Parametrized free functions and saddle stresses in modified gravity

Abstract

Building on previous work, we explore the parameter space of free functions in non-relativistic modified gravity theories more widely, showing that in fact the two broad regimes present have similar functional forms between different models. Using different parameterisations, we investigate the effects on scaling tidal stresses as well as attempt to constrain the (hitherto poorly understood) deep MONDian scaling C. We also consider a new intermediate MOND limit in these theories and what it tells us about the transition between these regimes. Finally we suggest a model independent framework, with the aim of constraining the MONDian parameter space using future data, such as the forthcoming LISA Pathfinder mission.

Tests of modified gravity theories in the Solar System

“…. , w ≫ 1 whereas in the type I case [8], S yy was found to scale much more conservatively in the DM regime.…”

“…Now we can consider numerical solutions, using a relaxation code to solve (2) on an adaptive lattice. Such a code was first employed to study these theories in [4] and subsequently adapted for more general free functions in [8].…”

“…With these in mind, we can solve the inhomogenous ODE, as before, to find the variation in profile functions for different a, b. To make a connection with other modified force laws [8], consider under spherical symmetry:…”

“…This would involve redirecting the spacecraft from its location parked at Lagrange point L1 to a saddle of the Sun-Earth-Moon system [7] once its nominal mission is completed. Previous analysis have considered non-linear theories with modified Poisson equations, which naturally give rise to modified gravity behaviour (as seen most clearly in [8]). A review of the different non-relativistic limits of preferred acceleration scale theories [5] categorised these as types I, II and III (we summarise these briefly in Appendix A).…”

Screening Solutions in Modified Gravity Theories

“…where S 3 (ψ) is calculated from the change of variable and components of ∇φ (more details of which can be found in [11]). These results show that the tidal stresses diverge with radial exponent 1 < c < 2.…”