  I deduce an exact and analytic Bianchi type I solution of Einsteins field
equations, which generalizes the isotropic LambdaCDM universe model to a
corresponding model with anisotropic expansion. The main point of the article
is to present the anisotropic generalization of the LambdaCDM universe model in
a way suitable for investigating how anisotropic expansion modifies observable
properties of the LambdaCDM universe model. Although such generalizations of
the isotropic LambdaCDM 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 LambdaCDM universe model. The solution is then used to
investigate the Hubble tension. It has recently been suggested that the cosmic
largescale 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.
