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A New Perspective on DGP Gravity with R. Gregory, N. Kaloper & A. Padilla hep-th /070?.???? TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A A A A A A in the late 1990’s, motivated by the fact that the

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slide1

A New Perspective on

DGP Gravity

with R. Gregory, N. Kaloper & A. Padilla

hep-th/070?.????

TexPoint fonts used in EMF.

Read the TexPoint manual before you delete this box.: AAAAAAAAA

slide2

in the late 1990’s, 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

slide3

in the late 1990’s, 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

slide4

in the late 1990’s, 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?

slide5

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 Λ! )

brane is self-accelerated

slide6

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 Λ! )
  • 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)
slide7

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 Λ! )
  • 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

slide8

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
slide9

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

slide10

(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)

slide11

DGP phenomenology versus fine-tuning:

Hubble scale

Planck scale

pheno. requires severe fine-tuning!

slide12

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

slide13

New solutions (and new problems):

(with negative mass):

5-D Schwarzschild

Mass:

Singularity

slide14

New solutions (and new problems):

(with negative mass):

5-D Schwarzschild

Mass:

But cut-and-paste will remove

center of space with SA brane!

slide15

New solutions:

(with negative mass):

5-D Schwarzschild

FRW brane:

embedding:

Israel junction conditions:

slide16

Classical point particle:

Open Trajectory

=

Bouncing Cosmology

slide17

Classical point particle:

?

?

?

For large , solution singular but

still have smooth initial data

slide18

spectrum of DGP is unbounded below!

  • many more general solutions with M<0

SA brane shields solution from bulk singularity

  • expect theory unstable; no ground state
slide19

Tunneling (with M=0; so complementary to previous)

  • Euclidean instanton describing appearance of SA brane

flat R5

S4 brane

  • tunneling probability

Tunneling is not suppressed!

Quantum effects strongly modify classical picture!

Tunneling is not suppressed!

Minkowski space is not good vacuum!

slide20

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 modelis pathological!

Does not provide a consistent framework to study gravity!

(not useful for astro/cosmo phenomenology studies!!)

“MODEL” is no good!

slide21

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

slide22

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 modelis 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!