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. 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 $K^{\mu }=\{K^0,\mathbf{K}\}$ 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${}^{-1}$.

LaTex2e, 18 pages, 1 table, 2 figures, 29 references. Accepted for publication in Classical and Quantum Gravity

References in corpus (12)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extra force in $f(R)$ modified theories of gravity
• The faint young Sun problem
• Nonminimal coupling of perfect fluids to curvature
• Relativistic effects and dark matter in the Solar system from observations of planets and spacecraft
• Constraints on Dark Matter in the Solar System
• Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling
• Orbital effects of Lorentz-violating Standard Model Extension gravitomagnetism around a static body: a sensitivity analysis
• Celestial Ephemerides in an Expanding Universe
• A Closer Earth and the Faint Young Sun Paradox: Modification of the Laws of Gravitation, or Sun/Earth Mass Losses?
• Local cosmological effects of the order of H in the orbital motion of a binary system
• Unraveling gravity beyond Einstein with extended test bodies

Cited by in corpus (8)

• Thermodynamic interpretation of the generalized gravity models with geometry - matter coupling
• Gravitational Anomalies in the Solar System?
• Perturbation of the metric around a spherical body from a nonminimal coupling between matter and curvature
• Cosmic strings in $f\left(R,L_m\right)$ gravity
• Improved upper bounds on Kaluza-Klein gravity with current Solar System experiments and observations
• The Flyby Anomaly and the Effect of a Topological Torsion Current
• The 1/c expansion of nonminimally coupled curvature-matter gravity model and constraints from planetary precession
• The emission of Gamma Ray Bursts as a test-bed for modified gravity