Matching Scherrer's k essence arguement with behavior of scalar fields permitting derivation of a cosmological constant

Abstract

We previously showed that we can use particle-anti particle pairs as a model of how nucleation of a new universe occurs. We now can construct a model showing evolution from a dark matter- dark energy mix to a pure cosmological constant cosmology due to changes in the slope of the resulting scalar field, using much of Scherrer's k-essence model. This same construction permits a use of the speed of sound, in k essence models,evolving from zero to one. Having the sound speed eventually reach unity permits matching conventional cosmological constant observations in the aftermath of change of slope of a soliton anti soliton pair during the nucleation process of a new universe. This also assumes that Scherrer's derivation of a sound speed being zero is appropriate during initial inflationary cosmology.