Are we close to putting the anomalous perihelion precessions from Verlinde’s emergent gravity to the test?

Abstract

In the framework of the emergent gravity scenario by Verlinde, it was recently observed by Liu and Prokopec that, among other things, an anomalous pericenter precession would affect the orbital motion of a test particle orbiting an isolated central body. Here, it is shown that, if it were real, its expected magnitude for the inner planets of the Solar System would be at the same level of the present-day accuracy in constraining any possible deviations from their standard perihelion precessions as inferred from long data records spanning about the last century. The most favorable situation for testing the Verlinde-type precession seems to occur for Mars. Indeed, according to recent versions of the EPM and INPOP planetary ephemerides, non-standard perihelion precessions, of whatsoever physical origin, which are larger than some ≈0.02-0.11 milliarcseconds per century are not admissible, while the putative precession predicted by Liu and Prokopec amounts to 0.09 milliarcseconds per century. Other potentially interesting astronomical and astrophysical scenarios like, e.g., the Earth's LAGEOS II artificial satellite, the double pulsar system PSR J0737-3039A/B and the S-stars orbiting the Supermassive Black Hole in Sgr A * are, instead, not viable because of the excessive smallness of the predicted precessions for them.

Gravitational microlensing in Verlinde's emergent gravity

“…Since the effect of dark mass is cumulative, a much larger effect is generated by galaxies and clusters of galaxies, and a preliminary discussion of that effect (that mimics dark matter) can be found in the original reference [1]. We point out that after the first version of this work several references have appeared [14], [15] that also discuss how to test Verlinde's emergent gravity.…”

“…The first integral was evaluated by assuming that the source and the observer are infinitely far from the star, which is for small lensing angles an excellent approximation. It is instructive to compare the first two contributions in (15).…”

“…Due to the conical geometry, to a very good approximation that ray will exhibit an angle deflection of one half of the total deficit angle, i.e. The total deflection angle is then simply the sum of (15) and (16),…”

The impact of the spin-orbit misalignment and of the spin of B on the Lense-Thrirring orbital precessions of the Double Pulsar PSR J0737-3039A/B

“…The full analytical expression of the Lense-Thirring periastron precession of a two-body system whose spin angular momenta are arbitrarily oriented in space is (Iorio 2017…”

“…It is important to stress that, contrary to the periastron, neither the inclination nor the node undergo 1pN+2pN mass-dependent gravitoelectric shifts. Their full spin-orbit rates can be explicitly expressed as (Iorio 2017)…”