  Although the new era of high precision cosmology of the cosmic microwave
background (CMB) radiation improves our knowledge to understand the infant as
well as the presentday Universe, it also leads us to question the main
assumption of the exact isotropy of the CMB. There are two pieces of
observational evidence that hint towards there being no exact isotropy. These
are first the existence of small anisotropy deviations from isotropy of the CMB
radiation and second, the presence of large angle anomalies, although the
existence of these anomalies is currently a huge matter of debate. These hints
are particularly important since isotropy is one of the two main postulates of
the Copernican principle on which the FRW models are built. This almost
isotropic CMB radiation implies that the universe is almost a FRW universe, as
is proved by previous studies.
  Assuming the matter component forms the deviations from isotropy in the CMB
density fluctuations when matter and radiation decouples, we here attempt to
find possible constraints on the FRW type scale and Hubble parameter by using
the Bianchi type I (BI) anisotropic model which is asymptotically equivalent to
the standard FRW. To obtain constraints on such an anisotropic model, we derive
average and late-time shear values that come from the anisotropy upper limits
of the recent Planck data based on a model independent shear parameter of
Maartens et al. (1995a,b) and from the theoretical consistency relation. These
constraints lead us to obtain a BI model which becomes an almost-FRW model in
time, and which is consistent with the latest observational data of the CMB.
