Modified theories of gravity with nonminimal coupling and orbital particle dynamics

Abstract

We consider a non-rotating, massive test particle acted upon by a ‘pressure’-type, non-geodesic acceleration arising from a certain general class of gravitational theories with nonminimal coupling between the matter and the metric. The resulting orbital perturbations for a two-body system are investigated both analytically and numerically. Remarkably, a secular increase of the two-body relative distance occurs. In principle, it may yield a physical mechanism for the steady recession of the Earth from the Sun recently proposed to explain the Faint Young Sun Paradox in the Archean eon. At present, the theorists have not yet derived explicit expressions for some of the key parameters of the model, such as the integrated ‘charge’ ξ, depending on the matter distribution of the system, and the 4-vector connected with the nonminimal function F. Thus, we phenomenologically treat them as free parameters, and preliminarily infer some indications on their admissible values according to the most recent Solar System’s planetary ephemerides. From the latest determinations of the corrections to the standard perihelion precessions, estimated by the astronomers who produced the EPM2011 ephemerides without modeling the theory considered here, we preliminarily obtain |ξK| ≲ 0.1 kg s−1 for the Sun and Mars. From guesses on what could be the current bounds on the secular rates of change of the planetary semimajor axes, we get |ξK0| ≲ 1249 kg s−1 for Mars. More effective constraints could be posed by reprocessing the same planetary data sets with dedicated dynamical models including the effects studied here, and explicitly estimating the associated parameters. The Earth and the COBE and GP-B satellites yield |ξK| ≲ 2 × 10−4 kg s−1 and |ξK0| ≲ 2 × 10−10 kg s−1, respectively .