Can Anisotropic Cosmic Expansion or Stiff Matter Solve the Hubble Tension?

Abstract

I deduce a new form of an exact anisotropic solution of Einstein’s field equations which was originally found and presented in a different way by Saunders (1969) in 1969. This form of the solution shows in an explicit way how it generalizes the isotropic \(\Lambda\)CDM universe model to a corresponding model with anisotropic expansion – an A\(\Lambda\)CDM model. It is used here to investigate whether anisotropy of the cosmic expansion can resolve the Hubble tension, which is a long-standing problem in cosmology. The conclusion is that cosmic anisotropy, even in a general Bianchi type I framework, cannot solve the Hubble tension. Due to its mathematical similarity to the A\(\Lambda\)CDM model, a universe model with stiff matter, a S\(\Lambda\)CDM model, is also discussed in this chapter, and it is shown that observational restrictions on the amount of stiff matter in the universe, mean that there is too little stiff matter to solve the Hubble tension.