We investigate a possibility to restrict various inflationary models with nonminimally coupled inflaton field $\varphi$ by future measurement of nonlinear parameter $f_{\mathrm{NL}}$ which characterizes the non-Gaussianity in the cosmic microwave background temperature fluctuation. These models are related to the minimally coupled inflationary models by conformal transformation. We show that the curvature perturbation is invariant under the conformal transformation up to the second order. By using this property we show that nonminimal coupling $f(\varphi )R$ does not produce large non-Gaussianity, and, in particular, the nonlinear parameter takes a narrow range $-0.022<f_{\mathrm{NL}}<-0.007$ in the case of $f(\varphi )=1+\xi {\varphi }^2/m_P^2$ with a wide range of parameter $\xi$.

• Received 8 July 2009

DOI:https://doi.org/10.1103/PhysRevD.81.023504