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

Abstract

We consider corrections in the form of $\Delta L(R_{ijkl}{R}^{ijkl})$ 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 $\Delta L_3={\alpha }_{1/3}(R_{ijkl}{R}^{ijkl}{)}^{1/3}$ gives rise to a constant anomalous acceleration for objects orbiting the Sun onward the Sun. This leads to the conclusion that ${\alpha }_{1/3}=(13.91\pm 2.11)\times 10^{-26}(\frac{1}{\text{meters}}{)}^{2/3}$ would have covariantly resolved the Pioneer anomaly if this value of ${\alpha }_{1/3}$ had not contradicted other observations. We notice that the experimental bounds on $\Delta L_3$ 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 $\Delta L(R_{ijkl}{R}^{ijkl})$ and in particular $\Delta L={\alpha }_n(R_{ijkl}{R}^{ijkl}{)}^n$. This bound requires ${\alpha }_{1/3}\le 6.12\times 10^{-29}(\frac{1}{\text{meters}}{)}^{2/3}$. Therefore it refutes the covariant resolution of the Pioneer anomaly.

...v5: references added, new discussions added

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Cited by in corpus (8)

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• The Pioneer Anomaly
• Solar system constraints on Rindler acceleration
• Notes on "quantum gravity" and non-commutative geometry
• Phenomenological covariant approach to gravity
• Does the Neptunian system of satellites challenge a gravitational origin for the Pioneer anomaly?
• A Model for the Pioneer Anomaly