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Testing Modified Newtonian Dynamics with LISA Pathfinder
Christian TrenkelAstrium Ltd, Stevenage, UK
On behalf of the “LPF and MOND” team
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Overview
Dark Matter and Modified Gravity
Modified Newtonian Dynamics (MOND)
LISA Pathfinder
Testing MOND with LISA Pathfinder
Summary and Discussion
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Overview
Dark Matter and Modified Gravity
Modified Newtonian Dynamics (MOND)
LISA Pathfinder
Testing MOND with LISA Pathfinder
Summary and Discussion
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Dark Matter and Modified Gravity
If we simply apply the gravitational laws to the matter that we can observe outside the Solar System, things don’t make sense…
This may be for the following reasons: there are other constituents that we cannot see (Dark
Matter, Dark Energy) our laws of Gravity are incomplete and require
modifications
Of course these are not mutually exclusive…
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Dark Matter and Modified Gravity
This problem is not new – in fact we used to have it within the Solar System:
Le Verrier predicted Neptune from Uranus orbital anomalies using Newtonian gravity (1846) – first example of Dark Matter!
Attempts to explain anomalous precession of Mercury with “Vulcan”, which was never found – eventually explained through General Relativity (1915)
So we have already had precedents for both –Dark Matter and Modified Gravity!
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Dark Matter and Modified Gravity Now the problem has moved to galactic and extragalactic scales Already 80 years ago (~1934) Zwicky noticed that we have a
“missing mass” problem at galactic scales:
Expect – not flat rotation curves!r
vrv
rGM 12
2
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Dark Matter and Modified Gravity What is the correct explanation this time – Dark Matter, Modified
Gravity, a combination of both…?
Direct search for Dark Matter particles underway (dedicated underground searches, LHC and predecessors) for decades now – so far largely fruitless
Problem with most proposed Gravity modifications: almost by definition they predict significant deviations from GR only outside the Solar System – and are therefore hard to test directly!
Direct experimental evidence (for Dark Matter or Modified Gravity) would clearly be of great value!
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Overview
Dark Matter and Modified Gravity
Modified Newtonian Dynamics (MOND)
LISA Pathfinder
Testing MOND with LISA Pathfinder
Summary and Discussion
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Modified Newtonian Dynamics Newtonian dynamics are modified when total gravitational acceleration
approaches a0 ≈ 10-10ms-2 (Milgrom 1983):
Newtonianwith
“MONDian”
Many forms possible for :
Automatically describes flat rotation curves – on the outskirts of galaxies we have:
Can also be seen as modification of Newton’s law of Gravity:
4/1
02
0
4
20
2
aGMv
rav
rGM
aamF
aaamF
0
000
00 1
aa
aaaa
aaaa
Ngrav aar
GMaa 020 0aaN
)/( 0aa
2/120
00
0
00
/1
/)/(/1
/)/(aa
aaaaaa
aaaa
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Purely phenomenological, non-relativistic formula with no underlying theory
Extremely successful in describing many (MANY!) galactic rotation curves without Dark Matter:
Less successful on extragalactic scales Bullet cluster still needs Dark Matter – but less Gravitational lensing still needs Dark Matter – just as much
Modified Newtonian Dynamics
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Modified Newtonian Dynamics Much more recently: a relativistic theory (TeVeS) was developed
with MOND as non-relativistic limit (Bekenstein 2004) In the non-relativistic limit, the total potential is sum of Newtonian
potential and new scalar field:
This scalar field is solution of modified Poisson equation
TeVeS gave MOND some “respectability” and generated renewed interest
Other theories with MONDian non-relativistic behaviour have been proposed: bimetric theories, Einstein-Aether theory…
)( Na
Ga
04
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Modified Newtonian Dynamics
A priori, prospects of MONDian tests within Solar System poor:
At 1AU, Sun’s gravitational pull is almost 108a0!
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
0.1 1 10 100 1000 10000
Distance from Sun [AU]
a [m
s-2]
Earth Saturn Neptune
PioneerMercury
108
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Modified Newtonian Dynamics
Bekenstein & Magueijo (2006): gravitational Saddle Points provide MONDian “habitats” within the Solar System
Anomalous gravitational accelerations also result in anomalous gravity gradients
TeVeS predicts MOND gravity gradients ≥10-13s-2 within elliptical bubble around SP – for standard interpolation function
766km259000km
1532km
Sun
Earth
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Overview
Dark Matter and Modified Gravity
Modified Newtonian Dynamics (MOND)
LISA Pathfinder
Testing MOND with LISA Pathfinder
Summary and Discussion
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder LISA Pathfinder (LPF) is a technology
demonstrator for Laser Interferometer Space Antenna (LISA) – a low-frequency gravitational wave detector in space
Will demonstrate two key requirements for gravitational wave detection:
Reduction of acceleration noise on macroscopic Test Masses in Space at ~1mHz
Positional read-out of Test Masses in Space with sufficiently low displacement noise at ~1mHz
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Acceleration Noise Displacement Noise
LISA Pathfinder Quantitative Science Requirements:
Differential Acceleration Noise between 2 Test Masses* Displacement Noise
*Simply divide by separation 0.4m to obtain gradiometer performance
3x10-14ms-2/√Hz @ 1mHz
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder LPF performance compared to other missions (not quite fair)
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder Mission Profile:
LPF launches into parking orbit 200x1600km on VEGA 9 apogee raising manoeuvres required to deliver LPF to L1 Propulsion Module separates during transfer phase Final orbit is 500000km x 800000km Lissajous orbit around L1 Very quiet and stable environment
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder
Instrument at the core of LISA Pathfinder:
Two Au/Pt Test Masses of ~2kgs, housed in separate vacuum enclosures – baseline ~ 0.4m
Relative position of Test Masses read-out by: Heterodyne laser interferometry
on sensitive axis joining the two Test Masses
Capacitive sensing on all axes
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder
Drag-free control crucial to eliminate Solar Radiation Pressure fluctuations as significant noise source
Now we “only” need to worry about the following noise sources: Electrostatics Magnetism Thermal Effects Charging Residual Gas Damping Self-Gravity …
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder
The main purpose of LPF is to understand the noise sources that limit its performance
A detailed noise budget has been created with over 120 entries
Where possible, relevant parameters have been verified by test on the ground
A suite of experiments will be run during the mission to investigate specific couplings and noise sources
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder
Spacecraft Integration is almost fully complete
All Spacecraft and Payload Electronic boxes are on-board
Only parts of Central Payload and Micropropulsion System are missing
Propulsion Module is “done”
Spacecraft has (successfully) completed On-Station Thermal Test at IABG
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LISA Pathfinder
Current Schedule:
Spacecraft and Propulsion Module go into Hibernation (March/April 2012)
Missing elements (Payload parts and Micropropulsion system) completed by end 2012 / early 2013
End of Hibernation phase early 2013 –working towards launch!
Launch on VEGA Summer 2014
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Overview
Dark Matter and Modified Gravity
Modified Newtonian Dynamics (MOND)
LISA Pathfinder
Testing MOND with LISA Pathfinder
Summary and Conclusions
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder In MOND (TeVeS) we have a theory of modified gravity that
predicts potentially measureable anomalous gravity gradients in macroscopic regions around gravitational Saddle Points
In LISA Pathfinder we have a spacecraft that will be launched just a few years from now, with the most sensitive gravity gradiometer ever on-board, at least in the mHz frequency band.
→ Obvious question:Can we use LISA Pathfinder to test MOND?
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder Need to:
(1)Understand dynamic location of gravitational Saddle Points (SPs) in the Sun-Earth-Moon System
(2)Establish that LPF can be made to fly through the region around a SP following its nominal mission
(3)Calculate the anomalous MONDian gravity gradients that LPF will experience, including temporal behaviour
(4)Confirm that the gravity gradiometer on-board LPF is sensitive enough to detect the anomalous gradients
… using LPF “as built”, and no interference with nominal mission allowed
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder
Saddle Points are defined by zero total gravitational field – not to be confused with Lagrange points L1, L2, etc
SPs are not a stable location for spacecraft In the Sun-Earth-Moon system, there are two SPs:
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
The Sun-Earth SP offers much more stability than the lunar SP, and also lower background gradients → will focus on Sun-Earth SP as target
The Sun-Earth SP position is shifted from its nominal two-body position due to the influence of other gravitating bodies: Moon: ≤ 6000km Jupiter: ≤ 20km Venus: ≤ 10km …
Eccentricity of Earths orbit around Sun results in shifts of order ±4000km (annual modulation)
All these shifts are well-known and predictable. The “true”gravitational SP can be pinpointed as a function of time to better than 1km – more than enough
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder Need to:
(1)Understand dynamic location of Saddle Points (SPs) in the Sun-Earth-Moon System
(2)Establish that LPF can be made to fly through the region around a SP following its nominal mission
(3)Calculate the anomalous MONDian gravity gradients that LPF will experience, including temporal behaviour
(4)Confirm that the gravity gradiometer on-board LPF is sensitive enough to detect the anomalous gradients
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
LPF will lie nominally on a stable manifold whilst orbiting the Earth-Sun L1 point
Only a small manoeuvre is needed to reach an unstable manifold
This allows an option to return towards Earth and access the gravitational saddle point between Sun and Earth
Testing MOND with LISA Pathfinder
Saddle Point
Sun
Earth
1.5mio km
Sun
Earth
1.5mio km
Nominal Orbit around L1
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Search for suitable trajectories - assumptions and constraints:
Single dV manoeuvres up to 2m/s have been considered: compatible with estimated residual FEEP control authority (≈
6m/s) and also cold gas control authority (≈4m/s) following nominal mission reasonable timescales for manoeuvres, including single thruster
failure
Consider both Rockot and VEGA launch options
Proof of Principle sought at this stage – exact trajectory can only be chosen once nominal mission is underway
Figures of merit for trajectories: transfer time from L1 to SP SP miss distance
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Search Space Analysis First step: understand structure of search space Initial dV from 0 to 2 m/s Initial Time of manoeuvre from 0 to 60 days Chaotic search space
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Further Optimisation – zoom into the search space After several iterations: Parameter Space finally well behaved
at the 10-4m/s, 10min scale – characteristic “valleys” emerge
Optimisation tools have been developed to search within valleys
10min
10-4
m/s
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Example trajectories – Rockot
First example: direct low-miss distance Manoeuvre: 0.4237 m/s Miss Distance: 1407 km after 577 days
Saddle point Saddle point
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Example trajectories – Rockot
Second example: LGA low-miss distance Manoeuvre: 0.8673 m/s Miss Distance: 396 km after 464 days
Saddle point Saddle point
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Best trajectories – VEGA
Saddle point Saddle point
• Second example:
• Manoeuvre: -1.232 m/s
• Miss Distance: 130 km after 512 days
• First example:
• Manoeuvre 0.2301m/s
• Miss Distance: 2333 km after 348 days
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Typical total DV budget: ~2 m/s Very substantial improvement due to second manoeuvre
Rockot 1635
Rockot LGA
VEGA LGA fast VEGA 130
One manoeuvre
strategy
Total DV 0.3225 m/s 0.8673 m/s 0.2301 m/s -1.232 m/s
Miss distance 1635 km 396 km 2333 km 130 km
Two manoeuvres
strategy
DV1 0.3225 m/s 0.8673 m/s 0.2301 m/s -1.232 m/s
DV2 1.4 m/s 1.8 m/s 1.87 m/s 0.05 m/s
Total DV 1.7225 m/s 2.6673 m/s 2.1001 m/s 1.282 m/s
Miss distance 242 km 253 km 355 km 72 km
Obvious strategy to reduce further the miss distance: additionalmanoeuvres
Add second manoeuvre only at the apogees, starting with the best solutions from the single-manoeuvre search
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Third Iteration: can we find solutions with multiple SP crossings?
Impossible to find (with reasonable effort) by “forward propagation”. Instead:
Start at SP at certain date & time, with initial SC velocity vector
Find trajectories that cross SP for at least one more time (“exactly”)
Identify those that, propagated backwards, originate from a suitable LPF orbit around L1 – including single dV manoeuvre
Further backpropagation back to Earth, to ensure compatibility with LPF launcher
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Results so far:
Trajectories with >2 SP crossings are too stable – they cannot be reached from L1!
Numerous candidate solutions for double crossings found, even for single dV manoeuvres – again multiple manoeuvres will improve chances further
However at the moment we cannot say for sure whether a suitable double crossing solution exists for every launch date – more work required
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Example of solution found (Rockot):
Testing MOND with LISA Pathfinder
a: Launch, 24/2/2013.inclination = 57.6°perigee altitude: 322 km
b: Libration orbit, 73 days after launch
c: Exiting libration orbit, 258 days after launch. The spacecraft has spent 185 days around L1.
d: Reaching the SP for the first time, 543 days after launch (285 days after escaping from L1).
e: Reaching the SP for the second time, 582 days after launch (39 days after the first passage).
Major/minor axes of libration orbit:out of ecliptic: 417,000 kmin plane: 775,000 km
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
The issue of navigation – just as critical: Assume that you have identified the trajectory that you want
LPF to follow Can you in practice navigate the spacecraft along this nominal
trajectory, given the limitations of the micropropulsion system and non-zero tracking errors?
Not obvious at all because: Earth and Moon perturbations may be too high to be corrected –
the real trajectory may diverge from the nominal one despite your best efforts!
Total dV requirements may exceed available propellant Application of required trajectory correction manoeuvre may
take too long
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Earth / Moon fly-by
Results so far: the navigation issue should be manageable – in 6 out of 7 cases, a chosen trajectory could be successfully followed
During transfer, contact to SC will be required every few days for navigation purposes
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Many possible trajectories exist to take LPF from L1 to the SP – many “needles in the haystack”
Transfer time to reach the SP from L1 is typically 1 - 1.5 years with Rockot, and around 1 year with VEGA
Using multiple manoeuvres, the miss distance for a single SP crossing will be limited by SC tracking – conservatively estimated at 10km
Navigation issue seems under control – but should be taken into account when selecting trajectory
Some simple candidate solutions with double SP crossings found –but jury is still out on abundance / practicality of these
Large computational overheads due to chaotic nature of search space – but proof of principle obtained!
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Gravitational Environment during SP region crossing – a few relevant parameters:
LPF speed through SP region typically ≈1.5km/s (essentially free-fall)
Newtonian gradients around SP are ≥ 2x10-11s-2. For a miss distance of 50km, the lowest gravitational acceleration level experienced by LPF will be ag ≈ 1x10-6ms-2
Even if LPF flies through the SP exactly, it will spend, at most, ≈6s in an environment with ag ≤ 1x10-7ms-2
(-) LPF will only be able to test the intermediate MOND region
(+) Spacecraft self-gravity (< 10-8ms-2 ) is not an issue
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Experiencing ag ≈ 1x10-6ms-2 to 1x10-5ms-2 at 1AU from the Sun is not bad:
Equivalent to travelling out to between 25 and 75 AU!
Testing MOND with LISA Pathfinder
1.E-11
1.E-10
1.E-09
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
0.1 1 10 100 1000 10000
Distance from Sun [AU]
a [m
s-2]
Earth Saturn Neptune
PioneerMercury
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Need to:
(1)Understand dynamic location of Saddle Points (SPs) in the Sun-Earth-Moon System
(2)Establish that LPF can be made to fly through the region around a SP following its nominal mission
(3)Calculate the anomalous MONDian gravity gradients that LPF will experience, including temporal behaviour
(4)Confirm that the gravity gradiometer on-board LPF is sensitive enough to detect the anomalous gradients
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Prediction of anomalous MOND gravity gradients in TeVeS:
Numerical relaxation method has been developed (Bevis & Magueijo) to calculate anomalous gradients at grid points of cubic volume around SP
Assumes standard interpolation function between Newtonian and MONDian behaviour
Includes effects of Sun, Earth and Moon position – in principle accepts arbitrary sources outside volume
Used to investigate signal as function of lunar phase –dependence found to be insignificant
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
A typical LPF trajectory is propagated through the volume and the anomalous gradients are extracted at each point:
45°
45°
Earth
Sun
Typical LPF Trajectory
Sun-Earth SP
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Due to sun-pointing constraints, only (one) gravity gradient orthogonal to Sun-Earth line can be measured:
LPF speed through SP region – 1.5km/s – is used to convert spatial into temporal gradient variations
Testing MOND with LISA Pathfinder
Sun Earth
Test Mass
Test Mass
Sun Earth
Test Mass
Test Mass
Solar Array
or
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Results Anomalous MOND gradients as a function of miss distance:
0km50km100km400km
Testing MOND with LISA Pathfinder
MOND signal ≈ 500s - 1000s long → ~ mHz (!!)
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Total external gravity gradient seen by LPF for 50km miss distance
Smooth Newtonian background is predictable and can be subtractedor filtered out
Newtonian onlyNewtonian + MOND
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Need to:
(1)Understand dynamic location of Saddle Points (SPs) in the Sun-Earth-Moon System
(2)Establish that LPF can be made to fly through the region around a SP following its nominal mission
(3)Calculate the anomalous MONDian gravity gradients that LPF will experience, including temporal behaviour
(4)Confirm that the gravity gradiometer on-board LPF is sensitive enough to detect the anomalous gradients
Testing MOND with LISA Pathfinder
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder Comparison of predicted MOND signal to LPF differential
acceleration performance requirement (divided by Test Mass separation to give gradiometer performance):
→ If LPF “only” meets its requirements, MOND gradient detection does not look good!
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder However, extensive test campaigns on flight hardware show that
the currently predicted LPF performance is substantially better than the requirement:
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder Even the above estimate can be regarded as conservative and
“worst case”. The actual LPF performance could be as good as
Of course we won’t really know until LPF flies!
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder Signal-to-Noise Ratio can be calculated in analogy with
gravitational wave detection. Assuming stationary instrument noise, the following SNR plot is obtained (Magueijo):
→ SNRs between 15 and 60
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Testing MOND with LISA Pathfinder The LPF speed through the SP crossing is virtually optimal:
1.5km/s
This remarkable coincidence just has to be exploited!
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Need to:
Understand dynamic location of Saddle Points (SPs) in the Sun-Earth-Moon System
Establish that LPF can be made to fly through the region around a SP following its nominal mission
Calculate the anomalous MONDian gravity gradients that LPF will experience, including temporal behaviour
Confirm that the gravity gradiometer on-board LPF is sensitive enough to detect the anomalous gradients
Testing MOND with LISA Pathfinder
Can we use LISA Pathfinder to test MOND? If everything works as we currently expect it to, we can!
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Overview
Dark Matter and Modified Gravity
Modified Newtonian Dynamics (MOND)
LISA Pathfinder
Testing MOND with LISA Pathfinder
Summary and Discussion
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Summary and Discussion It seems pretty clear that a direct test of MONDian behaviour is
possible, by flying LPF through the Sun-Earth SP region once the nominal LPF mission is completed
MONDian gradients (derived from TeVeS) could not just be detected, but measured in detail, with substantial SNR, based onexpected LPF performance and standard interpolation function
LPF presents us with the rare chance to subject an alternative gravitational theory to a direct experimental test – at the relatively minor cost of extended operations
A positive detection would represent a major breakthrough in fundamental physics
Constraints on theories with MONDian behaviour from a null result are being investigated
2nd Iberian Gravitational Wave Meeting – Barcelona 15-17 February 2012
Summary and Discussion The idea of using LPF to look for MONDian gradients near the SP
is slowly gaining traction – it is being appreciated that this really is a “once-in-a-lifetime” opportunity that should not be wasted
The “LPF and MOND team” plans to submit a proposal to ESA for a Mission Extension to LPF to test MOND – we think there is enough value for money!
Meetings / workshops so far held in July 2010 (RAL), June 2011 (ICL), December 2011 (Oxford) – next one planned June 2012 (Astrium, UK)