Unifying Inflation and DE/DM from Multi Field in a spontaneously broken
  scale invariant TMT
  A two scalar field model that incorporates the Two Measures Theory (TMT) is
introduced, in order to unify the early and present universe. We define the
scale invariant couplings of the scalar fields to the different measures
through exponential potentials. Spontaneous breaking of scale invariance takes
place when integrating the fields that define the measures. When going to the
Einstein frame we obtain: (i) An effective potential for the scalar fields with
three flat regions which allows for a unified description of both early
universe inflation (in the higher energy density flat region) as well as of
present dark energy epoch which can be realized with a double phase, i.e., in
two flat regions. (ii) In the slow roll inflation, only one field combination
the ``dilaton", which transforms under scale transformations, has non trivial
dynamics, the orthogonal one, which is scale invariant remains constant. The
corresponding perturbations of the dilaton are calculated. (iii) For a
reasonable choice of the parameters the present model perturbations conforms to
the Planck Collaboration data. (iv) In the late universe we define scale
invariant couplings of Dark Matter to the dilaton.(v) We calculate the
evolution of the late universe under these conditions with the realization of
two different possible realizations of $\Lambda$CDM type scenarios depending of
the flat region in the late universe. These two phases could appear at
different times in the history of the universe.(vi) From the Planck data, we
find the constraints on the parameters during the inflationary epoch and these
values are used to obtain constraints relevant to the present epoch.
