Transcript How stable are extra dimensions?

Modern cosmology: a challenge
for fundamental physics
Diederik Roest
(University of Groningen, The Netherlands)
November 6, 2009 – UAM, Ciudad de México
Why is there any relation at
Size matters!
all between cosmology and
string theory?
Outline
1.
2.
3.
Modern Cosmology
Fundamental Physics
How to Realise Cosmic Acceleration
in String Theory
1. Modern Cosmology
Cosmological principle
Universe has no structure at large scales:
stars -> galaxies -> clusters -> superclusters -> …
No preferred points or directions: homogeneous and
isotropic.
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) / ρcrit(t)
Table of content?
What are the ingredients of the universe?
Dominant components:
 w=0
- non-relativistic matter M (attractive)
 w=-1
- cosmological constant Λ (repulsive)
History of CC
Who ordered Λ?
 First introduced by Einstein
to counterbalance matter
 Overtaken by expansion
of universe
Convoluted history through the 20th century.
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

[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
Concordance Model
Open questions:
 What are dark components made of?
 CC unnaturally small: 30 orders below Planck mass!
 Fine-tuning mechanism?
 Anthropic reasoning?
 Cosmic coincidence problem
Inflation
Period of accelerated expansion in very early universe
(~10-36 sec) to explain:
 Cosmological principle
 Why universe is flat
 Absence of magnetic monopoles
Bonus: quantum fluctuations during inflation can become
source for structure formation ( CMB).
Probes physics of very high energies (GUT scale ~ 1016
GeV).
The future is bright!

Many models of inflation are
possible

Inflationary properties are
now being measured

Planck satellite:
– Tensor modes?
– Constraints on inflation?
… three, two, one,
and TAKE-OFF!
[May 14, 2009]
2. Fundamental Physics
Elementary particle physics

Standard Model (1970 - )
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).

Unprecedented
experimental
verification!
Any questions?
Where is Higgs particle?
Why three generations?
Include gravity?
Effective description of fundamental theory?
Experimental input?
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

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!
energy
simple
comp.
with fluxes
and branes
Scalar field
3. How to Realise
Cosmic Acceleration
in String Theory
Cosmic acceleration
Cosmic challenges
for fundamental
physics!
Two periods of accelerated expansion:

inflation in very early universe

present-time acceleration
No microscopic understanding
Cosmic acceleration
Modelled by scalar field with non-trivial scalar potential V
¡ V 0¢2
² = 1M 2
¿ 1;
P V
2
Slow-roll parameters:
V 00
´ = M2
¿ 1:
P V
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.
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 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
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.
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 slowroll 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]
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]
4. Conclusions
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
(University of Groningen, The Netherlands)
November 6, 2009 – UAM, Ciudad de México