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Solar System constraints to nonminimally coupled gravity

2013; American Physical Society; Volume: 88; Issue: 6 Linguagem: Inglês

10.1103/physrevd.88.064019

1550-7998

Orfeu Bertolami, Riccardo March, Jorge Páramos,

Geophysics and Gravity Measurements

We extend the analysis of Chiba et al. [Phys. Rev. D 75, 124014 (2007)] of Solar System constraints on $f(R)$ gravity to a class of nonminimally coupled (NMC) theories of gravity. These generalize $f(R)$ theories by replacing the action functional of general relativity with a more general form involving two functions ${f}^{1}(R)$ and ${f}^{2}(R)$ of the Ricci scalar curvature $R$. While the function ${f}^{1}(R)$ is a nonlinear term in the action, analogous to $f(R)$ gravity, the function ${f}^{2}(R)$ yields a NMC between the matter Lagrangian density ${\mathcal{L}}_{m}$ and the scalar curvature. The developed method allows for obtaining constraints on the admissible classes of functions ${f}^{1}(R)$ and ${f}^{2}(R)$, by requiring that predictions of NMC gravity are compatible with Solar System tests of gravity. Then we consider a NMC model which accounts for the observed accelerated expansion of the Universe and we show that such a model cannot be constrained by the present method.