Theoretical Foundations of PGWs Printed in the CMB and its Observational
  Status
  The anisotropy study cosmic microwave background (CMB) is one of the main
observational tools for modern cosmology. However, alongside the study of the
thermal fluctuations of the CMB are other equally important information, which
is known as the polarization of the CMB. The inflationary model predicts that
the CMB is linearly polarized and the physical mechanism of this polarization
is studied from the Thompson scattering, the dominant process on the surface of
last scattering. There are basically two types of polarization called E and B
modes, the first produced by scalar perturbations and the latter by tensor
perturbations, such as those due to gravitational waves in the primordial
universe. So if we are able to measure these types of polarization will have an
entry to the study of the inflationary epoch. This paper presents the main
physical mechanisms that support theoretically the polarization of the CMB due
to primordial gravitational waves (PGW) and the revision of the main
observables, grouped in so-called Stokes parameters (Q, U, I), Which brings us
information to achieve the contrast the angular power spectrum produced by the
polarization of the CMB, which shows to be in excellent agreement with the
$\Lambda$CDM model.
