content_image/346225.jpg content_image/346228.jpg
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] 

<img src='content_image/346225.jpg'>

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. 

<img src='content_image/346228.jpg'>

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 

