The flatness problem as a natural cosmological phenomenon

Abstract

An interplay between elementary particle interactions at very high energies and the expansion of the Universe is studied in the context of the inflationary model to find a possible explanation for an observed flatness which remains a cosmological puzzle. As is well known from observation, the universe is at least fairly flat implying that the relative energy density is almost unity. This value of energy is extrapolated from the matter dominated and the radiation dominated phases of the false unbroken grand unified vacua separately, to the true vacuum. This present relative energy density of order unity must have been of order 10-61 at the Planck time of 10-43 seconds that leads to the gravity breaking from strong and weak interactions. A very fine tuning of one part in 10-61 is needed to keep the relative energy density close to unity over a very longtime to ensure that the universe is very old as observed. This in itself does not ensure that the curvature term in the Friedman field equations of motion is unimportant. These equations are solved separately, for the open, closed and flat universes corresponding to the value of the curvature term being minus one, zero and plus one. Analysis of these solutions indicates that the open and closed solutions converge to the flat universe solution. A power series expansion done for the relative energy density in the case of open and closed universes shows that even a first order correction is negligible and in this case the hyperbolic solutions become exponential which is the flat universe result. The flatness problem is then seen as a natural phenomenon in an inflationary