Inflation in the nonminimal theory with ‘K(φ)R’ term

It is widely accepted that the idea of inflation [2] is the best solution to many cosmological problems such as flatness, homogeneity and isotropy of the observed universe [3]. In models of particle physics models of inflation, it took place essentially due to a scalar field, the inflaton field, whose potential is so flat that the inflaton can roll down only very slowly [4]. Under such a ‘slowroll’ condition, the curvature perturbation is produced nearly scale invariant way and this feature is precisely confirmed by the measurements of the anisotropies of the CMB and the observations of the large scale structure [5]. The biggest question is the origin of the inflaton field itself and the form of its nearly flat potential. Very Recently Bezrukov and Shaposhnikov (BS) reported an intriguing possibility that the standard model with an additional non-minimal coupling term of the Higgs field (H) and the Ricci scalar (∼ a|H|2R) can give rise to inflation [6] without introducing any additional scalar particle in the theory. 2. The new thing that the BS showed was that the “physical Higgs potential” in Einstein frame is indeed nearly flat at the large field value limit and fit the COBE data U/ε = (0.027MPl) once the ratio between the quartic coupling of the Higgs field (λ ) and the non-minimal coupling constant (a) is chosen to be small as √