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

Abstract

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 demonstrating that there is 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 that are shown as real features by the Planck satellite results. These evidences 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 these deviations by using the Bianchi type I (BI) anisotropic model which is asymptotically equivalent to the standard FRW. Then we obtain the separations from the FRW type scale factor and the Hubble parameter in the form of time dependent functions. Hence we put constraints on the anisotropy coefficients from the anisotropy upper limits of the recent Planck data and from the theoretical consistency relation. These constraints lead us to obtain a BI model which becomes to be an almost FRW in time that is consistent with observational data of the CMB.

The Hubble IR cutoff in holographic ellipsoidal cosmologies

“…We see that the present shear is constrained by σ/θ 10 −9 [4], which implies for the metric (58) that 1 ≤ α ≤ 1.000000004, and 0 ≤ ≤ 1.33333 × 10 −9 . Note that Eq.…”

“…Specifically, for Bianchi type-I models the present shear is constrained by σ/θ 10 −9 [4], and since for metric (58) is valid σ/θ = 2 3…”

Cosmologies with Scalar Fields from Higher Dimensions Applied to Bianchi Type VIh=-1 Model: Classical and Quantum Solutions

“…The evidence given by these data leads us to the possibility of considering that there is no exact isotropy, since there exist small anisotropy deviations of the CMB radiation and apparent large angle anomalies. In that context, there have been recent attempts to fix constraints on such deviations by using the Bianchi anisotropic models [2]. The basic idea behind these models is to consider the present observational anisotropies and anomalies as imprints of an early anisotropic phase on the CMB which in turn can be explained by the use of different Bianchi models.…”

“…The basic idea behind these models is to consider the present observational anisotropies and anomalies as imprints of an early anisotropic phase on the CMB which in turn can be explained by the use of different Bianchi models. In particular, Bianchi I model seems to be related to large angle anomalies [2] (and references therein).…”

Wheeler–DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

“…Anisotropies observed in the cosmic microwave background (CMB) are small enough to suggest that anisotropic models of spacetimes become isotropic ones by evolving in time [2][3][4]. One can expect that pre-inflationary anisotropies played an important role (for example they can be responsible for the coupling between the gravitational field and the inflaton field) so if inflationary models are considered, one should understand the dynamics of anisotropies.…”