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A generic test for Modified Gravity Models*

A generic test for Modified Gravity Models*. Emre Onur Kahya. University of Florida. * astro-ph/0705.0153. Why do we need Dark Matter ?. • The missing mass problem Zwicky (1933). • The rotation curves of spiral galaxies Rubin, Ford, Thonnard 1970’s.

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A generic test for Modified Gravity Models*

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  1. A generic test for Modified Gravity Models* Emre Onur Kahya University of Florida * astro-ph/0705.0153

  2. Why do we need Dark Matter ? • The missing mass problem Zwicky (1933) • The rotation curves of spiral galaxies Rubin, Ford, Thonnard 1970’s • Weak lensing to probe DM in galactic clusters 1990’s Rotation Curves  Classical theory doesn’t work !

  3. Possible Solutions I. Dark Matter Isothermal Halo: where a => core radius • plausible candidates, axions, wimps, sterile neutrinos… • none yet observed for 20 years !

  4. II. Modified Gravity Models • MOND, Milgrom (1983)  designed to explain rot. curves • can’t explain gravitational lensing and many other cosmological events, other problems… • Question : Can we make a compare the two ? • without having a (complete) relativistic formulation, no real comparison • Question : What can we do about it ?

  5. No-Go Theorem * Assumptions: • gravitation force is carried by the metric, and the source is usual • the theory of gravitation is generally covariant. • MOND force is realized in weak field perturbation theory. • the theory of gravitation isabsolutely stable. • E&M couples conformally to gravity * Soussa, Woodard (2003) astro-ph/0307358

  6. Static, spherically symmetric geometries • Geodesic  motion along a circle geodesic equations: • A factors out !

  7. The first three assumptions have led us: • Question: Which components? •• All components ?  unstable • the theory of gravitation isabsolutely stable.  Some components, but which (should obey gen. coord. inv.)? Thm: A sym. 2nd rank tensor field contains two distinguished substes: i) divergence ii) trace •can’t be div. zero to all orders • Answer: The trace

  8. Result:  Linearized field equations are traceless • But that’s bad news! • traceless metric field equations  conformal invariance • E&M couples conformally to gravity • photons are unaware of MOND Conclusion: No-Go theorem: If all the assumptions are correct MOND can’t give enough lensing. Question: Which assumption is incorrect ?

  9. Question: Which assumption is incorrect ? • Answer: 1st one  Multiple metric formulations (e.g. TeVeS) TeVeS Bekenstein (2004) •gravitational waves and matter follow different metrics : •non-relativistic MOND limit √ •post Newtonian parameters √ •structure formation √ TeVeS is just one example of the class of models that we are considering ! Dark Matter Emulators: All the alternate gravity models which give both the gravitational lensing and the rotation curves right to agree with DM+GR without dark matter.

  10. Static, spherically symmetric geometries • Geodesic  motion along a circle geodesic equations: • A factors out !

  11. How to mimic DM?

  12. Time Lag Calculation Geodesic Equations: Conclusion: Neutrinos from 1987A should arrive 5.3 days earlier than the gravitational waves.

  13. Observational Prospects Neutrinos • We have already detected neutrinos from 1987A with Kamiokande-II and Irvine-Michigan-Brookhaven detectors. • Super-Kamiokande, Sudbury Neutrino Observatory (SNO+), Ice Cube, Kam-LAND and MiniBooNE Gravitational Waves • amount of GW from SN  oblateness of it from spherical symmetry • Current detectors  can’t detect sun-like stars • Advanced LIGO will Other possibilities • • Light can also be used instead of neutrinos • • will get the effect but not the precision.

  14. CONCLUSIONS • No real comparison between alternate gravity models vs. GR+DM can be made until we have a complete, fully relativistic model • Multiple metric theories, a generic property due to No-Go theorem • This gives rise to, even at this stage, decisive tests. • If MOND is correct neutrinos from 1987A should arrive 5.3 days before the gravitational waves. • Possibility of an incredible and doable test of simultaneous detection of neutrinos and gravitational waves in the future.

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