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Gravity and Extra Dimensions
José Santiago
Theory Group (Fermilab)
APS April meeting, Session Y4
(Gravity and Cosmology)
Jacksonville (FL) April 14-17, 2007
Outline
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Introduction
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Breakthrough: Braneworld gravity
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Understanding the Acceleration of the Universe
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Infinite Extra Dimensions: DGP
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Higher Codimension Branes and SUSY: SLED
Conclusions
APS meeting, April 17, 2007
J. Santiago, Gravity and Extra Dimensions
Introduction
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Once upon a time (1920s) Kaluza and Klein tried to
unify gravity and electromagnetism in 5 dimensions
4D graviton
4D vector
(GR)
(QED)
4d scalar
The idea did not work ....
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Gravity couples universally to energy
... and was forgotten for many years
APS meeting, April 17, 2007
J. Santiago, Gravity and Extra Dimensions
Introduction
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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
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APS meeting, April 17, 2007
Higher dimensional fields
decompose in massless modes
plus modes with masses
ED effects irrelevant at low
energies
J. Santiago, Gravity and Extra Dimensions
Braneworld Gravity
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String theory motivated a breakthrough in gravity
and extra dimensions (1990s)
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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
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Braneworld gravity allows many new possibilities
ED Bulk
SM
Gravity
APS meeting, April 17, 2007
J. Santiago, Gravity and Extra Dimensions
Braneworld Gravity
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Braneworld gravity allows many new possibilities
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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
...
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ED Bulk
SM
Gravity
J. Santiago, Gravity and Extra Dimensions
Understanding the Acceleration of the Universe
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The Universe is currently accelerating
All cosmological data agrees very well with a
cosmological constant
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It’s 60 orders of magnitude smaller than expected!
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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
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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
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DGP: Gravitational action in M5 plus a flat brane
with an induced Einstein-Hilbert term
Dvali, Gabadadze, Porratti ’00; ...
Generated by quantum corrections
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Gravity due to a bound state of the continuum of
graviton KK modes
Modification of gravity at large (cosmological) scales
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4D at short distances but turn 5D at large distances
APS meeting, April 17, 2007
J. Santiago, Gravity and Extra Dimensions
DGP Cosmology
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Modified Friedman equation with two branches
Deffayet ’01; Deffayet, Dvali, Gabadadze ’02; ...
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Standard branch (-)
 Standard early cosmology
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5D late time cosmology
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Selfaccelerating branch (+)
 Standard early cosmology
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Late time acceleration
J. Santiago, Gravity and Extra Dimensions
Comparison with Experiment
Song, Sawicki, Hu ‘06
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Flat DGP excluded by geometrical probes
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Open DGP only
marginally worse
than flat ΛCDM
(1 extra parameter)
Non-geometrical
probes can tell DGP
and ΛCDM apart
J. Santiago, Gravity and Extra Dimensions
Caveats
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There is an intrinsic strong coupling in the model
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Vainshtein ’72; Deffayet, Dvali,
Gabadadze, Vainshtein ’01; Gruzinov ’01;
Luty, Porrati, Rattazzi ’03; Rubakov ’03
Difficult to compute solutions valid at all scales
Ghosts (negative energy states) present in linear
perturbations around the selfaccelerating branch
Luty, Porrati, Rattazzi ’03; Nicolis, Rattazzi ’04; Koyama ’05; Gorbunov, Koyama, Sibiryakov ’05;
Charmousis, Gregory, Kaloper, Padilla ’06; Carena, Lykken, Park, Santiago ‘06
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The model may have problems with a local, causal,
Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi ‘06
unitary UV completion
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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
Generalizations of DGP
Bao, Carena, Lykken, Park, Santiago ’05-06
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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
Generalizations of DGP
Bao, Carena, Lykken, Park, Santiago ’05-06
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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
Supersymmetric Large Extra DimensionS (SLEDS)
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Brane with two extra dimensions
Aghababaie, Burgess,
Parameswaran, Quevedo ’04
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Brane tension does not curve the bulk
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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
SLEDS
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The Model:
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6D Supergravity with two 3-branes
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Compactification by fluxes with R~0.1 mm
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Conical singularities at brane locations
APS meeting, April 17, 2007
flat branes
J. Santiago, Gravity and Extra Dimensions
SLEDS
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The Model:
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6D Supergravity with two 3-branes
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Most general solution
with axial symm. and
maximally 4D symm.
has flat branes
Gibbons, Guvens, Pope, 03
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Compactification by fluxes with R~0.1 mm
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Conical singularities at brane locations
APS meeting, April 17, 2007
flat branes
J. Santiago, Gravity and Extra Dimensions
SLEDS
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Contribution to low-energy cosmological constant:
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Brane tension: SUSY badly broken on the brane
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Classical bulk contribution: conical singularity
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Bulk quantum contribution: determined by bulk SUSY
APS meeting, April 17, 2007
J. Santiago, Gravity and Extra Dimensions
Caveats
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Fundamental explanation of scales
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How to explain 0.1 mm extra dimensions?
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But relates hierarchy and cosmological constant problems
Detailed analysis of dynamics of relaxation
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Higher curvature terms
Bostock, Gregory, Navarro, Santiago 04
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Thick branes
Navarro, Santiago 05
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Quantum corrections might be too big
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Will be experimentally tested in the near future
APS meeting, April 17, 2007
J. Santiago, Gravity and Extra Dimensions
Conclusions
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Extra dimensions give a new perspective to gravity
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Braneworlds: New freedom to attack old problems
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DGP model:
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Can explain acceleration without a cosmological constant
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Strongly coupled: difficult to compute at all scales
SLEDS
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Can explain the smallness of the “cosmological constant”
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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