content_image/371201.jpg content_image/371199.jpg
temporarily [206] or constantly [151]. It is one of the best methods to carry a bayesian analysis for a model selection based on the data. Their disadvantage is that they require to treat each model individually and cannot provide ways to use current constraints to build new models. 

## 2. Cosmic strings and CMB fluctuations 

As we shall also see below (at Sec. IV) that several models of inflation can produce cosmic strings (see Sec. III G). This has important consequences when confronting the model to the data as some degeneracy has been observed between the spectral index and the fraction of cosmic strings responsible for the temperature anisotropies at the 10th multipole f$_{10}$ [263]. The 2D likelihood function when f$_{10}$ is included is represented in Fig. 2. 

<img src='content_image/371201.jpg'>

When a certain fraction of cosmic strings is present, the spectral index best fit and error bars - from WMAP 3years data - are shifted and enlarged, and (at 1 σ ) we read approximately: 

<img src='content_image/371199.jpg'>

Once other data sets are taken into account (BBN, large scale structures), the current data can only put an upper constraint on the fraction of cosmic strings f$_{10}$ < 0 . 11 at 2 σ [263]. This constraint should be improved by the future PLANCK data, both at large multipole and from confrontation to the polarized data, notably the B-modes. Luckily, if cosmic string are present then they should contribute to them [264–266], and their fraction is not degenerate 

