parameters (in particular n$_{s}$ with Ω$_{b}$ h $^{2}$, the optical depth τ , its running, the tensor-to-scalar ratio, r , and the fraction of cosmic strings). If the tensor-to-scalar ratio r and/or a running α$_{s}$ are introduced, the best fit and error bars 18 (at 1 σ ) [13] n$_{s}$ = 1 . 017 +0 . 042 − 0 043 , α$_{s}$ = − 0 . 028 ± 0 . 020 , n$_{s}$ = 0 . 970 ± 0 . 015 , r < 0 . 22 (at 2 σ ) , n$_{s}$ = 1 . 089 +0 . 070 − 0 068 , r < 0 . 55 (at 2 σ ) , α$_{s}$ = − 0 . 053 ± 0 . 028 . (69) These data therefore suggest that a red spectrum is favored ( n$_{s}$ = 1 excluded at 2 . 5 σ from WMAP and at 3 . 1 σ when other data sets are included) if there is no running. Although, the reader and the model builder should keep in mind that a lot more data is necessary before these results can be used as bench-mark points (see for e.g. [262] for a pedagogical presentation about Bayesian model selection). These various best fit values are consistent with a model that predicts a non-negligible level of tensor or a running of the spectral index. These results are summarized in Fig. 1. FIG. 1: Two-dimensional likelihood for the spectral index, the running and the ratio tensor/scalar, from the WMAP data only (blue) and the WMAP data combined with the BAO and supernovae data sets (red) at 1 σ and 2 σ . Figures are taken from [13]. The confrontation of inflationary models to data can also be done by directly constraining the parameters of the potential for each model [207] (see also [208] for a pedagogical review). These methods have the advantage of not relying on a generic parameterization of the power spectrum/potential, or the slow-roll conditions, as some models violate those assumptions 18 Note that the results vary significantly when WMAP data only or combined observations are used, see Ref. [13] for details. 29