Testing scalar-tensor theories and PPN parameters in Earth orbit

TL;DR

This paper calculates PPN parameters for scalar-tensor theories in Earth orbit, proposing a satellite experiment with atomic clocks to detect deviations from general relativity.

Contribution

It introduces a formalism for scalar-tensor theories in the Einstein frame and assesses the potential of satellite-based atomic clock experiments to test these theories.

Findings

Potential detection of PPN deviations at the level of 10^{-6} using existing atomic clock technology.

Satellite experiments could observe environment-dependent PPN parameters predicted by chameleon and symmetron theories.

Constraints on scalar-tensor theories from the Cassini experiment are incorporated into the analysis.

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.