Principles of the wave dark matter detection in gravitational redshift experiments in the Solar System

We explore the possibility of using measurements of the gravitational redshift effect as a means to constrain wave dark matter – a class of models in which the dark matter is accounted for by light scalar particles that behave like classical waves. We construct a mathematical framework that is appropriate for clock comparison experiments with remote clocks and can be used to determine the values of the coupling constants of such dark matter with particles of the Standard Model. Using this framework, we consider an experiment to detect dark matter of the Galactic halo using two satellites equipped with accurate and stable atomic clocks and placed into elliptical heliocentric orbits. We demonstrate that, in most cases, the accuracy of this experiment turns out to be not better than that of ground-based experiments with colocated clocks. The limitation of theaccuracy of the space-based experiment is found to be due to the non-relativistic Doppler compensation system, required when using moving clocks, which decreases the amplitude of the useful signal. Possible solutions to this problem are discussed.