Can Stiff Matter Solve the Hubble Tension?

Abstract

A new form of the mathematical expression for the co-moving volume element of a flat universe with cosmological constant, cold matter, and stiff matter is presented. It is used to determine the constraints from the Planck measurements of the Hubble parameter on the amount of stiff matter in the universe. These constraints are used to investigate whether the presence of stiff matter can solve the Hubble tension. It is found that the Planck measurements lead to an upper bound on the present value of the density parameter of stiff matter ΩS0<5⋅10−23, and that this is too small to solve the Hubble tension. Report. The main objective of this article is to introduce a novel mathematical expression for the co-moving volume element in a flat universe that includes a cosmological constant, cold matter, and stiff matter. This expression is utilized to derive constraints on the amount of stiff matter in the universe based on the Planck measurements of the Hubble parameter. These constraints are then examined to assess whether stiff matter could potentially resolve the Hubble tension. The findings indicate that the Planck measurements impose an upper limit on the current value of the density parameter of stiff matter, ΩS0<5⋅10−23, which is insufficient to resolve the Hubble tension.