Case for testing modified Newtonian dynamics using LISA pathfinder

Abstract

We quantify the potential for testing modified Newtonian dynamics (MOND) with Laser Interferometer Space Antenna pathfinder, should a saddle point fly-by be incorporated into the mission. We forecast the expected signal-to-noise ratio for a variety of instrument noise models and trajectories past the saddle. For standard theoretical parameters, the signal-to-noise ratio reaches middle to high double figures even with modest assumptions about instrument performance and saddle approach. Obvious concerns, like systematics arising from Laser Interferometer Space Antenna pathfinder self-gravity, or the Newtonian background, are examined and shown not to be a problem. We also investigate the impact of a negative observational result upon the free function determining the theory. We demonstrate that, if Newton's gravitational constant is constrained to not be renormalized by more than a few percent, only contrived MONDian free functions would survive a negative result. There are exceptions, e.g. free functions not asymptoting to 1 in the Newtonian limit, but rather diverging or asymptoting to zero (depending on their mother relativistic MONDian theory). Finally, we scan the structure of all proposed relativistic MONDian theories, and classify them with regards to their nonrelativistic limit, finding three broad cases (with a few subcases depending on the form of the free function). It is appears that only the Einstein-Aether formulation, and the subcases where the free function does not asymptote to 1 in other theories, would survive a negative result without resorting to ''designer'' free functions.

Session Summary: Experimental Gravitation

“…56. There are also proposals for doing further fundamental physics experiments in space. Examples are Lisa Pathfinder for testing MOND theories, 57,58 or STE-QUEST for doing tests of the Einstein Equivalence Principle with a set of clocks and with atom interferometry. 59,60 In the field of astronomy and astrophysics many new projects for hugely improving the accuracy of astronomical measurements are under development.…”

Triangular Libration Points in the CR3BP with Radiation, Triaxiality and Potential from a Belt

“…The collinear libration points L 1 , L 2 , L 3 are unstable, while the triangular libration points L 4 , L 5 are stable for the mass ratio of the primaries less than 0.03852 · · · , [38]. The 3BP, under different forms and aspects, has been used for studies in fundamental physics, general relativity and alternative theories of gravity [1,2,5,10,20,24,31,41].…”

Tests of modified gravity theories in the Solar System

“…Their complexity and differences arise from the requirement that they should explain relativistic phenomena (such as lensing and structure formation) without appealing to dark matter, whilst in the nonrelativistic regime have some Newtonian and other modified limit. The manner in which such effects are manifest may however vary widely and there have been many previous studies as to the phenomenology of these ideas, particularly in this non-relativistic regime [7,9,35,40,41]. We will briefly outline some of these here, with the caveat that this list is neither exhaustive, nor represents the final story on gravity theories at the time of writing and for a more in depth look at gravity theories, we point the reader towards [18].…”

“…The average of c over noise realizations is the expected signal, S, and its variance is the square of the noise in the correlator, N 2 ; the forecast signal to noise ratio is therefore ρ = S/N . A straightforward calculation (under general assumptions, namely the Gaussianity of the noise, see [41] for discussions of relaxing this requirement) shows that ρ is maximized by choosing a template with Fourier transform:…”