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String/Brane Cosmology
…for those who have not yet
drunk the Kool-Aid
C.P. Burgess
with J.Blanco-Pillado, J.Cline, C. de Rham, C.Escoda, M.Gomez-Reino, D. Hoover, R.Kallosh,
A.Linde,F.Quevedo and A. Tolley
Outline
• Motivation• String Cosmology: Why Bother?
• Branes and ‘late-Universe’ cosmology• Some Dark (Energy) Thoughts
• String inflation• A Sledgehammer for a Nutcracker?
• Outlook
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
Science progresses because short- distance physics decouples from long distances.
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
Science progresses because short distance physics decouples from long distances.
* Inflationary fluctuations could well arise at very high energies: MI » 10-3 Mp
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
Science progresses because short distance physics decouples from long distances.
* Inflationary fluctuations could well arise at very high energies: MI » 10-3 Mp
* Cosmology (inflation, quintessence, etc) relies on finely-tuned properties of scalar potentials, which are extremely sensitive to short distances.
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
Science progresses because short distance physics decouples from long distances.
* Inflationary fluctuations could well arise at very high energies: MI » 10-3 Mp
* Cosmology (inflation, quintessence, etc) relies on finely-tuned properties of scalar potentials, which are extremely sensitive to short distances.
* Modifications to gravity (MOND, Bekenstein, DGP, etc) are very strongly constrained by UV consistency issues.
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
D branes in string theory are surfaces on which some strings must end, ensuring their low-energy modes are trapped on the brane.
Polchinski
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
In some cases this is where the Standard Model particles live.
Ibanez et al
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
Leads to the brane-world scenario, wherein we are all brane-bound.
Rubakov & Shaposhnikov
Strings, Branes and Cosmology
• Why doesn’t string theory decouple from cosmology?
• Why are branes important for cosmology and particle physics?
Identifies hidden assumptions which particle physicists and cosmologists have been making: eg: all interactions don’t see the same number of dimensions.
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
ADD
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
Horava & Witten, Lykken, Antoniadis
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
* Ordinary physics in extra dimensions (eg: warping) can have extraordinary implications for the low-energy 4D theory.
Randall & Sundrum
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
* Ordinary physics in extra dimensions (eg: warping) can have extraordinary implications for the low-energy 4D theory.
* Shows that the vacuum energy need not be directly tied to the cosmological constant, as had been thought.
ADKS, KSS
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
* Shows that the vacuum energy is not as directly tied to the cosmological constant
In 4D the cosmological constant problem arises because a vacuum energy is equivalent to a cosmological constant, and so also to a curved universe.
0 RgT
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
* Shows that the vacuum energy is not as directly tied to the cosmological constant
In higher D solutions exist having large 4D energy, but for which the 4D geometry is absolutely flat!
CG, ABPQ
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
* Shows that the vacuum energy is not as directly tied to the cosmological constant
Are the choices required for 4D flatness stable against renormalization?
With SUSY, quantum corrections are usually order M2/r2 but can be as small as 1/r4 .
BH
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
* Shows that the vacuum energy is not as directly tied to the cosmological constant
Are the choices required for 4D flatness stable against renormalization?
With SUSY, quantum corrections are usually order M2/r2 but can be as small as 1/r4
ABPQ
This can be small enough because 1/r can be as small as 10-3 eV (since r ~ m is possible)!!!
Branes and Naturalness
• Removal of such assumptions has allowed new insights into low-energy naturalness problems.
* Shows that extra dimensions can be as large as microns;
* Shows that the string scale could be as small as TeV
* Shows that the vacuum energy is not as directly tied to the cosmological constant
Are the choices required for 4D flatness stable against renormalization?
So far so good: quantum corrections are usually order M2/r2 but can be as small as 1/r4
BMQ, ,ABB, BC
Very predictive: time-dependent Dark Energy; tests of GR at both micron and astrophysical distances;
implications for the LHC; etc
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
]exp[)( 2 cbaV
42 1
)](log)log([r
rMcrMbaV
2
22
r
rML pkin
)/exp(0' baMrifV
Potential domination when:
Canonical Variables:
SLED: Observational Consequences
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
log vs log a
Radiation
Matter
Total Scalar
SLED: Observational Consequences
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
Radiation
Matter
Total Scalar
w Parameter:
andw vs log a
~ 0.7
w ~ – 0.9
m ~ 0.25
SLED: Observational Consequences
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
vs log a
03.0
SLED: Observational Consequences
• Quantum vacuum energy lifts flat direction.
• Specific types of scalar interactions are predicted.• Includes the Albrecht-
Skordis type of potential
• Preliminary studies indicate it is possible to have viable cosmology:• Changing G; BBN;…
• Quintessence cosmology
• Modifications to gravity
• Collider physics
• Neutrino physics
• Astrophysics
Albrecht, CB, Ravndal & Skordis
log r vs log a
SLED: Observational Consequences
SLED: Present Status
• Stability against loops?• What choices ensure
4D flatness?• Are these choices
stable against renormalization?
• Tuned initial conditions?• Do only special initial
conditions lead to the Universe we see around us?
SLED: Present Status
• 4D space is not flat for arbitrary brane - bulk couplings.
• Stability against loops?• What choices ensure
4D flatness?• Are these choices
stable against renormalization?
• Tuned initial conditions?• Do only special initial
conditions lead to the Universe we see around us?
ABPQ
SLED: Present Status
• 4D space is not flat for arbitrary brane - bulk couplings.
• Most brane pairs do not produce static solutions.
• Stability against loops?• What choices ensure
4D flatness?• Are these choices
stable against renormalization?
• Tuned initial conditions?• Do only special initial
conditions lead to the Universe we see around us?
BQTZ, TBDH
SLED: Present Status
• 4D space is not flat for arbitrary brane - bulk couplings.
• Most brane pairs do not produce static solutions.
• In some cases these choices appear to be stable against renormalization.
• Stability against loops?• What choices ensure
4D flatness?• Are these choices
stable against renormalization?
• Tuned initial conditions?• Do only special initial
conditions lead to the Universe we see around us?
BH
SLED: Present Status
• Initial conditions exist which lead to dynamics which can describe the observed Dark Energy.
• Stability against loops?• What choices ensure
4D flatness?• Are these choices
stable against renormalization?
• Tuned initial conditions?• Do only special initial
conditions lead to the Universe we see around us?
ABRS
SLED: Present Status
• Initial conditions exist which lead to dynamics which can describe the observed Dark Energy.
• Successful initial condition are scarce.
• Stability against loops?• What choices ensure
4D flatness?• Are these choices
stable against renormalization?
• Tuned initial conditions?• Do only special initial
conditions lead to the Universe we see around us?
TBDH
SLED: Present Status
• Initial conditions exist which lead to dynamics which can describe the observed Dark Energy.
• Successful initial condition are scarce.
• Explained by earlier dynamics (eg inflation)?
• Stability against loops?• What choices ensure
4D flatness?• Are these choices
stable against renormalization?
• Tuned initial conditions?• Do only special initial
conditions lead to the Universe we see around us?
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
Inflationary models must be embedded into a fundamental theory in order to explain:
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
Inflationary models must be embedded into a fundamental theory in order to explain:
* Why the inflaton potential has its particular finely-tuned shape
(and if anthropically explained, what assigns the probabilities?)
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
Inflationary models must be embedded into a fundamental theory in order to explain:
* Why the inflaton potential has its particular finely-tuned shape
(and if anthropically explained, what assigns the probabilities?)
* What explains any special choices for initial conditions
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
Inflationary models must be embedded into a fundamental theory in order to explain:
* Why the inflaton potential has its particular finely-tuned shape
(and if anthropically explained, what assigns the probabilities?)
* What explains any special choices for initial conditions
* Why the observed particles get heated once inflation ends.
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
Inflationary models must be embedded into a fundamental theory in order to explain:
* Why the inflaton potential has its particular finely-tuned shape
(and if anthropically explained, what assigns the probabilities?)
* What explains any special choices for initial conditions
* Why the observed particles get heated once inflation ends.
Can identify how robust inflationary predictions are to high-energy details, and so also what kinds of very high-energy physics might be detectable using CMB measurements.
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
String theory has many scalars having very flat potentials.
These scalars (called moduli) describe the shape and size of the various extra dimensions
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
String theory has many scalars having very flat potentials.
BUT their potentials are usually very difficult to calculate.
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
String theory has many scalars having very flat potentials.
BUT their potentials are usually very difficult to calculate.
A convincing case for inflation requires knowing the potential for all of the scalars.
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
String theory has many scalars having very flat potentials.
BUT their potentials are usually very difficult to calculate.
A convincing case for inflation requires knowing the potential for all of the scalars.
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
For Type IIB strings it is now known how to compute the potentials for some of the low-energy string scalars.
GKP
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
Branes want to squeeze extra dimensions while the fluxes they source want the extra dimensions to grow. The competition stabilizes many of the ‘moduli’
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned? The moduli which remain after
this stabilization can also acquire a potential due to nonperturbative effects. Plausibly estimated…KKLT models
KKLT, KKLMMT
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned? The moduli which remain after
this stabilization can also acquire a potential due to nonperturbative effects. Improved for P4[11169]
‘The Better Racetrack’Douglas & Denef
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned? The inflaton in these models can
describe the relative positions of branes; or the volume or shape of the extra dimensions.
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
The motion of several complex fields must generically be followed through a complicated landscape: many possible trajectories for each vacuum
String Inflation
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned? The potential can inflate, e.g. for
some choices for the properties of P4[11169] – giving rise to realistic inflationary fluctuations
The ‘Racetrack Eight’
String Inflation
CMB measurements begin to distinguish different inflationary models
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
Barger et al hep-ph/0302150
- model comparisons
String Inflation
CMB measurements begin to distinguish different inflationary models
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
WMAP preferred
- model comparisons
String Inflation
Trajectories through string landscape predict same regions as do their low-energy effective theories.
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
brane-antibrane
racetrack
- model comparisons
String Inflation
The measurements can already distinguish amongst some stringy inflationary models.
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
KKLMMT*
P4[11169]
WMAP preferred
- model comparisons
KKLMMT, BCSQ, Racetrack 8
String Inflation
Most inflationary trajectories require fine tuning as do their field theory counterparts…
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
- model comparisons
- naturalness
KKLMMT, BCSQ, Racetrack 8
String Inflation
‘Kahler moduli’ inflation may be an important exception: slow roll relies largely on generic approximations.
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
- model comparisons
- naturalness
BCSQ, Conlon & Quevedo
nn MbMBAV )/(exp)/(
srM
M 1,
String Inflation
Although robust against most stringy details, predictions for CMB can be sensitive to specific kinds of physics near horizon exit
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
H-1(t) (t)
Inflation Post-Inflation
Length
Time
p
oscillations 60 e-foldings
10-30 e-foldings
- model comparisons
- naturalness
- robustness
String Inflation
Although robust against most stringy details, predictions for CMB can be sensitive to specific kinds of physics near horizon exit
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
- model comparisons
- naturalness
- robustness
String Inflation
Although robust against most stringy details, predictions for CMB can be sensitive to specific kinds of physics near horizon exit
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
- model comparisons
- naturalness
- robustness
String Inflation
Although robust against most stringy details, predictions for CMB can be sensitive to specific kinds of physics near horizon exit
• Why try to embed inflation into string theory?
• Why is it hard?
• What have we learned?
- model comparisons
- naturalness
- robustness
Outlook
• Branes continue to provide a useful approach for naturalness problems.• Dark Energy, Inflation,…possibly more.
• We are getting very close to finding inflation in explicit controlled string calculations• Possible progress on fine-tunings;• New insights on reheating (eg cosmic strings);• Signals largely robust, except near horizon exit
• Possibly even more novel physics can arise!
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