A Measure on a Subspace of FRW Solutions and ``The Flatness Problem" of Standard Cosmology

Abstract

We use the metric on the space of gravity fields given by DeWitt to construct a unique kinematic measure on the space of FRW simple fluids and show that when the mass parameter $Ω$ is used as a coordinate this measure is singular at $Ω= 1$. This singularity, combined with the time evolution of $Ω$, distorts distributions of $Ω$ values to be concentrated in the neighborhood of 1 at early times. It is a distorted distribution of $Ω$ values that sometimes misleads the casual observer to conclude that $Ω$ must be exactly equal to 1.