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

This paper presents a new exact inflationary solution to thenon-minimally coupled scalar field. The inflation is driven by theevolution 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 densityfluctuations $n_s $ is consistent with the result of WMAP3(Wilkinson Microwave Anisotropy Probe 3) for $Lambda$CDM(Lambda-Cold Dark Matter). This model relaxes the constraint to thequartic coupling constant. And it can enter smoothly into aradiation-dominated stage when inflation ends.