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
The schism “dark matter vs modified
gravity” is an old story
LeVerrier prediction of
Neptune from Uranus
orbital anomalies
VERSUS
 his attempts to explain
the anomalous precession
of the perihelion of
Mercury with “Vulcanus”

The issue is very topical:
History shows that anomalies can be either
dark matter or modified gravity (or a
combination).
 Experiment will settle the matter.
 A direct (solar system or laboratory test)
would be cleaner.

(Spiral) Galaxy rotation curves:

Flattening of rotation curves
GM v 2
1
 v
2
r
r
r
v  v

Anomalous behaviour triggered by
a0  1010 ms2

Tully-Fisher relation
v LM
4

Take these facts as “Kepler’s laws”
for a new theory of gravity

Milgrom’s insight:
FN |  | a0 

F  FN a0
Explains observations:
a2
GM
v4
FN 
 2 
a0 r
a0 r 2
(often quoted as a rule of thumb)
This rule of thumb can be
incorporated into a consistent theory

There are several Lagrangian relativistic
theories that do this

In the non-relativistic limit they typically
reduce to a non-linear Poisson equation
LISA Pathfinder mission
LISA Pathfinder as Gravitational Laboratory

LISA Pathfinder and its Payload will offer the following (see
ESA-SCI(2007)1):
 Differential Force Measurement Sensitivity:
≈ 1.3x10-14N / √Hz around 1mHz
 Drag-Free Platform Stability:
Platform Free-Fall Quality of
≈ 10-13ms-2/ √Hz around 1mHz
≈ 10-9ms-2 at DC
 Gravity Gradiometer Sensitivity:
≈ 1.5x10-14s-2/ √Hz around 1mHz
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:


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=1.5Km/sec
THE ELEPHANT IN
THE ROOM
Lagrange points
VS.
 Saddle points.

Potential Trajectories for LISA Pathfinder

Illustration of the chaotic nature of the problem:
1.5mio km
Earth
Sun
Single dV manoeuvres between 0.5m/s and 1m/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 the theory
 It should be constrained:
- To produce the required
astrophysical effects
- Not to renormalize the
gravitational constant by
more then a few percent

A negative result would be pretty
damning
A triple power law
in
would
bypass a negative
result
 The intermediate
power would have
to be very large
 RIDICULOUS!

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.
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:

Is dark matter a “Vulcan”?

Is modifying gravity
unwarranted lunacy?