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

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 !

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

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

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

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

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

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

Answer: 1 st one  Multiple metric formulations (e.g. TeVeS) TeVeS Bekenstein (2004) gravitational waves and matter follow different metrics : post Newtonian parameters √ structure formation √ non-relativistic MOND limit √ 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.

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

How to mimic DM?

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

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

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