A Generic Test of Modified Gravity Models which Emulate Dark Matter

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A Generic Test of Modified Gravity Models which
Emulate Dark Matter

• arXiv0705.0153 astro-ph
• with Emre Kahya

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Dark Matter vs Modified Gravity

• Gµ? 8pG?µ? works for solar system
• But not for galaxies
• Theory v²GM/r
• Obs v²va0GM
• Could be missing M
• Or modified gravity

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ds²-B(r)dct²A(r)dr²r²dO²

• A'/(r A) (A - 1)/r² (A/B) 8pG?/c²
• B'/(r B) - (A - 1)/r² 0
• Spherical Mass M
• e 2GM/(c²r)
• B 1 - e and A 1/(1 - e) 1 e
• e .0000006 at rs 8 kpc
• With Isothermal Halo for r gt rs
• e 2va0GM/c²
• B 1 e e ln(r/rs) and A 1 e e
• e .0000006

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No-Go Thm for metric modelsWith Soussa,
astro-ph/0307358

• ?µ? 8pG Tµ? GM for gµ? ?µ? hµ?
• hµ? v² va0GM some ?µ? s h²
• If all ?µ? h² unstable!
• Distinguished subsets
• Divergence (0 to all orders)
• Trace conf. invariant for ?µ? h¹
• Extra force in conf. factor no lensing!

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Five Assumptions

• Gravity carried by hµ? with source Tµ?
• General coordinate invariance
• Extra force in ultra-weak field regime
• Stability (forbids all ?µ? h²)
• Light couples conformally
• Known models violate (1) (5)
• Violating (4) may also work

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Known Models

• TeVeS
• Bekenstein (astro-ph/0403694)
• OK Cosmology (astro-ph/0505519, 0606216, 0608602,
  0611255)
• SVTG
• Moffat (gr-qc/0506021)
• astro-ph/0506370

• Fields gµ?, Aµ f
• Extra force from f
• Matter couples to
• gµ? Exp(-2f) gµ?
• 2 sinh(2f)Aµ A?
• R term for solar system
• Gravitons couple to gµ?
• gµ? from GR with D.M.
• gµ? from GR w/o D.M.

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Dark Matter Emulatorsds²-B(r)dt²A(r)dr²r²dO

• Without Dark Matter, e2GM/(c²r)
• B 1-e and A 1/(1-e) 1e
• e .0000006 for rs 8 kpc
• Weak gravity waves see this geometry
• With Isothermal Halo, e2va0GM/c²
• B 1-eeln(r/rs) and A 1ee
• e .0000006
• Ordinary matter sees this geometry

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Light-like Pulses from (0,xL)

• Gravitons follow gµ? to (t,xs)
• B 1 - e and A 1 e
• e 2GM/(rc²) .0000006 at rs 8 kpc
• ?'s and ?'s follow gµ? to (T,xs)
• B 1 e e ln((r/rs) and A 1 e e
• e 2va0GM/c² .0000006
• ?t T t e ?x/c
• SN 1987a ?t -.144 36.7 day -5.3 day
• hrs diff. between ?s and ?s irrelevant
• Advanced LIGO will see to .8 Mpc!

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Radial Prop v/c B(r)/A(r)

• Gravitons v/c 1 2e
• ?s ?s V/c 1 - 2e e ln(r/rs) - e
• Typically faster than gravitons
• But depends on r and rs
• Moore Nelson, hep-ph/0106220
• (V-v)/c lt 2 x E-15 for galaxy (maybe ok)
• (V-v)/c lt 2 x E-19 for extra-gal. (not ok)

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Conclusions

• Mod. Gravity may explain rot. curves
• But unstable if pure metric
• Otherwise new fields and two metrics
• Gravitons couple to gµ? of GR w/o D.M.
• Matter couples to gµ? of GR with D.M.
• Big time lag for gravitons vs ?s ?s