Time delays across saddles as a test of modified gravity

Abstract

Modified gravity theories can produce strong signals in the vicinity of the saddles of the total gravitational potential. In a sub-class of these models this translates into diverging time-delays for echoes crossing the saddles. Such models arise from the possibility that gravity might be infrared divergent or confined, and if suitably designed they are very difficult to rule out. We show that Lunar Laser Ranging during an eclipse could probe the time-delay effect within meters of the saddle, thereby proving or excluding these models. Very Large Baseline Interferometry, instead, could target delays across the Jupiter-Sun saddle. Such experiments would shed light on the infrared behaviour of gravity and examine the puzzling possibility that there might be well-hidden regions of strong gravity and even singularities inside the solar system.

Tests of modified gravity theories in the Solar System

“…It is well known preferred acceleration scale effects are not properly covered by the PPN formalism, e.g. time delay effects across MONDian bubbles as characterised in [60]. Perhaps a way forward would be developing a Post Parametrised Saddle formalism?…”

From Galactic Bars to the Hubble Tension: Weighing Up the Astrophysical Evidence for Milgromian Gravity

“…This severely limits the prospects for a decisive test of gravity in the low-acceleration regime. Similar issues are likely to arise with the Earth-Moon saddle region [863]. Those authors suggested measuring the time taken for light to cross this region using retroreflectors installed on the Moon.…”