Gravity and Extra Dimensions José Santiago Theory Group (Fermilab) APS April meeting, Session Y4...

Gravity and Extra DimensionsGravity and Extra Dimensions

José SantiagoJosé Santiago

Theory Group (Fermilab)Theory Group (Fermilab)

APS April meeting, Session Y4 (Gravity and

Cosmology)

Jacksonville (FL) April 14-17, 2007

J. Santiago, Gravity and Extra DimensionsAPS meeting, April 17, 2007

OutlineOutline

IntroductionIntroduction

Breakthrough: Braneworld gravityBreakthrough: Braneworld gravity

Understanding the Acceleration of the Understanding the Acceleration of the

UniverseUniverse Infinite Extra Dimensions: DGPInfinite Extra Dimensions: DGP

Higher Codimension Branes and SUSY: SLEDHigher Codimension Branes and SUSY: SLED

ConclusionsConclusions



Once upon a time (1920s) Kaluza and Once upon a time (1920s) Kaluza and Klein tried to unify gravity and Klein tried to unify gravity and electromagnetism in 5 dimensionselectromagnetism in 5 dimensions

The idea did not work ....The idea did not work .... Gravity couples universally to energyGravity couples universally to energy

... and was forgotten for many ... and was forgotten for many yearsyears

4D graviton

(GR)

4d scalar

4D vector

(QED)



New motivation for Extra Dimensions New motivation for Extra Dimensions came from string theory (1980s)came from string theory (1980s)

6 extra dimensions are predicted in 6 extra dimensions are predicted in consistent string models consistent string models

They were considered to be tiny small They were considered to be tiny small

Higher dimensional fields Higher dimensional fields decompose in massless decompose in massless modes plus modes with modes plus modes with massesmasses

ED effects irrelevant at ED effects irrelevant at low energieslow energies


Braneworld GravityBraneworld Gravity

String theory motivated a breakthrough String theory motivated a breakthrough in gravity and extra dimensions in gravity and extra dimensions (1990s) (1990s) Gravity (Gravity (closed stringsclosed strings) propagate the extra ) propagate the extra dimensionsdimensions

Gauge theories (Gauge theories (open stringsopen strings) are stuck at branes) are stuck at branes

Extra Dimensions

Graviton

Gauge boson



Braneworld gravity allows many new Braneworld gravity allows many new possibilitiespossibilities

Gravity

SMED Bulk



Braneworld gravity allows many new Braneworld gravity allows many new possibilitiespossibilities

Gravity

SMED Bulk

ADDADD (1998): 2 or more ED with (1998): 2 or more ED with R~0.1 mm~1/(10R~0.1 mm~1/(10-4-4 eV) are eV) are allowedallowed

RSRS (1999): Infinite (strongly (1999): Infinite (strongly curved) ED are allowedcurved) ED are allowed

DGPDGP (2000): Even infinite (2000): Even infinite flat ED are allowed ... and flat ED are allowed ... and could explain the could explain the acceleration of the Universeacceleration of the Universe

......


Understanding the Acceleration of the Understanding the Acceleration of the UniverseUniverse

The Universe is currently acceleratingThe Universe is currently accelerating All cosmological data agrees very well All cosmological data agrees very well with a cosmological constantwith a cosmological constant

It’s 60 orders of magnitude smaller It’s 60 orders of magnitude smaller than expected!than expected!


Extra-dimensional takes at the Cosmological Constant

problem


Dvali-Gabadadze-Porratti ModelDvali-Gabadadze-Porratti Model

DGPDGP: Gravitational action in : Gravitational action in MM55 plus a plus a flat brane with an induced Einstein-flat brane with an induced Einstein-Hilbert termHilbert term

Generated by quantum corrections


Dvali-Gabadadze-Porratti ModelDvali-Gabadadze-Porratti Model

DGPDGP: Gravitational action in : Gravitational action in MM55 plus a plus a flat brane with an induced Einstein-flat brane with an induced Einstein-Hilbert termHilbert term

Gravity due to a bound state of the Gravity due to a bound state of the continuumcontinuum of graviton KK modes of graviton KK modes

Modification of gravity at large Modification of gravity at large (cosmological) scales(cosmological) scales 4D at short distances but turn 5D at large 4D at short distances but turn 5D at large distancesdistances

Generated by quantum corrections

Dvali, Gabadadze, Porratti ’00; ...


DGP CosmologyDGP Cosmology

Modified Friedman equation with two Modified Friedman equation with two branchesbranches

Deffayet ’01; Deffayet, Dvali, Gabadadze ’02; ...

Standard branch (-)Standard branch (-) Standard early cosmologyStandard early cosmology

5D late time cosmology5D late time cosmology

Selfaccelerating Selfaccelerating branch (+)branch (+) Standard early Standard early cosmologycosmology

Late time Late time accelerationacceleration


Comparison with ExperimentComparison with Experiment

Flat DGP excluded by geometrical Flat DGP excluded by geometrical probesprobes

Open DGP only Open DGP only marginally worse marginally worse than flat than flat ΛΛCDMCDM (1 extra (1 extra parameter)parameter)

Non-geometrical Non-geometrical probes can tell probes can tell DGP and DGP and ΛΛCDM CDM apartapart

Song, Sawicki, Hu ‘06


CaveatsCaveats

There is an intrinsic strong coupling in the There is an intrinsic strong coupling in the modelmodel Difficult to compute solutions valid at all scalesDifficult to compute solutions valid at all scales

Ghosts (negative energy states) present in Ghosts (negative energy states) present in linear perturbations around the linear perturbations around the selfaccelerating branchselfaccelerating branch

The model may have problems with a local, The model may have problems with a local, causal, unitary UV completioncausal, unitary UV completion Might be solved at the non-linear levelMight be solved at the non-linear level

Not obvious solution (yet) to the Not obvious solution (yet) to the cosmological constant problemcosmological constant problem

Luty, Porrati, Rattazzi ’03; Nicolis, Rattazzi ’04; Koyama ’05; Gorbunov, Koyama, Sibiryakov ’05; Charmousis, Gregory, Kaloper, Padilla ’06; Carena, Lykken, Park, Santiago ‘06

Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi ‘06

Vainshtein ’72; Deffayet, Dvali, Gabadadze, Vainshtein ’01; Gruzinov ’01; Luty, Porrati, Rattazzi ’03; Rubakov ’03


Let us consider a more general model Let us consider a more general model with a negative bulk cosmological with a negative bulk cosmological constant and two branes with arbitrary constant and two branes with arbitrary tensions and localized curvature termstensions and localized curvature terms

We can have (Anti) de Sitter or flat We can have (Anti) de Sitter or flat branes at an arbitrary separationbranes at an arbitrary separation

Bulk curvature can help understand Bulk curvature can help understand problemsproblems

Generalizations of DGPGeneralizations of DGPBao, Carena, Lykken, Park, Santiago ’05-06


We can study all the models at once, We can study all the models at once, as a function of the input parametersas a function of the input parameters

We have not found completely ghost-We have not found completely ghost-free solutions but there are examples free solutions but there are examples of self-accelerating solutions with a of self-accelerating solutions with a ghost that is different from the one ghost that is different from the one in DGP in DGP

Generalizations of DGPGeneralizations of DGP

No DGP ghost

There is a massless graviton ghost that does not decouple in the limit of an infinite extra dimension

Bao, Carena, Lykken, Park, Santiago ’05-06


Brane with two extra dimensionsBrane with two extra dimensions Brane tension does not curve the bulkBrane tension does not curve the bulk Conical singularity that cancels the brane Conical singularity that cancels the brane tensiontension

Supersymmetry cancels out quantum Supersymmetry cancels out quantum corrections to the cosmological corrections to the cosmological constant above Mconstant above MSUSYSUSY

Supersymmetric Large Extra DimensionS Supersymmetric Large Extra DimensionS (SLEDS)(SLEDS)

Aghababaie, Burgess, Parameswaran, Quevedo ’04


The Model:The Model: 6D Supergravity with two 3-branes6D Supergravity with two 3-branes

Compactification by fluxes with R~0.1 mmCompactification by fluxes with R~0.1 mm Conical singularities at brane locations Conical singularities at brane locations flat branes flat branes

SLEDSSLEDS


The Model:The Model: 6D Supergravity with two 3-branes6D Supergravity with two 3-branes

Compactification by fluxes with R~0.1 mmCompactification by fluxes with R~0.1 mm Conical singularities at brane locations Conical singularities at brane locations flat branes flat branes

SLEDSSLEDS

Most general Most general solution with solution with axial symm. and axial symm. and maximally 4D symm. maximally 4D symm. has has flat branes flat branes Gibbons, Guvens, Pope, 03


Contribution to low-energy cosmological Contribution to low-energy cosmological constant:constant: Brane tension: SUSY badly broken on the Brane tension: SUSY badly broken on the branebrane

Classical bulk contribution: conical Classical bulk contribution: conical singularitysingularity

Bulk quantum contribution: determined by Bulk quantum contribution: determined by bulk SUSYbulk SUSY

SLEDSSLEDS


Fundamental explanation of scalesFundamental explanation of scales How to explain 0.1 mm extra dimensions?How to explain 0.1 mm extra dimensions? But relates hierarchy and cosmological constant But relates hierarchy and cosmological constant problemsproblems

Detailed analysis of dynamics of relaxationDetailed analysis of dynamics of relaxation Higher curvature termsHigher curvature terms Thick branesThick branes

Quantum corrections might be too bigQuantum corrections might be too big

Will be experimentally tested in the near Will be experimentally tested in the near futurefuture

CaveatsCaveats

Navarro, Santiago 05

Bostock, Gregory, Navarro, Santiago 04


Extra dimensions give a new perspective to Extra dimensions give a new perspective to gravitygravity

Braneworlds: New freedom to attack old problemsBraneworlds: New freedom to attack old problems

DGP model:DGP model: Can explain acceleration without a cosmological Can explain acceleration without a cosmological constantconstant

Strongly coupled: difficult to compute at all scalesStrongly coupled: difficult to compute at all scales

SLEDSSLEDS Can explain the smallness of the “cosmological Can explain the smallness of the “cosmological constant”constant”

Full time-dependent equations difficult to solveFull time-dependent equations difficult to solve

Not yet a solution to the CC problem but ...Not yet a solution to the CC problem but ...

ConclusionsConclusions


It’s difficult to make predictions ... ... especially about the future

Yogi Berra

Gravity and Extra Dimensions José Santiago Theory Group (Fermilab) APS April meeting, Session Y4...

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