Paper detail

Constraints on $f(R_{ijkl}R^{ijkl})$ gravity: An evidence against the covariant resolution of the Pioneer anomaly

We consider corrections in the form of $ΔL(R_{ijkl}R^{ijkl})$ to the Einstein-Hilbert Lagrangian. Then we compute the corrections to the Schwarszchild geometry due to the inclusion of this general term to the Lagrangian. We show that $ΔL_3=α_{1/3}(R_{ijkl}R^{ijkl})^{1/3}$ gives rise to a constant anomalous acceleration for objects orbiting the Sun onward the Sun. This leads to the conclusion that $α_{1/3}=(13.91\pm 2.11) \times 10^{-26}(\frac{1}{\text{meters}})^{2/3}$ would have covariantly resolved the Pioneer anomaly if this value of $α_{1/3}$ had not contradicted other observations. We notice that the experimental bounds on $ΔL_3$ grows stronger in case we examine the deformation of the space-time geometry around objects lighter than the Sun. We therefore use the high precision measurements around the Earth (LAGEOS and LLR) and obtain a very strong constraint on the corrections in the form of $ΔL(R_{ijkl}R^{ijkl})$ and in particular $ΔL=α_n(R_{ijkl}R^{ijkl})^n$. This bound requires $α_{1/3}\leq6.12\times 10^{-29}(\frac{1}{\text{meters}})^{2/3}$. Therefore it refutes the covariant resolution of the Pioneer anomaly.