Modified theories of gravity with nonminimal coupling and orbital particle dynamics

TL;DR

This paper explores how nonminimal coupling in modified gravity theories affects orbital dynamics, potentially explaining phenomena like Earth's recession from the Sun, and derives preliminary constraints on model parameters from planetary and satellite data.

Contribution

It introduces a phenomenological approach to nonminimal coupling effects on orbital motion and provides initial bounds on model parameters using Solar System and satellite data.

Findings

Secular increase in two-body distance could explain Earth's recession.

Preliminary bounds on parameters from planetary perihelion precessions.

Tighter constraints possible with dedicated data reanalysis.

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. Among the other long-term effects, 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" $\xi$, depending on the matter distribution of the system, and the 4-vector $K^{\mu}=\{K^0,\boldsymbol{K}\}$ 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 $\Delta\dot\varpi$ to the standard perihelion precessions, estimated by the astronomers who produced the EPM2011 ephemerides without modeling the theory considered here, we preliminarily obtain $|\xi K|\lesssim 0.1$ kg s$^{-1}$ for Mars. From guesses on what could be the current bounds on the secular rates of change of the planetary semimajor axes, we get $|\xi K^0|\lesssim 1249$ 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. COBE and GP-B terrestrial satellites yield $|\xi K|\lesssim 2\times 10^{-4}$ kg s$^{-1}$ and $|\xi K_0|\lesssim 2\times 10^{-10}$ kg s$^{-1}$.