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## E. Confrontation to the CMB and other observational data 

The CMB data is currently providing (including WMAP, CBI $^{13}$, VSA $^{14}$, ACBAR $^{15}$, Boomerang $^{16}$) and will provide (including PLANCK) stringent observational data to con- strain the power spectrum of density fluctuations. There are other data set which can be used in conjunction; type Ia supernovae (SN), Baryon Acoustic Oscillations (BAO), large scale structures, Lyman- α forest, etc. In this section, we briefly review the current bounds on the amplitude of the power spectrum, spectral index, and tensor to scalar ratio, running of the spectral index, non-Gaussianities, cosmic strings, and isocurvature perturbations. 

## 1. Primordial power spectrum for scalar and tensor 

Most of the observational tests of inflation models arise from the 2 point correlation function, related to the power spectrum of the primordial perturbations, both for scalar and tensor perturbations. The most recent update on the WMAP results, combined with SN and BAO data confirmed that so far the minimal 6-parameter ΛCDM model provides a very good fit of the combined observations. It contains the baryon, CDM, and dark energy fractions; Ω$_{b}$ h $^{2}$, Ω$_{c}$ h $^{2}$, Ω$_{Λ}$ , the spectral index n$_{s}$ , the optical depth of reionization, τ$_{reion}$ , and the normalization of the power-spectrum P $_{ζ}$( k$_{0}$ ), with central values and 1 σ error bars for the inflation related parameters given by [13]: 

<img src='content_image/349280.jpg'>

In this minimal model, the primordial power spectrum is approximated by the expression of Eq. (35) and the tensor contribution or the k − dependence of the spectral index are ne- glected $^{17}$. It is important to stress that these central values and error bars vary significantly when other parameters are introduced to fit the data, in part because of degeneracies between 

