The relic gravitational waves are the cleanest probe of the violent times in the very early history of the Universe .
They are expected to leave signatures in the observed cosmic microwave background anisotropies .
We significantly improved our previous analysis ( ( 1 ) ) of the 5-year WMAP TT and TE data at lower multipoles \ell .
This more general analysis returned essentially the same maximum likelihood ( ML ) result ( unfortunately , surrounded by large remaining uncertainties ) : the relic gravitational waves are present and they are responsible for approximately 20 \% of the temperature quadrupole .
We identify and discuss the reasons by which the contribution of gravitational waves can be overlooked in a data analysis .
One of the reasons is a misleading reliance on data from very high multipoles \ell , another - a too narrow understanding of the problem as the search for B -modes of polarization , rather than the detection of relic gravitational waves with the help of all correlation functions .
Our analysis of WMAP5 data has led to the identification of a whole family of models characterized by relatively high values of the likelihood function .
Using the Fisher matrix formalism we formulated forecasts for Planck mission in the context of this family of models .
We explore in details various ‘ optimistic ’ , ‘ pessimistic ’ and ‘ dream case ’ scenarios .
We show that in some circumstances the B -mode detection may be very inconclusive , at the level of signal-to-noise ratio S / N = 1.75 , whereas a smarter data analysis can reveal the same gravitational wave signal at S / N = 6.48 .
The final result is encouraging .
Even under unfavourable conditions in terms of instrumental noises and foregrounds , the relic gravitational waves , if they are characterized by the ML parameters that we found from WMAP5 data , will be detected by Planck at the level S / N = 3.65 .