An exact inflationary solution in the chaotic model with non-minimal coupling

This paper presents a new exact inflationary solution to the non-minimally coupled scalar field. The inflation is driven by the evolution of a scalar field with inflation potential V(\varphi ) = (\lambda / 4)\varphi ^4 + b_1 \varphi ^2 + b_2 + b_3 \varphi ^ - 2 + b_4 \varphi ^ - 4. The spectral index of the scalar density fluctuations n_s is consistent with the result of WMAP3 (Wilkinson Microwave Anisotropy Probe 3) for \LambdaCDM (Lambda-Cold Dark Matter). This model relaxes the constraint to the quartic coupling constant. And it can enter smoothly into a radiation-dominated stage when inflation ends.