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#### Testing scalar-tensor theories and parametrized post-Newtonian parameters in Earth orbit

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##### Citation

Schärer, A., Angélil, R., Bondarescu, R., Jetzer, P., & Lundgren, A. (2014). Testing
scalar-tensor theories and parametrized post-Newtonian parameters in Earth orbit.* Physical Review
D,* *90*: 123005. doi:10.1103/PhysRevD.90.123005.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-68CC-C

##### Abstract

We compute the PPN parameters $\gamma$ and $\beta$ for general scalar-tensor
theories in the Einstein frame, which we compare to the existing PPN
formulation in the Jordan frame for alternative theories of gravity. This
computation is important for scalar-tensor theories that are expressed in the
Einstein frame, such as chameleon and symmetron theories, which can incorporate
hiding mechanisms that predict environment-dependent PPN parameters. We
introduce a general formalism for scalar-tensor theories and constrain it using
the limit on $\gamma$ given by the Cassini experiment. In particular we discuss
massive Brans-Dicke scalar fields for extended sources. Next, using a recently
proposed Earth satellite experiment, in which atomic clocks are used for
spacecraft tracking, we compute the observable perturbations in the redshift
induced by PPN parameters deviating from their general relativistic values. Our
estimates suggest that $|\gamma - 1| \sim |\beta -1| \sim 10^{-6}$ may be
detectable by a satellite that carries a clock with fractional frequency
uncertainty $\Delta f/f \sim 10^{-16}$ in an eccentric orbit around the Earth.
Such space experiments are within reach of existing atomic clock technology. We
discuss further the requirements necessary for such a mission to detect
deviations from Einstein relativity.