Averaging matter before solving the Klein-Gordon equation mis-estimates the coarse-grained scalar-field energy density and pressure, by factors up to about 10^5 for a Yukawa model and with mean-field deviations exceeding 10^5 for screened chameleons.
This also the case in models [48, 49] in which the scalar field coupled simply to a dark matter component to avoid varia- tions of fundamental constants [52]
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Scalar-tensor theories at different scales: averaging the scalar sector
Averaging matter before solving the Klein-Gordon equation mis-estimates the coarse-grained scalar-field energy density and pressure, by factors up to about 10^5 for a Yukawa model and with mean-field deviations exceeding 10^5 for screened chameleons.