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 inthe Ginzburg-Landau spirit.In this new approach, the precise form of theinflationary potential is constructed from the present WMAP data, and a usefulscheme is prepared to confront with the forthcoming data. In this approach, theWMAP statement excluding the pure phi^4 potential implies the presence of aninflaton mass term at the scale m sim 10^{13}GeV. Chaotic, new and hybridinflation is studied in an unified way. In all cases the inflaton potentialtakes the form V(phi) = m^2 M_{Pl}^2 v(phi/M_{Pl}), where all coefficients inthe polynomial v(x) are of order one. If such potential corresponds to supersymmetry breaking, the susy breaking scale is sqrt{m M_{Pl}} \sim 10^{16}GeVwhich turns to coincide with the GUT scale. The inflaton mass is thereforegiven by a see-saw formula m sim M_{GUT}^2/M_{Pl}. The observables turn to betwo valued functions: one branch corresponds to new inflation and the other tochaotic inflation,the branch point being the pure quadratic potential.For redtilt spectrum, the potential which fits the best the present data and whichbest prepares the way for the forthcoming data is a trinomial polynomialwithnegative quadratic term (new inflation).For blue tilt spectrum, hybridinflation turns to be the best choice. In both cases we find a formula relatingthe inflaton mass with the ratio r of tensor/scalar perturbations and thespectral index ns of scalar perturbations: 10^6 m/M_{Pl}= 127 sqrt{r|1-n_s|};(the coefficient 127 follows from the WMAP amplitude.Implications for stringtheory are discussed.Comment: LaTeX, 33 pages, 24 .ps figures. Improved version published in Phys Rev