$1/c$ expansion of nonminimally coupled curvature-matter gravity models and constraints from planetary precession

The effects of a nonminimally coupled curvature-matter model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. This work expands upon previous results, extending the framework developed there to compute corrections up to order $O(1/c^4)$ of the 00 component of the metric tensor. It is shown that additional contributions arise due to both the nonlinear form $f^1(R)$ and the nonminimal coupling $f^2(R)$, including exponential contributions that cannot be expressed as an expansion in powers of $1/r$. Some possible experimental implications are assessed with application to perihelion precession.

Figure 1

Exclusion plot for the model parameters $(\theta ,\nu )$, for $\lambda =50L$ and $\mu =0$.

Figure 2

Exclusion plot for the model parameters $(\theta ,\mu )$, for $\lambda =50L$ and $\nu =0$.

Figure 3

Exclusion plot for the model parameters $(\lambda ,\theta )$, for $\mu =\nu =0$.

Figure 4

Exclusion plot for the model parameters $(\lambda ,\nu )$, for $\mu =0$ and $\theta =\{1+{10}^{-13},1+2\times {10}^{-13},1+{10}^{-12}\}$ (light, medium, dark grey).

Figure 5

Exclusion plot for the model parameters $(\lambda ,\nu )$, for $\mu =0$ and $\theta =\{1+{10}^{-10},1+2\times {10}^{-10},1+{10}^{-9}\}$ (light, medium, dark grey).