  Scalar fields are widely and popularly used in cosmology in order to explain
different phenomena among which, inflation and dark energy are two of the most
popular ones. Specifically, in recent years, scale invariance in the
gravitational sector has gained interest due to its simplicity, ability to
model inflation and the dynamical generation of the Planck scale. In this
paper, motivated by a non minimally coupled scale invariant $R^{2}$
gravitational model originally proposed by M.Rinaldi and L. Vanzo, we
investigate how the inclusion of a vector scalar interaction that respects the
scale invariance of the original model may affect the early and late time
dynamics. We employ dynamical analysis tools in order to find the fixed points
of the system and the local solutions for each variable around each fixed point
finding out that the early universe solution of the extended model is
compatible with that found in the original model with the exception of a new
unstable fixed point appearing in the extended model. This new fixed point
however has the same linealized solutions as the unstable fixed point found for
the original model. We later employ numerical calculations in order to check
that the analytical approach holds. Furthermore we show how the dynamical
generation of the Planck mass is unaffected by the new field content of the
model. Finally, we motivate and investigate a reduced version of the extended
model finding out that, at late times, the extended model has only stable de
Sitter fixed points where the scalar field becomes constant taking the role of
the cosmological constant and the vector field is washed out.
