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We use cosmic microwave background data from WMAP, ACBAR, VSA and CBI, and galaxy power spectrum data from 2dF, to constrain flat cosmologies based on the Jordan-Brans-Dicke theory, using a Markov chain Monte Carlo approach. Using a parametrization based on =1/4, and performing an exploration in the range ln-9, 3, we obtain a 95% marginalized probability bound of ln120.
Acquaviva et al. (Fri,) studied this question.