Cosmic Acceleration Cosmic Acceleration in String Theoryin String Theory

Diederik RoestDiederik RoestDRSTP symposium DRSTP symposium

`Trends in Theory 2009’`Trends in Theory 2009’

Size matters!Size matters!Why is there any relation at all between cosmology

and string theory?

OutlineOutline

1.1. Modern CosmologyModern Cosmology

2.2. String TheoryString Theory

3.3. How to Realise Cosmic How to Realise Cosmic Acceleration in String TheoryAcceleration in String Theory

1. Modern Cosmology1. Modern Cosmology

Cosmological principleCosmological principle

Universe is homogeneous and isotropic at large Universe is homogeneous and isotropic at large scales.scales.

Space-time described by Space-time described by –scale factor scale factor a(t)a(t)

–curvaturecurvature k k Matter described by ‘perfect fluids’ with Matter described by ‘perfect fluids’ with

–energy density energy density ρρ(t)(t)

–equation of state parameter equation of state parameter ww

Fractions of critical energy density: Fractions of critical energy density: ΩΩ(t) = (t) = ρρ(t) / (t) / ρρcritcrit(t)(t)

Table of content?Table of content?What are the ingredients of the universe? Dominant What are the ingredients of the universe? Dominant

components:components: w=0w=0 - non-relativistic matter - non-relativistic matter MM (attractive - (attractive -

a(t)~ta(t)~t2/3 2/3 )) w=-1w=-1 - cosmological constant - cosmological constant ΛΛ (repulsive – (repulsive – a(t)~ea(t)~et t ))

Who ordered Who ordered ΛΛ?? First introduced by Einstein First introduced by Einstein

to counterbalance matterto counterbalance matter Overtaken by expansion Overtaken by expansion

of universeof universe

Modern cosmologyModern cosmology

Supernovae (SNe)

Cosmic Microwave Background (CMB)

Baryon AcousticOscillations (BAO)

SupernovaeSupernovae

Explosions of fixed Explosions of fixed brightnessbrightness

Standard candlesStandard candles Luminosity vs. redshift Luminosity vs. redshift

plotplot SNe at high redshift SNe at high redshift

((z~0.75z~0.75) appear dimmer) appear dimmer Sensitive to Sensitive to ΩΩMM - - ΩΩΛΛ

[Riess et al (Supernova Search Team Collaboration) ’98][Perlmutter et al (Supernova Cosmology Project Collaboration) ’98]

Cosmic Microwave Cosmic Microwave BackgroundBackground

Primordial radiation from recombination eraPrimordial radiation from recombination era Blackbody spectrum of Blackbody spectrum of T=2.7 KT=2.7 K

Anisotropies of Anisotropies of 1 1 in in 101055

Power spectrum of Power spectrum of

correlation in correlation in δδTT Location of first peakLocation of first peak

is sensitive to is sensitive to ΩΩMM + + ΩΩΛΛ

[Bennett et al (WMAP collaboration) ’03]

Baryon acoustic oscillationsBaryon acoustic oscillations

Anisotropies in CMB are Anisotropies in CMB are the seeds for structure the seeds for structure formation.formation.

Acoustic peak also Acoustic peak also seen in large scale seen in large scale surveys around surveys around z=0.35z=0.35

Sensitive to Sensitive to ΩΩMM

[Eisenstein et al (SDSS collaboration) ’05] [Cole et al (2dFGRS collaboration) ’05]

Putting it Putting it all togetherall together

Concordance ModelConcordance ModelNearly flat Universe, 13.7 billion years old.Nearly flat Universe, 13.7 billion years old.

Present ingredients: Present ingredients: 73% dark energy73% dark energy 23% dark matter23% dark matter 4% SM baryons4% SM baryons

Open questions:Open questions: What are dark components made of?What are dark components made of? CC unnaturally small: 30 orders below Planck CC unnaturally small: 30 orders below Planck

mass!mass! Fine-tuning mechanism?Fine-tuning mechanism? Anthropic reasoning?Anthropic reasoning?

Cosmic coincidence problemCosmic coincidence problem

InflationInflation Period of accelerated Period of accelerated

expansion in very early expansion in very early universeuniverse

CMB anisotropies confirm CMB anisotropies confirm inflation as source of inflation as source of fluctuationsfluctuations

Inflationary properties Inflationary properties are now being measuredare now being measured

Planck satellite:Planck satellite:– Tensor modes?Tensor modes?– Constraints on inflation?Constraints on inflation?

… three, two, one, and TAKE-

OFF!

2. String Theory2. String Theory

StringsStrings

Quantum gravityQuantum gravity No point particles, but small stringsNo point particles, but small strings Unique theoryUnique theory Bonus: gauge forcesBonus: gauge forces

Unification of four forces of Unification of four forces of Nature?Nature?

……and then some!and then some!

Super-symmetry

Branes& fluxes

Many vacua (~10500)?

Extradimensions

Dualities

String theory has many implications:

How can one extract 4D physics

from this?

CompactificationsCompactifications

Stable compactificationsStable compactifications

Simple compactifications Simple compactifications yield massless scalar yield massless scalar fields, so-called fields, so-called modulimoduli, in , in 4D.4D.

Would give rise to a new Would give rise to a new type of force, in addition type of force, in addition to gravity and gauge to gravity and gauge forces. Has not been forces. Has not been observed!observed!

Need to give mass terms Need to give mass terms to these scalar fields to these scalar fields ((moduli stabilisationmoduli stabilisation).).

Extra ingredients of string Extra ingredients of string theory, such as branes theory, such as branes and fluxes, are crucial!and fluxes, are crucial!

energy

Scalar field

with fluxes and branes

simple comp.

Moduli stabilisationModuli stabilisation

Flux compactificationsFlux compactifications Lots of progress in understanding moduli Lots of progress in understanding moduli

stabilisation in string theory (2002-…)stabilisation in string theory (2002-…) Using gauge fluxes one can stabilise the Calabi-Yau Using gauge fluxes one can stabilise the Calabi-Yau

modulimoduli Classic results:Classic results:

– IIB complex structure moduli stabilised by gauge fluxes [1]IIB complex structure moduli stabilised by gauge fluxes [1]– IIB Kahler moduli stabilised by non-perturbative effects [2]IIB Kahler moduli stabilised by non-perturbative effects [2]– All IIA moduli stabilised by gauge fluxes [3]All IIA moduli stabilised by gauge fluxes [3]

But:But:– Vacua are supersymmetric AdSVacua are supersymmetric AdS– IIA flux compactifications do not lead to inflation and/or IIA flux compactifications do not lead to inflation and/or

dark energy [4]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-geometricfluxes

3. How to Realise 3. How to Realise Cosmic AccelerationCosmic Acceleration

in String Theoryin String Theory

Cosmic challenges for fundamental

physics!

Cosmic acceleration Cosmic acceleration

Two periods of accelerated expansion:Two periods of accelerated expansion:- inflation in very early universe- inflation in very early universe- present-time acceleration- present-time acceleration

No microscopic understandingNo microscopic understanding

Modelled by scalar field with Modelled by scalar field with non-trivial scalar potential non-trivial scalar potential VV

Slow-roll parameters:Slow-roll parameters:

εε = ½ (M = ½ (Mpp V’ / V) V’ / V)22

ηη = M = Mpp22 V’’ / V V’’ / V

Extreme case Extreme case εε=0 =0 corresponds to positive CC with corresponds to positive CC with w=-1 w=-1 Leads to De Sitter space-timeLeads to De Sitter space-time Benchmark solution for string theoryBenchmark solution for string theory

Top-down approachTop-down approach

Generically string compactifications lead to Anti-Generically string compactifications lead to Anti-De Sitter space-timesDe Sitter space-times

Is it even possible to get De Sitter from string Is it even possible to get De Sitter from string theory?theory?

A number of working models:A number of working models:– Start with IIB moduli stabilisation in AdS using gauge Start with IIB moduli stabilisation in AdS using gauge

fluxes and non-perturbative effectsfluxes and non-perturbative effects– Uplift scalar potential usingUplift scalar potential using

Anti-D3-branes [1]Anti-D3-branes [1] D7-brane fluxes [2]D7-brane fluxes [2] ……

[1: Kallosh, Kachru, Linde, [1: Kallosh, Kachru, Linde, Trivedi ’03]Trivedi ’03][2: Burgess, Kallosh, Quevedo [2: Burgess, Kallosh, Quevedo ’03]’03]

Bottom-up approachBottom-up approach

Analysis of De Sitter in supergravity:Analysis of De Sitter in supergravity:– N=4,8N=4,8: unstable solutions with : unstable solutions with ηη= O(1)= O(1) [1] [1]– N=2N=2: stable solutions [2]: stable solutions [2]– Recent no-go theorems for stable solutions in Recent no-go theorems for stable solutions in

various various N=1,2N=1,2 theories [3,4] theories [3,4]– Requirements for De Sitter similar to those for Requirements for De Sitter similar to those for

slow-roll inflation [4]slow-roll inflation [4]

Interplay between supersymmetry and cosmic Interplay between supersymmetry and cosmic acceleration!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 bridgeBuilding a bridge

Connecting bottom-up and top-down approaches? Connecting bottom-up and top-down approaches? How can 4D supergravity results be embedded in How can 4D supergravity results be embedded in string theory?string theory?

One of the topics of my VIDI project 2008-2013.One of the topics of my VIDI project 2008-2013.

An example: moduli stabilisation in An example: moduli stabilisation in N=4N=4..

Moduli stabilisation in Moduli stabilisation in N=4N=4

To realise De Sitter in supergravity one needs to To realise De Sitter in supergravity one needs to stabilise the modulistabilise the moduli

In In N=4N=4 theories this requires a particular feature theories this requires a particular feature of the gauge group and the scalar potential: so-of the gauge group and the scalar potential: so-called called SU(1,1)SU(1,1) angles [1] angles [1]

Proposed in 1985 in supergravity, their origin in Proposed in 1985 in supergravity, their origin in string theory was unclearstring theory was unclear

Related to orientifold reductions with particular Related to orientifold reductions with particular fluxes turned on [2]fluxes turned on [2]

[1: De Roo, Wagemans ’85][2: DR ’09]

De Sitter in De Sitter in N=4 & N=2?N=4 & N=2?

Previous result leads to Minkowski vacuaPrevious result leads to Minkowski vacua Can this be extended such that Minkowski is lifted Can this be extended such that Minkowski is lifted

to De Sitter?to De Sitter? Inclusion of gauge and geometric fluxes [1]Inclusion of gauge and geometric fluxes [1] Similar approach to embed stable De Sitter Similar approach to embed stable De Sitter

solutions of solutions of N=2N=2 in string theory? in string theory?

[1: Dibitetto, [1: Dibitetto, Linares, DR - work Linares, DR - work in progress]in progress]

ConclusionsConclusions

Modern cosmological paradigm involves inflation Modern cosmological paradigm involves inflation and dark energyand dark energy

Link with fundamental physicsLink with fundamental physics Can one stabilise the moduli of string theory in a Can one stabilise the moduli of string theory in a

De Sitter vacuum?De Sitter vacuum? What about inflation?What about inflation? Many interesting (future) developments!Many interesting (future) developments!

Thanks for your Thanks for your attention!attention!

Diederik RoestDiederik RoestDRSTP symposium DRSTP symposium

`Trends in Theory 2009’`Trends in Theory 2009’