Adventures with Superstrings

1
A New Perspective on DGP Gravity
with R. Gregory, N. Kaloper A. Padilla
hep-th/070?.????
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in the late 1990s, motivated by the fact that
the gravitational force is not well-measured at
short distances
for
combined with ideas from string theory D-branes
Brane-world scenarios
3
in the late 1990s, motivated by the
realization that the gravitational force is not
well-measured at short distances
for
combined with ideas from string theory D-branes
Brane-world scenarios

• large extra dimensions Arkani-Hamed,
  Dimopoulos Dvali (1998)

• warped extra dimensions Randall Sundrum
  (1999)

brane
extra dimension
4
in the late 1990s, motivated by the
realization that the gravitational force is not
well-measured at short distances
for
combined with ideas from string theory D-branes
Brane-world scenarios

• large extra dimensions Arkani-Hamed,
  Dimopoulos Dvali (1998)

• warped extra dimensions Randall Sundrum
  (1999)

Gravity is also not well understood at very large
distances!!
i.e., cosmic acceleration
Can brane-worlds help with this puzzle?
5
DGP Gravity Dvali, Gabadadze Porrati
(hep-th/0005016)

• 4-D gravity on a brane in 5-D Minkowski space

• extra dimension is not warped or even
  compactified

• additional Einstein term appears in brane action

• behaviour of gravity on brane modified at large
  distances

at short distances, see 4-D gravity at long
distances, see 5-D gravity
( this is subtle!)

• may explain cosmic acceleration ( without ?! )

brane is self-accelerated
6
DGP Gravity Dvali, Gabadadze Porrati
(hep-th/0005016)

• 4-D gravity on a brane in 5-D Minkowski space

• behaviour of gravity on brane modified at large
  distances

• may explain cosmic acceleration ( without ?! )

• a controversial history

• DGP can be realized with string theory
  constructions
• 
  (Antoniadis, Minasian Vanhove 02)

• DGP has no UV completion (Dubovsky et al
  Adams et al 06)

• DGP is unstable spectrum has ghosts and
  tachyons!
• (Koyama et al
  Charmouis et al Shtanov et al 06)

• DGP is stable
  (Koyama Deffayet et al Dvali 06)

7
DGP Gravity Dvali, Gabadadze Porrati
(hep-th/0005016)

• 4-D gravity on a brane in 5-D Minkowski space

• behaviour of gravity on brane modified at large
  distances

• may explain cosmic acceleration ( without ?! )

• a controversial history

We argue DGP gravity is a BAD theory/model !!
New perspective take a 5-D point of view!
DGP model is 5-D Einstein gravity coupled to
certain class of matter/branes
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Solutions of DGP Gravity
Equations of motion
Bulk
Brane
Israel junction conditions

• brane stress tensor modified by geometric terms

• assumed Z2 symmetry about the brane

• assumed no additional matter on brane

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Solutions of DGP Gravity
Equations of motion
Bulk
Brane
(Deffayet 01)
cut-and-paste to build symmetric solutions

• choose a known solution of 5-D Einstein
  equations, eg,

Minkowski
X 2

• choose a simple symmetric brane geometry, eg,

FRW

• choose simple embedding ansatz, eg,

and cut-and-paste with Israel conditions solving
trajectory
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(Deffayet 01)
solution
with
Brane geometry corresponds to 4-D deSitter space!
Self-Accelerating brane!
hyperboloid in 5-D Minkowski
remove center of space
(also find normal branch)
11
DGP phenomenology versus fine-tuning
Hubble scale
Planck scale
pheno. requires severe fine-tuning!
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DGP phenomenology versus fine-tuning
Hubble scale
Planck scale
pheno. requires severe fine-tuning!
SA brane is a wormhole
hyperboloid in 5-D Minkowski
X 2
remove center of space
wormhole issues ameliorated if brane is
Z2-orbifold
13
New solutions (and new problems)
5-D Schwarzschild
(with negative mass)
Mass
Singularity
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New solutions (and new problems)
5-D Schwarzschild
(with negative mass)
Mass
But cut-and-paste will remove center of space
with SA brane!
15
New solutions
5-D Schwarzschild
(with negative mass)
FRW brane
embedding
Israel junction conditions
16
Classical point particle
Open Trajectory Bouncing Cosmology
17
Classical point particle
?
?
?
For large , solution singular but still have
smooth initial data
18

• spectrum of DGP is unbounded below!

• many more general solutions with Mlt0

SA brane shields solution from bulk singularity

• expect theory unstable no ground state

19
Tunneling (with M0 so complementary to previous)

• Euclidean instanton describing appearance of SA
  brane

flat R5
S4 brane

• tunneling probability

Tunneling is not suppressed! Minkowski space is
not good vacuum!
Tunneling is not suppressed! Quantum effects
strongly modify classical picture!
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Summary of 5d perspective
1. SA branes are effectively wormholes
fixed by orbifold branes
2. Spectrum of DGP model is unbounded below
(resolves any possible debate theory unstable)
3. Spontaneous creation of SA branes is
unsupressed
Quantum effects strongly modify classical picture
DGP model is pathological! Does not provide a
consistent framework to study gravity! (not
useful for astro/cosmo phenomenology studies!!)
MODEL is no good!
21
Could problems be evaded by UV completion of DGP
model?

• Marolf Trodden analysis of original
  Randall-Sundrum model

negative tension brane is Z2-orbifold no
obvious instability
new instability collision with black hole
creates big crunch
but, no such instability for orientifold or
geometric brane
RS model still useful to produce intuition for
stringy realizations
22
Summary of 5d perspective
1. SA branes are effectively wormholes
fixed by orbifold branes
2. Spectrum of DGP model is unbounded below
(resolves any possible debate theory unstable)
3. Spontaneous creation of SA branes is
unsupressed
Quantum effects strongly modify classical picture
DGP model is pathological! Does not provide a
consistent framework to study gravity!
Severe challenges for any proposed UV completion!
Most important question
Does DGP have UV completion?
Our methods easy diagnostic for brane-world
gravity models!