Unification: Emergent universe followed by inflation and dark epochs from multi-field theory

A two scalar field model that incorporates non Riemannian Measures of integration or usually called Two Measures Theory (TMT) is introduced, in order to unify the early and present universe. In the Einstein frame a K-essence is generated and as a consequence for the early universe, we can have a Non Singular Emergent universe followed by Inflation and for the present universe dark epochs with consistent generation of dark energy (DE), dark matter (DM) and stiff matter. The scale invariance is introduced and then is spontaneously broken from the integration of the degrees of freedom associated with the modified measures. The resulting effective potentials and K-essence in the Einstein frame produce three flat regions corresponding to the different epochs mentioned before. For the first flat region we can associate an emergent and an inflationary universe. Here for a parameter-space region this flat plateau possesses a non singular stable emergent universe solution which characterizes an initial epoch of evolution that precedes the inflationary scenario. Also assuming this first plateau, we study the inflation in the framework of the slow-roll approximation. In this scenario under the slow roll approximation we obtain a linear combination that is a constant. The corresponding cosmological perturbations in our model are determined and we also obtain the different constrains on the parameter-space from the Planck data. In the following flat region DE and also the DM, which does not need to be introduced separately, it is instead a result of a K-essence induced by the multi measures, multi field theory. Also stiff matter component is automatically generated from the K-essence theory from two scalar fields. From the perturbative analysis associated to the perturbation solution of background, we find a correlation between the two scalars. Besides, we obtain that our model during the dark epoch has a behavior of tracking freezing model.