Clarifying inflation models: The precise inflationary potential from effective field theory and the WMAP data

We clarify inflaton models by considering them as effective field theories in the Ginzburg-Landau spirit. In this new approach, the precise form of the inflationary potential is constructed from the present WMAP data, and a useful scheme is prepared to confront with the forthcoming data. In this approach, the WMAP statement excluding the pure ${\varphi }^4$ potential implies the presence of an inflaton mass term at the scale $m\sim {10}^{13}\mathrm{GeV}$. Chaotic, new and hybrid inflation models are studied in an unified way. In all cases the inflaton potential takes the form $V(\varphi )=m^2{M}_{\mathrm{Pl}}^{2}v(\varphi /M_{\mathrm{Pl}})$, where all coefficients in the polynomial $v(\phi )$ are of order one. If such potential corresponds to supersymmetry breaking, the corresponding susy breaking scale is $\sqrt{m{M}_{\mathrm{Pl}}}\sim {10}^{16}\mathrm{GeV}$ which turns to coincide with the grand unification (GUT) scale. The inflaton mass is therefore given by a seesaw formula $m\sim M_{\mathrm{GUT}}^2/M_{\mathrm{Pl}}$. The observables turn to be two-valued functions: one branch corresponds to new inflation and the other to chaotic inflation, the branch point being the pure quadratic potential. For red tilted spectrum, the potential which fits the best the present data ($|1-n_s|\lesssim 0.1,r\lesssim 0.1$) and which best prepares the way for the forthcoming data is a trinomial polynomial with negative quadratic term (new inflation). For blue tilted spectrum, hybrid inflation turns to be the best choice. In both cases we find an analytic formula relating the inflaton mass with the ratio $r$ of tensor to scalar perturbations and the spectral index $n_s$ of scalar perturbations: ${10}^6(m/M_{\mathrm{Pl}})=127\sqrt{r|1-n_s|}$ where the numerical coefficient is fixed by the WMAP amplitude of adiabatic perturbations. Implications for string theory are discussed.