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The evolution of primordial fluctuations in a Brans-Dicke type scalar-tensor gravity theory is comprehensively investigated. The harmonic attractor model, in which the scalar field has its harmonic effective potential in the Einstein conformal frame and the theory relaxes toward Einstein gravity with time, is considered. The evolution of adiabatic initial perturbations in flat SCDM models is examined from the radiation-dominated epoch up to the present. We discuss how the scalar-tensor gravity affects the evolution of metric and matter perturbations, mainly focusing on the observational consequences, i.e., the matter power spectrum and the power spectrum of cosmic microwave background temperature. We find that the early time deviation is characterized only by the large static gravitational constant while the late time behavior is qualitatively different from that in Einstein gravity because the time variation of the gravitational constant and its fluctuation have non-negligible effects. The attracting scalar-tensor gravity affects only small scale modes due to its attracting nature, the degree of which is far beyond the post-Newtonian deviation at the present epoch.
Nagata et al. (Mon,) studied this question.