Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension

I deduce an exact and analytic Bianchi type I solution of Einstein's field equations, which generalizes the isotropic Lambda CDM universe model to a corresponding model with anisotropic expansion. The main point of the article is to present the anisotropic generalization of the Lambda CDM universe model in a way suitable for investigating how anisotropic expansion modifies observable properties of the Lambda CDM universe model. Although such generalizations of the isotropic Lambda CDM universe model have been considered earlier, they have never been presented in this form before. Several physical properties of the model are pointed out and compared with properties of special cases, such as the isotropic Lambda CDM universe model. The solution is then used to investigate the Hubble tension. It has recently been suggested that the cosmic large-scale anisotropy may solve the Hubble tension. I consider those earlier suggestions and find that the formulae of these papers lead to the result that the anisotropy of the cosmic expansion is too small to solve the Hubble tension. Then, I investigate the problem in a new way, using the exact solution of the field equations. This gives the result that the cosmic expansion anisotropy is still too small to solve the Hubble tension in the general Bianchi type I universe with dust and LIVE (Lorentz Invariant Vacuum Energy with a constant energy density, which is represented by the cosmological constant) and anisotropic expansion in all three directions-even if one neglects the constraints coming from the requirement that the anisotropy should be sufficiently small so that it does not have any significant effect upon the results coming from the calculations of the comic nucleosynthesis during the first ten minutes of the universe. If this constraint is taken into account, the cosmic expansion anisotropy is much too small to solve the Hubble tension.