Gravity and Extra Dimensions

Gravity and Extra Dimensions

Jos? Santiago Theory Group (Fermilab)

APS April meeting, Session Y4 (Gravity and Cosmology) Jacksonville (FL) April 14-17, 2007

Outline

Introduction Breakthrough: Braneworld gravity Understanding the Acceleration of the Universe Infinite Extra Dimensions: DGP Higher Codimension Branes and SUSY: SLED Conclusions

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Introduction

Once upon a time (1920s) Kaluza and Klein tried to unify gravity and electromagnetism in 5 dimensions The idea did not work .... Gravity couples universally to energy ... and was forgotten for many years

4d scalar

4D graviton (GR)

4D vector (QED)

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Introduction

New motivation for Extra Dimensions came from string theory (1980s) 6 extra dimensions are predicted in consistent string models They were considered to be tiny small

Higher dimensional fields decompose in massless modes plus modes with masses ED effects irrelevant at low energies

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Braneworld Gravity

String theory motivated a breakthrough in gravity and extra dimensions (1990s)

Gravity (closed strings) propagate the extra dimensions Gauge theories (open strings) are stuck at branes

Extra Dimensions

Gauge boson

Graviton

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Braneworld Gravity

Braneworld gravity allows many new possibilities

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Braneworld Gravity

Braneworld gravity allows many new possibilities

ADD (1998): 2 or more ED with R~0.1 mm~1/(10-4 eV) are allowed RS (1999): Infinite (strongly curved) ED are allowed DGP (2000): Even infinite flat ED are allowed ... and could explain the acceleration of the Universe ...

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Understanding the Acceleration of the Universe

The Universe is currently accelerating All cosmological data agrees very well with a cosmological constant It’s 60 orders of magnitude smaller than expected!

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Extra-dimensional takes at the Cosmological Constant problem

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Dvali-Gabadadze-Porratti Model

DGP: Gravitational action in M5 plus a flat brane with an induced Einstein-Hilbert term

Generated by quantum corrections

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Dvali-Gabadadze-Porratti Model

DGP: Gravitational action in M5 plus a flat brane with an induced Einstein-Hilbert term Gravity due to a bound state of the continuum of graviton KK modes Modification of gravity at large (cosmological) scales 4D at short distances but turn 5D at large distances

Generated by quantum corrections

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Dvali, Gabadadze, Porratti ’00; ...

DGP Cosmology

Modified Friedman equation with two branches

Standard branch (-) Standard early cosmology 5D late time cosmology

Selfaccelerating branch (+) Standard early cosmology Late time acceleration

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

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

Comparison with Experiment

Flat DGP excluded by geometrical probes

Open DGP only marginally worse than flat ?CDM (1 extra parameter) Non-geometrical probes can tell DGP and ?CDM apart

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Song, Sawicki, Hu ‘06

Caveats

There is an intrinsic strong coupling in the model Difficult to compute solutions valid at all scales Ghosts (negative energy states) present in linear perturbations around the selfaccelerating branch The model may have problems with a local, causal, unitary UV completion Might be solved at the non-linear level Not obvious solution (yet) to the cosmological constant problem

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

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

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

Generalizations of DGP

Let us consider a more general model with a negative bulk cosmological constant and two branes with arbitrary tensions and localized curvature terms We can have (Anti) de Sitter or flat branes at an arbitrary separation Bulk curvature can help understand problems

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

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

Generalizations of DGP

We can study all the models at once, as a function of the input parameters We have not found completely ghost-free solutions but there are examples of self-accelerating solutions with a ghost that is different from the one in DGP

No DGP ghost

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

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

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

Supersymmetric Large Extra DimensionS (SLEDS)

Brane with two extra dimensions Brane tension does not curve the bulk Conical singularity that cancels the brane tension Supersymmetry cancels out quantum corrections to the cosmological constant above MSUSY

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Aghababaie, Burgess, Parameswaran, Quevedo ’04

SLEDS

The Model: 6D Supergravity with two 3-branes Compactification by fluxes with R~0.1 mm Conical singularities at brane locations flat branes

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

SLEDS

The Model: 6D Supergravity with two 3-branes Compactification by fluxes with R~0.1 mm Conical singularities at brane locations flat branes

Most general solution with axial symm. and maximally 4D symm. has flat branes

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Gibbons, Guvens, Pope, 03

SLEDS

Contribution to low-energy cosmological constant: Brane tension: SUSY badly broken on the brane Classical bulk contribution: conical singularity Bulk quantum contribution: determined by bulk SUSY

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Caveats

Fundamental explanation of scales How to explain 0.1 mm extra dimensions? But relates hierarchy and cosmological constant problems Detailed analysis of dynamics of relaxation Higher curvature terms Thick branes Quantum corrections might be too big Will be experimentally tested in the near future

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

Bostock, Gregory, Navarro, Santiago 04

Navarro, Santiago 05

Conclusions

Extra dimensions give a new perspective to gravity Braneworlds: New freedom to attack old problems DGP model: Can explain acceleration without a cosmological constant Strongly coupled: difficult to compute at all scales SLEDS Can explain the smallness of the “cosmological constant” Full time-dependent equations difficult to solve Not yet a solution to the CC problem but ...

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions

It’s difficult to make predictions

.. ... especially about the future

Yogi Berra

APS meeting, April 17, 2007

J. Santiago, Gravity and Extra Dimensions