In this paper, we study the effect of the quantum backreaction on Brans–Dicke cosmology in inflation era. We consider an inflaton field in the D-dimensional spacetime in the framework of Brans–Dicke model. We use a new notation for the Brans–Dicke field in terms of the dilaton field. Then we obtain the vacuum expectation value of the full energy–momentum tensor using WKB approximation of the mode functions which satisfy the equations of motion. The obtained vacuum expectation values of energy– momentum tensor are divergent. In order to renormalize it, we introduce a constant cut-off Ω. The vacuum expectation value of energy–momentum tensor is separated to the UV and IR parts by using Ω cut-off. Then, we use the dimensional regularization method to eliminate divergences by introducing a counterterm action. Also, we calculate the IR contribution of the vacuum expectation value of energy–momentum tensor. Thus, we obtain a physically finite result for the quantum energy–momentum tensor. Finally, we find the effect of backreaction on scale factor.
