Abstract

Motivated by the back-reaction debate, and some unexplained characteristics of the CMB, we investigate the possibility of some anisotropy in the universe observed around us. To this aim, we build up a novel prediction for the Hubble law for the late universe from a Bianchi type I model, taken as proof of concept, transcribing the departure of such model from a ΛCDM model. We dicussed the redshift measurement in this universe, and finally formalized the Hubble diagram.

Highlights

  • One of the main assumption of the ΛCDM model is that, on large scales, an isotropic and homogeneous spacetime can describe accurately the universe, at least at the background level

  • Together with the result that fundamental observers measuring isotropic Cosmic Microwave Background [7,8] [CMB] radiation implied, we are in a spatially almost homogeneous and isotropic region [9,10,11], this favored the dominant idea that the universe is an almost Friedman–Lemaître–Robertson–Walker [12,13,14,15] [FLRW] spacetime over keeping a fading out anisotropic behavior, as in Ref. [16]

  • The expansion rate can be found in the Bianchi identity, which can be recast as d ln ρ = − Θ = − 3 +

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Summary

Introduction

One of the main assumption of the ΛCDM model is that, on large scales, an isotropic and homogeneous spacetime can describe accurately the universe, at least at the background level. Anisotropy and inhomogeneity might either explain cosmic acceleration [1,2,3], or, according to other authors [4], have negligible effects Apart from this point, anisotropies in cosmological expansion have been discussed since the early works of [5,6], their early models were favoring the late smearing of such departures from isotropy. Together with the result that fundamental observers measuring isotropic Cosmic Microwave Background [7,8] [CMB] radiation implied, we are in a spatially almost homogeneous and isotropic region [9,10,11], this favored the dominant idea that the universe is an almost Friedman–Lemaître–Robertson–Walker [12,13,14,15] [FLRW] spacetime over keeping a fading out anisotropic behavior, as in Ref.

Anisotropic ΛCDM Model
Model Setup
Anisotropy-Scale Relation Interpretation
Redshift in Anisotropic Models
Comoving Distance
Redshift Calculation
Angle Averaging and Scale-Small Anisotropic Deviation Redshift Relation
Hubble Law in Anisotropic Models
Generalized Hubble Parameter
Hubble-Scale-Redshift Relation
Hubble-Redshift Relation
Preliminary Confrontation with Observations
Fit Method
Conclusions

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