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 1. Modern Cosmology 2. String Theory 3. How to Realise Cosmic Acceleration in String Theory

1. Modern Cosmology

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) / ρ crit (t)

Table of content? What are the ingredients of the universe? Dominant components: w=0 - non-relativistic matter M (attractive - a(t)~t 2/3 ) w=0 - non-relativistic matter M (attractive - a(t)~t 2/3 ) w=-1 - cosmological constant Λ (repulsive – a(t)~e t ) w=-1 - cosmological constant Λ (repulsive – a(t)~e t ) Who ordered Λ ? First introduced by Einstein First introduced by Einstein to counterbalance matter Overtaken by expansion Overtaken by expansion of universe

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

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]

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]

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]

Putting it all together

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 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

Inflation Period of accelerated expansion in very early universe Period of accelerated expansion in very early universe CMB anisotropies confirm inflation as source of fluctuations CMB anisotropies confirm inflation as source of fluctuations 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!

2. String Theory

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?

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

Compactifications

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.

Moduli stabilisation

Flux compactifications Lots of progress in understanding moduli stabilisation in string theory (2002-…) Lots of progress in understanding moduli stabilisation in string theory (2002-…) Using gauge fluxes one can stabilise the Calabi-Yau moduli Using gauge fluxes one can stabilise the Calabi-Yau moduli Classic results: 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: 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]

Going beyond flux compactifications Geometric fluxes G- structures Generalised geometries Non- geometric fluxes

3. How to Realise Cosmic Acceleration in String Theory

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

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 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]

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] ?

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 An example: moduli stabilisation in N=4.

Moduli stabilisation in N=4 To realise De Sitter in supergravity one needs to stabilise the moduli 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] 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 Proposed in 1985 in supergravity, their origin in string theory was unclear Related to orientifold reductions with particular fluxes turned on [2] Related to orientifold reductions with particular fluxes turned on [2] [1: De Roo, Wagemans ’85] [2: DR ’09]

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

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!

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