The Cosmological Flatness Problem and Limits on Dark Matter

Abstract

The traditional argument to justify Omega_0 = rho/rho_{crit} = 1 which suggests an absurdly close agreement between the initial expansion energy of the universe and its binding energy is reversed to show that it is unreasonable to expect the current value of W to be within a factor of ten or more of unity. The Uncertainty Principle is applied to the initial value of the mass require to close the universe. The tiny fractional uncertainty is amplified so that the current fractional uncertainty is of the order of unity. This suggests that the requirement of exact initial agreement between the binding energy and the expansion energy is unreasonable as it can never be tested by contemporary measurement.