TESTING MOND WITH LISA PATHFINDER Joo Magueijo Theoretical

TESTING MOND WITH LISA PATHFINDER João Magueijo Theoretical Physics Group Imperial College Based on Bekenstein & Magueijo, astro-ph/0602266; Bevis, Magueijo, Trenkel, Kemble, ar. Xiv: 0912. 0710; Trenkle, Kemble, Bevis, Magueijo, ar. Xiv: 1001. 1303

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

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

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

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

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

LISA Pathfinder mission

LISA Pathfinder as Gravitational Laboratory l LISA Pathfinder and its Payload will offer the following (see ESA-SCI(2007)1): § Differential Force Measurement Sensitivity: ≈ 1. 3 x 10 -14 N / √Hz around 1 m. Hz § Drag-Free Platform Stability: Platform Free-Fall Quality of ≈ 10 -13 ms-2/ √Hz around 1 m. Hz ≈ 10 -9 ms-2 at DC § Gravity Gradiometer Sensitivity: ≈ 1. 5 x 10 -14 s-2/ √Hz around 1 m. Hz We want to exploit this! § … and more… 8/29 Marcel Grossman 12 – Paris, 2009

The intuition behind the basic prediction Bekenstein & Magueijo, astro-ph/0602266 NEWTONIAN MOND

This intuition is corroborated by an exact calculation:

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

The coincidence of the century

Simulating the signal and noise

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

Optimal SNR for different b and noise, assuming v=1. 5 Km/sec

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

Potential Trajectories for LISA Pathfinder l Illustration of the chaotic nature of the problem: 1. 5 mio km Earth Sun Single d. V manoeuvres between 0. 5 m/s and 1 m/s applied at 0. 25 day intervals 17/29 Marcel Grossman 12 – Paris, 2009

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

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

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

Conclusions: n n 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…. ) SNR ratios hit double/triple figures easily. A negative result would kill MOND in (almost) all of its relativistic incarnations

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