2 P ¡ V 0 V ¢ 2 ¿ 1 ; ´ = M 2 P V 00 V ¿ 1 :

30. Cosmic acceleration in string theory String theory also gives rise to scalar potentials! Idea: use string theory potentials to model cosmic acceleration. Can provide information about e.g. possible inflationary scenarios at very high energies. Extreme case ε=0 corresponds to positive CC with w=-1. Leads to De Sitter space-time. Benchmark solution for string theory.

31. Top-down approach Generically string compactifications lead to Anti-De Sitter space-times Generically string compactifications lead to Anti-De Sitter space-times Is it even possible to get De Sitter from string theory? Is it even possible to get De Sitter from string theory? A number of working models: A number of working models: –Start with 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]

32. Bottom-up approach First understand 4D part and then connect to 10D. Effective description in 4D: supergravity theories. Field theories with local supersymmetry, which include gravity and gauge forces. Specified by number of supersymmetries N.

33. Bottom-up approach Analysis of De Sitter in different supergravity theories: –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] Tension 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]

34. Building a bridge Connecting bottom-up and top-down approaches? How can 4D supergravity results be embedded in string theory? [1: D.R. ’09] [2: Dibitetto, Linares, D.R. – in progress]

35. 4. Conclusions

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

37. Thanks for your attention! Diederik Roest (University of Groningen, The Netherlands) November 6, 2009 – UAM, Ciudad de México