String/Brane Cosmology

String/Brane Cosmology

COSMO 07 – University of Sussex

C.P. Burgess

String/Brane Cosmology

…for those who have not yet

drunk the Kool-Aid

with J.Blanco-Pillado, J.Cline, K. das Gupta, C. de Rham, C.Escoda, M.Gomez-Reino, D. Hoover, R.Kallosh,

A.Linde,F.Quevedo, G. Tasinato and A. Tolley

Cosmo 07

On the shoulders of giants

A. Salam, E. Sezgin, H. Nishino,G. Gibbons, S. Kachru E. Silverstein, R. Guven, C. Pope, K. Maeda, M. Sasaki, V. Rubakov, R. Gregory, I. Navarro, J. Santiago, S. Carroll, C. Guica, C. Wetterich, S. Randjbar-Daemi, F. Quevedo, Y. Aghababaie, S. Parameswaran, J. Cline, J. Matias, G. Azuelos, P-H. Beauchemin, A. Albrecht, C. Skordis, F. Ravndal, I. Zavala, G. Tasinato, J. Garriga, M. Porrati, H.P. Nilles, A. Papazoglou, H. Lee, N. Arkani-Hamad, S. Dimopoulos, N. Kaloper, R. Sundrum, D. Hoover, A. Tolley, C. de Rham, S. Forste, Z. Lalak, S. Lavingnac, C. Grojean, C. Csaki, J. Erlich, T. Hollowood, H. Firouzjahi, J. Chen, M. Luty, E. Ponton, P. Callin, D. Ghilencea, E. Copeland, O. Seto, V. Nair, S. Mukhoyama, Y. Sendouda, H. Yoshigushi, S. Kinoshita, A. Salvio, J. Duscheneau, J. Vinet, M. Giovannini, M. Graesser, J. Kile, P. Wang, P. Bostok, G. Kofinas, C. Ludeling, A. Nielsen, B. Carter, D. Wiltshire. C. K. Akama, S. Appleby, F. Arroja, D. Bailin, M. Bouhmadi-Lopez, M. Brook, R. Brown, C. Byrnes, G. Candlish, A. Cardoso, A. Chatterjee, D. Coule, S. Creek, B. Cuadros-Melgar, S. Davis, B. de Carlos, A. de Felice, G. de Risi, C. Deffayet, P. Brax, D. Easson, A. Fabbri, A. Flachi, S. Fujii, L. Gergely, C. Germani, D. Gorbunov, I. Gurwich, T. Hiramatsu, B. Hoyle, K. Izumi, P. Kanti, S. King, T. Kobayashi, K. Koyama, D. Langlois, J. Lidsey, F. Lobo, R. Maartens, N. Mavromatos, A. Mennim, M. Minamitsuji, B. Mistry, S. Mizuno, A. Padilla, S. Pal, G. Palma, L. Papantonopoulos, G. Procopio, M. Roberts, M. Sami, S. Seahra, Y. Sendouda, M. Shaeri, T. Shiromizu, P. Smyth, J. Soda, K. Stelle, Y. Takamizu, T. Tanaka, T. Torii, C. van de Bruck, D. Wands, V. Zamarias, H. Ziaeepour

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Outline

• Motivation• String Cosmology: Why Does it Make Sense?

• Branes and ‘late-Universe’ cosmology• Some Dark (Energy) Thoughts

• String inflation• A Sledgehammer for a Nutcracker?

• Outlook

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Strings, Branes and Cosmology

• Why doesn’t string theory decouple from cosmology?

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Science progresses because short- distance physics decouples from long distances.

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Science progresses because short distance physics decouples from long distances.

* Inflationary fluctuations could well arise at very high energies: MI » 10-3 Mp

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* Cosmology (inflation, quintessence, modified gravity, etc) relies on properties which can be extremely sensitive to short distances.

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* Cosmology (inflation, quintessence, modified gravity, etc) relies on properties which can be extremely sensitive to short distances.

* String theory suggests important changes in the low-energy degrees of freedom: branes.

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• 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

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In some cases this is where the Standard Model particles live.

Ibanez et al

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Leads to the brane-world scenario, wherein we are all brane-bound.

Rubakov & Shaposhnikov

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Identifies hidden assumptions about low energy theory whose relaxation might help with low energy naturalness problems.

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Naturalness

• Ideas for what lies beyond the Standard Model are largely driven by ‘technical naturalness’.• Motivated by belief that SM is an effective field theory.

HHmLSM*2 + dimensionless

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Naturalness



M ~ 1011 GeV

Mw102 GeV

Mp ~1018 GeV

20

2 mm

BUT: effective theory can be defined at many scales

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Naturalness



M ~ 1011 GeV

Mw102 GeV

Mp ~1018 GeV

20

2 mm

221

2 Mkmm


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Naturalness



M ~ 1011 GeV

Mw102 GeV

Mp ~1018 GeV

20

2 mm

221

2 Mkmm


Hierarchy Problem: These must cancel to 20 digits!!

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Naturalness


HHLSM*2 + dimensionless

Hierarchy problem: Since the largest mass dominates, why isn’t m ~ MGUT or Mp ??

• Three approaches to solve the Hierarchy problem:

Compositeness: H is not fundamental at energies E À Mw

Supersymmetry: there are new particles at E À Mw and a symmetry which ensures cancellations so m2 ~ MB

2 – MF2

Extra Dimensions: the fundamental scale is much smaller than Mp , much as

GF-1/2 > Mw

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Naturalness in Crisis


• The Standard Model’s dirty secret: there are really two unnaturally small terms.


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me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

440

4 mk

4441

4 mkmk ee

Can apply same argument to scales between TeV and sub-eV scales.

Cosmological Constant Problem: Must cancel to 32 decimal places!!

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• The Standard Model’s dirty secret: there are really two unnaturally small terms.


Harder than the Hierarchy problem:

Integrating out the electron already gives too large a contribution!!

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• Dark energy vs vacuum energy

• Why must the vacuum energy be large?

me ~ 106 eV

m10-2 eV

mw ~1011 eV

m ~ 108 eV

Seek to change properties of low-energy particles (like the electron) so that their zero-point energy does not gravitate, even though quantum effects do gravitate in atoms!

Why is this seen………………but not this?

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Cosmological constant problem: Why is ~ 10-3 eV rather than me , Mw , MGUT or Mp?

• Approaches to solve the Hierarchy problem at ~ 10-2 eV?

Compositeness: graviton is not fundamental at energies E À Supersymmetry: there are new particles at E À and a symmetry which ensures cancellations so 2 ~ MB

2 – MF2

Extra Dimensions: the fundamental scale is much smaller than Mp

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Cosmological constant problem: Why is ~ 10-3 eV rather than me , Mw , MGUT or Mp?

• Approaches to solve the Hierarchy problem at ~ 10-2 eV?

Compositeness: graviton is not fundamental at energies E À Supersymmetry: there are new particles at E À and a symmetry which ensures cancellations so 2 ~ MB

2 – MF2

Extra Dimensions: the fundamental scale is much smaller than Mp

??

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How Extra Dimensions Help

• 4D CC vs 4D vacuum energy

• Branes and scales

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A cosmological constant

TGgG 8

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A cosmological constant is not distinguishable from a Lorentz invariant vacuum energy

vs

gGTGG 488

TGgG 8

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A cosmological constant is not distinguishable* from a Lorentz invariant vacuum energy

vs

gGTGG 488

TGgG 8

* in 4 dimensions…

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In higher dimensions a 4D vacuum energy, if localized in the extra dimensions, can curve the extra dimensions instead of the observed four.

Chen, Luty & PontonArkani-Hamad et al

Kachru et al,Carroll & Guica

Aghababaie, et al

xtT NMMN2

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These scales are natural using standard 4D arguments.

m ~ mw2/Mp

~ 10-2 eV

H ~ m2/Mp

mw

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These scales are natural using standard 4D arguments.

m ~ mw2/Mp

~ 10-2 eV

H ~ m2/Mp

mw Extra dimensions

could start here, if there are only two of them.

Arkani Hamed, Dvali, Dimopoulos

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Only gravity gets modified over the most dangerous distance scales!

m ~ mw2/Mp

~ 10-2 eV

H ~ m2/Mp

mw Must rethink how the vacuum gravitates in 6D for these scales.

SM interactions do not change at all!

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The SLED Proposal

• Suppose physics is extra-dimensional above the 10-2 eV scale.

• Suppose the physics of the bulk is supersymmetric.

Aghababaie, CB, Parameswaran & Quevedo

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The SLED Proposal



• 6D gravity scale: Mg ~ 10 TeV

• KK scale: 1/r ~ 10-2 eV

• Planck scale: Mp ~ Mg2 r

Arkani-Hamad, Dimopoulos & Dvali

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The SLED Proposal




• Choose bulk to be supersymmetric(no 6D CC allowed)

Nishino & Sezgin

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The SLED Proposal




• SUSY Breaking on brane: TeVin bulk: Mg

2/Mp ~1/r

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The SLED Proposal

4D graviton

m ~ Mw2/Mp

H ~ m2/Mp

Mw

Particle Spectrum:

4D scalar: e r2 ~ const

SM on brane – no partners

Many KK modes in bulk

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What Needs Understanding

• Classical part of the argument:• What choices must be

made to ensure 4D flatness?

• Quantum part of the argument:• Are these choices stable

against renormalization?

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• Search for solutions to 6D supergravity: • What bulk geometry arises from a given

brane configuration?

• What is special about the ones which are 4D flat?

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• Search for solutions to 6D supergravity: • What bulk geometry arises from a given

brane configuration?

• What is special about the ones which are 4D flat?

• Bulk solutions known for most properties for 2 brane sources;

• Most have runaway behaviour, with extra dimensions growing or collapsing

• Sufficient condition for flatness is absence of brane-dilaton coupling.

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• When both branes have conical singularities all static solutions have 4D minkowski geometry.

• Conical singularities require vanishing dilaton coupling to branes (and hence scale invariant)

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• Brane loops on their own cannot generate dilaton couplings from scratch.

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• Bulk loops can generate brane-dilaton coupling but TeV scale modes are suppressed at one loop by 6D supersymmetry

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• Bulk loops can generate brane-dilaton coupling but TeV scale modes are suppressed at one loop by 6D supersymmetry

• Each bulk loop costs power of e ~ 1/r2 and so only a few loops must be checked…..

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Observational Consequences

• Quintessence cosmology

• Modifications to gravity

• Collider physics

• Neutrino physics?

• And more!

SUSY broken at

the TeV scale,

but not the MSSM!

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Summary

• It is too early to abandon naturalness as a fundamental criterion!

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Summary


• It is the interplay between cosmological phenomenology and microscopic constraints which will make it possible to solve the Dark Energy problem.• Technical naturalness provides a crucial clue.

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Summary



• 6D brane-worlds allow progress on technical naturalness:• Vacuum energy not equivalent to curved 4D

• Are ‘Flat’ choices stable against renormalization?

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Summary





• Tuned initial conditions• Much like for the Hot Big Bang Model.

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Summary





• Tuned initial conditions• Much like for the Hot Big Bang Model.

• Enormously predictive, with many observational consequences.• Cosmology at Colliders! Tests of gravity…

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String Inflation

• Why try to embed inflation into string theory?

• Why is it hard?

• What have we learned?

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String Inflation


• Why is it hard?


Inflationary models must be embedded into a fundamental theory in order to explain:

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String Inflation


• Why is it hard?



* Why the inflaton potential has its particular finely-tuned shape

(and if anthropically explained, what assigns the probabilities?)

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String Inflation


• Why is it hard?





* What explains any special choices for initial conditions

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String Inflation


• Why is it hard?






* Why the observed particles get heated once inflation ends.

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String Inflation


• Why is it hard?






* 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.

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String Inflation


• Why is it hard?


String theory has many scalars having very flat potentials.

These scalars (called moduli) describe the shape and size of the various extra dimensions

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String Inflation


• Why is it hard?



BUT their potentials are usually very difficult to calculate.

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String Inflation


• Why is it hard?



BUT their potentials are usually very difficult to calculate.

A convincing case for inflation requires knowing the potential for all of the scalars.

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String Inflation


• Why is it hard?


For Type IIB strings it is now known how to compute the potentials for some of the low-energy string scalars.

GKP

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String Inflation


• Why is it hard?


Branes want to squeeze extra dimensions while the fluxes they source want the extra dimensions to grow. The competition stabilizes many of the ‘moduli’

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String Inflation


• 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

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String Inflation


• 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

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String Inflation


• 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.

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String Inflation


• Why is it hard?


The motion of several complex fields must generically be followed through a complicated landscape: many possible trajectories for each vacuum

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String Inflation


• 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’

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String Inflation

CMB measurements begin to distinguish different inflationary models


• Why is it hard?


Barger et al hep-ph/0302150

- model comparisons

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String Inflation

CMB measurements begin to distinguish different inflationary models


• Why is it hard?


WMAP preferred

- model comparisons

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String Inflation

Trajectories through string landscape predict same regions as do their low-energy effective theories.


• Why is it hard?


brane-antibrane

racetrack

- model comparisons

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String Inflation

The measurements can already distinguish amongst some stringy inflationary models.


• Why is it hard?


KKLMMT*

P4[11169]

WMAP preferred

- model comparisons

KKLMMT, BCSQ, Racetrack 8

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String Inflation

Most inflationary trajectories require fine tuning as do their field theory counterparts…


• Why is it hard?


- model comparisons

- naturalness

KKLMMT, BCSQ, Racetrack 8

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String Inflation

Two possible exceptions:

DBI Inflation: relativistic brane motion where H changes slowly.

Kahler moduli inflation: slow roll from ‘generic’ approximations.


• Why is it hard?


- model comparisons

- naturalness

Silverstein & TongBCSQ, Conlon & Quevedo

nn MbMBAV )/(exp)/(

srM M 1,

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String Inflation

Although robust against most stringy details, predictions for CMB can be sensitive to specific kinds of physics near horizon exit


• Why is it hard?


H-1(t) (t)

Inflation Post-Inflation

Length

Time

p

oscillations 60 e-foldings

10-30 e-foldings

- model comparisons

- naturalness

- robustness

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String Inflation

Although robust against most stringy details, predictions for CMB can be sensitive to specific kinds of physics near horizon exit


• Why is it hard?


- model comparisons

- naturalness

- robustness

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Outlook

• Branes continue to provide a useful approach for naturalness problems.• Dark Energy, Hierarchy Problem, Inflation… more?

• We are 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

• Small tensor perturbations?

• Possibly even more novel physics can arise!

Cosmo 07

fin

String/Brane Cosmology

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