Complete constraints on a nonminimally coupled chaotic inflationary scenario from the cosmic microwave background

In spite of its many successes, the standard big-bang theory has faced serious problems, namely, the horizon, flatness, and monopole problems. In the beginning of the 1980s, an epoch-making idea called the inflationary scenario was advocated to solve these cosmological puzzles [1,2]. Later it was recognized that the concept gives us not only a solution to such puzzles, but also to the origin of density perturbations [3–6]. Among the various models of the inflationary scenario, Linde’s chaotic model [7] has been regarded as a feasible and natural mechanism for the realization of inflationary expansion. This model still has a serious problem; i.e., one has to fine-tune the self-coupling constant λ of the inflaton unacceptably small to have a reasonable amplitude of the density perturbations. On the other hand, the feasibility of inflation has been investigated in alternative theories of gravity, e.g., the Brans-Dicke scalar tensor theory [8,9], and nonminimal coupling theories of gravity [10,11]. Fakir and Unruh (FU) [12,13] proposed a way to avoid fine-tuning λ by introducing a relatively large nonminimal coupling constant |ξ| > 1 in the context of the chaotic inflationary model. According to their results, the large value of ξ, i.e., order of 10, allows us to have a reasonable value for the coupling constant λ = 10−2. Thus the FU scenario remains a reasonable model of the inflationary scenario. Constraints on the FU scenario are discussed by some authors [14,15] using the scalar perturbations generated during the inflationary phase. We investigated the spec-