A New Perspective on DGP Gravity

1. 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

2. 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

3. 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

4. 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?

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 Λ! ) 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 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)

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 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

8. 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

9. 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

10. (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!

12. 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): (with negative mass): 5-D Schwarzschild Mass: Singularity

14. New solutions (and new problems): (with negative mass): 5-D Schwarzschild Mass: But cut-and-paste will remove center of space with SA brane!

15. New solutions: (with negative mass): 5-D Schwarzschild 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 M<0 SA brane shields solution from bulk singularity • expect theory unstable; no ground state

19. 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!

20. 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!

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 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!