TESTING MOND WITH LISA PATHFINDER

JoJoãão o MagueijoMagueijoTheoretical Physics GroupTheoretical Physics Group

Imperial CollegeImperial 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 LeVerrier prediction of Neptune from Uranus Neptune from Uranus orbital anomalies orbital anomalies

VERSUSVERSUS his attempts to explain his attempts to explain

the anomalous precession the anomalous precession of the perihelion of of the perihelion of Mercury with Mercury with “Vulcanus”“Vulcanus”

The issue is very topical:

History shows that anomalies can be either History shows that anomalies can be either dark matter or modified gravity (or a dark matter or modified gravity (or a combination).combination).

Experiment will settle the matter.Experiment will settle the matter. A direct (solar system or laboratory test) A direct (solar system or laboratory test)

would be cleaner.would be cleaner.

(Spiral) Galaxy rotation curves:

Flattening of rotation curves Flattening of rotation curves

Anomalous behaviour triggered byAnomalous behaviour triggered by

Tully-Fisher relationTully-Fisher relation

rv

r

v

r

GM 12

2

2100 10 msa

MLv 4

vv

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)(often quoted as a rule of thumb)

€

FN ≈a2

a0

⇒GM

r2≈v 4

a0r2€

F ≈ FNa0 0|| aFN

This rule of thumb can be incorporated into a consistent theory

There are several Lagrangian relativistic There are several Lagrangian relativistic theories that do this theories that do this

In the non-relativistic limit they typically In the non-relativistic limit they typically reduce to a non-linear Poisson equationreduce to a non-linear Poisson equation

LISA Pathfinder mission

Marcel Grossman 12 – Paris, 20098/29

LISA Pathfinder as Gravitational Laboratory LISA Pathfinder and its Payload will offer the following (see

ESA-SCI(2007)1):

Differential Force Measurement Sensitivity:

≈ 1.3x10-14N / √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

… and more…We want to exploit this!

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 Borrow noise-matched filters from gravity wave detection (but with a significant simplification: we detection (but with a significant simplification: we know where the starting time of the signal).know where the starting time of the signal).

The optimal SNR is:The optimal SNR is: Fourier transform of the signal

Noise power spectrum

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

THE ELEPHANT IN THE ROOM

Lagrange pointsLagrange points

VS.VS. Saddle points.Saddle points.

Marcel Grossman 12 – Paris, 200917/29

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

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 There is a free function in the theory function in the theory

It should be constrained:It should be constrained:

- To produce the required - To produce the required astrophysical effects astrophysical effects

- Not to renormalize the - Not to renormalize the gravitational constant by gravitational constant by more then a few percent more then a few percent

A negative result would be pretty damning

A triple power law A triple power law in would in would bypass a negative bypass a negative resultresult

The intermediate The intermediate power would have power would have to be very largeto be very large

RIDICULOUS!RIDICULOUS!

Conclusions:

A LPF redirection to the Earth-Sun (Moon) saddle(s) A LPF redirection to the Earth-Sun (Moon) saddle(s) would be a direct test of MOND; it would add a science would be a direct test of MOND; it would add a science case to LPF.case to LPF.

Systematics are under control (Self-gravity isn’t an issue; Systematics are under control (Self-gravity isn’t an issue; the Moon 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 A negative result would kill MOND in (almost) all of its

relativistic incarnations relativistic incarnations

Let’s do the experiment! It would answer important questions:

Is dark matter a “Vulcan”?Is dark matter a “Vulcan”?

Is modifying gravity Is modifying gravity unwarranted lunacy? unwarranted lunacy?