Can we measure the Rφ2 coupling parameter at tree-level scattering?

The lowest order invariant amplitudes for the 2→2 processes concerning the action S[g,φ]=Fd4x -g [2R/κ2+1/2(gμν,μφ,νφ+λRφ2)] are computed. It is found that these results do not depend on the value of λ; therefore, it is impossible to measure the Rφ2 coupling parameter at tree-level scattering in this case. It is also shown that the theorydescribed by the above action is equivalent at the classical level to Einstein's theory with a massless minimally coupled scalar field provided that 1+λκ2φ2/4>0. Some consequences for cosmology and black holes are discussed. © 1995 The American Physical Society.