Induced Violation of Weak Equivalence Principle in the Brans-Dicke Theory

A quantum correction to the Brans-Dicke theory due to interactions among matter fields is calculated, resulting in violation of WEP, hence giving a constraint on the parameter ω far more stringent than accepted so far. The tentative estimate gives the lower bounds > ∼106 and > ∼108 for the assumed force-range > ∼1m and > ∼1AU, respectively. E-mail: [email protected] Many aspects of the Brans-Dicke (BD) theory [1], as a classical theory, have been the focus of extensive studies. Little attention seems to have been paid, however, to quantum effects due to the interaction among matter fields. This might be serious, because it results in violation of Weak Equivalence Principle (WEP) to the extent that the bound on the parameter ω will be made much more stringent than accepted so far, as will be demonstrated on the basis of a simple model. Assume the Lagrangian: L = √−g [ 1 8ω φR − 1 2 g∂μφ∂νφ+ Lmatter ]