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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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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
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
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
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?
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
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)
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
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
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
(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)
DGP phenomenology versus fine-tuning: Hubble scale Planck scale pheno. requires severe fine-tuning!
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
New solutions (and new problems): (with negative mass): 5-D Schwarzschild Mass: Singularity
New solutions (and new problems): (with negative mass): 5-D Schwarzschild Mass: But cut-and-paste will remove center of space with SA brane!
New solutions: (with negative mass): 5-D Schwarzschild FRW brane: embedding: Israel junction conditions:
Classical point particle: Open Trajectory = Bouncing Cosmology
Classical point particle: ? ? ? For large , solution singular but still have smooth initial data
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
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!
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!
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
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!