The Planck satellite, successfully launched on 2009 May 14 to measure with unprecedented accuracy the primary cosmic microwave background (CMB) anisotropies, is operating as expected. The Standard Model of the Universe ("concordance" model) provides the current realistic context to analyze the CMB and other cosmological/astrophysical data, inflation in the early universe being part of it. The Planck performance for the crucial primordial parameter r, the tensor-to-scalar ratio related to primordial B-mode polarization, will depend on the quality of data analysis and interpretation. The Ginzburg-Landau (G-L) approach to inflation allows us 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, taking into account 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 ΛCDMr model, i.e., the standard ΛCDM model augmented by r, and the ΛCDMrT model, where the scalar spectral index, ns , and r are related through the theoretical "banana-shaped" curve r = r(ns ) coming from the G-L theory with a double-well inflaton potential. In the latter case, the analytical expressions for ns and r are imposed as a hard constraint in a Monte Carlo Markov Chain (MCMC) data analysis. We consider two C ?-likelihoods (with and without B modes) and take into account the white noise sensitivity of Planck (LFI and HFI) in the 70, 100, and 143 GHz channels as well as the residuals from systematic errors and foregrounds. We also consider a cumulative channel of the three mentioned. We produce the sky (mock data) for the CMB multipoles CTT l , CTE l , CEE l , and CBB l from the ΛCDMr and ΛCDMrT models and obtain the cosmological parameter marginalized likelihood distributions for the two models. Foreground residuals affect only the cosmological parameters sensitive to the B modes. As expected, the likelihood r distribution is more clearly peaked near the fiducial value (r = 0.0427) in the ΛCDMrT model than in the ΛCDMr model. The best value for r in the presence of residuals turns out to be about r 0.04 for both the ΛCDMr and the ΛCDMrT models. The ΛCDMrT model is very stable; its distributions do not change by including residuals and the B modes. For r we find 0.028 r 0.116 at a 95% confidence level (CL) with the best value r = 0.04. We also 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 (1σ) detection is very likely. For a 95% CL detection (2σ), the level of foreground residual should be reduced to 10% or lower of the adopted toy model. The lower bounds (and most probable value) we infer for r support the searching of CMB B-mode polarization in the current data as well as the planned CMB missions oriented toward B polarization.
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