Bianchi I model: an alternative way to model the present-day Universe

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 present-day 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 secondly, 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 Friedmann Robertson Walker (FRW) models are built. This almost-isotropic CMB radiation implies that the universe is almost an FRW universe, as is proved by previous studies. Assuming that 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, Ellis & Stoeger 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.