Forecast for the Planck precision on the tensor to scalar ratio and
  other cosmological parameters
  The Planck satellite is right now measuring with unprecedented accuracy the
primary Background CMB anisotropies. The Standard Model of the Universe
(including inflation) provides the context to analyze the CMB and other data.
The Planck performance for r, the tensor to scalar ratio related to primordial
B mode polarization, will depend on the quality of the data analysis. The
Ginsburg Landau approach to inflation allows to take high benefit of the CMB
data. The fourth degree double well inflaton potential gives an excellent fit
to the current CMB+LSS data. We evaluate the Planck precision to the recovery
of cosmological parameters within a reasonable toy model for residuals of
systematic effects of instrumental and astrophysical origin based on publicly
available information.We use and test two relevant models: the LambdaCDMr
model, i.e. the standard LambdaCDM model augmented by r, and the LambdaCDMrT
model, where the scalar spectral index, n_s, and r are related through the
theoretical `banana-shaped' curve r = r(n_s) coming from the double-well
inflaton potential. In the latter case, r = r(n_s) is imposed as a hard
constraint in the MCMC data analysis. We take into account the white noise
sensitivity of Planck in the 70, 100 and 143 GHz channels as well as the
residuals from systematics errors and foregrounds. Foreground residuals turn to
affect only the cosmological parameters sensitive to the B modes. The best
value for r in the presence of residuals turns to be about r simeq 0.04 for
both the LambdaCDMr and the LambdaCDMrT models. We compute the B mode detection
probability by the most sensitive HFI-143 channel. At the level of foreground
residual equal to 30% of our toy model only a 68% CL detection of r is very
likely. For a 95% CL detection the level of foreground residual should be
reduced to 10% or lower of the adopted toy model (ABRIDGED).
