Transcript How stable are extra dimensions?

Cosmic Acceleration
in String Theory
Diederik Roest
DRSTP symposium
`Trends in Theory 2009’
Why is there any relation at
Size matters!
all between cosmology and
string theory?
Outline
1.
2.
3.
Modern Cosmology
String Theory
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) / ρcrit(t)
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
Modern cosmology
Supernovae (SNe)
Baryon Acoustic
Oscillations (BAO)
Cosmic Microwave
Background (CMB)
Supernovae
Explosions of fixed
brightness
 Standard candles
 Luminosity vs. redshift plot
 SNe at high redshift
(z~0.75) appear dimmer
 Sensitive to ΩM - ΩΛ
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[Riess et al (Supernova Search Team Collaboration) ’98]
[Perlmutter et al (Supernova Cosmology Project Collaboration) ’98]
Cosmic Microwave Background
Primordial radiation from recombination era
 Blackbody spectrum of T=2.7 K
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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]
Baryon acoustic oscillations
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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]
Putting it
all together
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?
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Cosmic coincidence problem
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:
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– Tensor modes?
– Constraints on inflation?
… three, two, one,
and TAKE-OFF!
2. String Theory
Strings
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Quantum gravity
No point particles, but small strings
Unique theory
Bonus: gauge forces
Unification of four forces of Nature?
…and then some!
String theory has
many implications:
Supersymmetry
Extra
dimensions
Many vacua
(~10500)?
Dualities
Branes
& fluxes
How can one extract
4D physics from this?
Compactifications
Stable compactifications
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Simple compactifications
yield massless scalar fields,
so-called moduli, in 4D.
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Would give rise to a new
type of force, in addition to
gravity and gauge forces.
Has not been observed!
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Need to give mass terms to
these scalar fields (moduli
stabilisation).
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Extra ingredients of string
theory, such as branes and
fluxes, are crucial!
energy
simple
comp.
with fluxes
and branes
Scalar field
Moduli stabilisation
Flux compactifications
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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]
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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
Non-geometric
fluxes
G-structures
Generalised
geometries
3. How to Realise
Cosmic Acceleration
in String Theory
Cosmic acceleration
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Two periods of accelerated expansion:
- inflation in very early universe
- present-time acceleration
No microscopic understanding
Cosmic challenges for
fundamental physics!
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
Top-down approach
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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]
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 slowroll 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 2008-2013.
An example: moduli stabilisation in N=4.
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]
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[1: De Roo, Wagemans ’85]
[2: DR ’09]
De Sitter in N=4 & N=2?
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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]
Conclusions
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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!
Thanks for your attention!
Diederik Roest
DRSTP symposium
`Trends in Theory 2009’