1. TESTING MOND WITH LISA PATHFINDER João Magueijo Theoretical Physics Group Imperial College Based on Bekenstein & Magueijo, astro-ph/0602266; Bevis, Magueijo, Trenkel, Kemble, arXiv: 0912.0710; Trenkle, Kemble, Bevis, Magueijo, arXiv: 1001.1303

2. The schism “dark matter vs modified gravity” is an old story LeVerrier prediction of Neptune from Uranus orbital anomalies LeVerrier prediction of Neptune from Uranus orbital anomaliesVERSUS his attempts to explain the anomalous precession of the perihelion of Mercury with “Vulcanus” his attempts to explain the anomalous precession of the perihelion of Mercury with “Vulcanus”

3. The issue is very topical: History shows that anomalies can be either dark matter or modified gravity (or a combination). History shows that anomalies can be either dark matter or modified gravity (or a combination). Experiment will settle the matter. Experiment will settle the matter. A direct (solar system or laboratory test) would be cleaner. A direct (solar system or laboratory test) would be cleaner.

4. (Spiral) Galaxy rotation curves: Flattening of rotation curves Flattening of rotation curves Anomalous behaviour triggered by Anomalous behaviour triggered by Tully-Fisher relation Tully-Fisher relation

5. Take these facts as “Kepler’s laws” for a new theory of gravity Milgrom’s insight: Milgrom’s insight: Explains observations: Explains observations: (often quoted as a rule of thumb)

6. This rule of thumb can be incorporated into a consistent theory There are several Lagrangian relativistic theories that do this There are several Lagrangian relativistic theories that do this In the non-relativistic limit they typically reduce to a non-linear Poisson equation In the non-relativistic limit they typically reduce to a non-linear Poisson equation

7. LISA Pathfinder mission

8. Marcel Grossman 12 – Paris, 2009 8/29 LISA Pathfinder as Gravitational Laboratory LISA Pathfinder and its Payload will offer the following (see ESA-SCI(2007)1):  Differential Force Measurement Sensitivity: ≈ 1.3x10 -14 N / √Hz around 1mHz  Drag-Free Platform Stability: Platform Free-Fall Quality of ≈ 10 -13 ms -2 / √Hz around 1mHz ≈ 10 -9 ms -2 at DC  Gravity Gradiometer Sensitivity: ≈ 1.5x10 -14 s -2 / √Hz around 1mHz  … and more… We want to exploit this!

9. The intuition behind the basic prediction Bekenstein & Magueijo, astro-ph/0602266 NEWTONIANMOND

10. This intuition is corroborated by an exact calculation:

11. Transverse tidal stress at impact 25, 100, 400 Km of the Earth-Sun saddle

12. The coincidence of the century

13. Simulating the signal and noise

14. Data analysis: Borrow noise-matched filters from gravity wave detection (but with a significant simplification: we know where the starting time of the signal). Borrow noise-matched filters from gravity wave detection (but with a significant simplification: we know where the starting time of the signal). The optimal SNR is: The optimal SNR is: Fourier transform of the signal Noise power spectrum

15. Optimal SNR for different b and noise, assuming v=1.5Km/sec

16. THE ELEPHANT IN THE ROOM Lagrange points Lagrange points VS. VS. Saddle points. Saddle points.

17. Marcel Grossman 12 – Paris, 2009 17/29 Potential Trajectories for LISA Pathfinder Illustration of the chaotic nature of the problem: Single dV manoeuvres between 0.5m/s and 1m/s applied at 0.25 day intervals Sun Earth 1.5mio km

19. Transverse tidal stress at impact 25, 100, 400 Km of the Earth-Sun saddle

21. How generic a test of MOND is this? There is a free function in the theory There is a free function in the theory It should be constrained: It should be constrained: - To produce the required astrophysical effects - Not to renormalize the gravitational constant by more then a few percent

22. A negative result would be pretty damning A triple power law in would bypass a negative result A triple power law in would bypass a negative result The intermediate power would have to be very large The intermediate power would have to be very large RIDICULOUS! RIDICULOUS!

23. Conclusions: A LPF redirection to the Earth-Sun (Moon) saddle(s) would be a direct test of MOND; it would add a science case to LPF. A LPF redirection to the Earth-Sun (Moon) saddle(s) would be a direct test of MOND; it would add a science case to LPF. Systematics are under control (Self-gravity isn’t an issue; the Moon isn’t an issue….) Systematics are under control (Self-gravity isn’t an issue; the Moon isn’t an issue….) SNR ratios hit double/triple figures easily. SNR ratios hit double/triple figures easily. A negative result would kill MOND in (almost) all of its relativistic incarnations A negative result would kill MOND in (almost) all of its relativistic incarnations

24. Let’s do the experiment! It would answer important questions: Is dark matter a “Vulcan”? Is dark matter a “Vulcan”? Is modifying gravity unwarranted lunacy? Is modifying gravity unwarranted lunacy?