  We study the cosmological role of a Tracking Field $\phi$ in Extended
Quintessence scenarios (TEQ), where the dynamical vacuum energy driving the
acceleration of the universe today is coupled with the Ricci scalar, $R$, with
a term of the form $F(\phi)R/2$, where $F(\phi) = 1/8\pi
G+\xi(\phi^{2}-\phi_{0}^{2})$. Tracker solutions for these NMC models, with
inverse power-law potentials, possess an initial enhancement of the scalar
field dynamics, named $R$-boost, caused by the Ricci scalar in the Klein-Gordon
equation. During this phase the field performs a "gravitational" slow rolling
which we model analytically, with energy density scaling as $(1+z)^{2}$. We
evolve linear perturbations in TEQ models assuming Gaussian scale-invariant
initial spectrum. We obtain significant changes in the Integrated Sachs Wolfe
effect and in the acoustic peaks locations on the Cosmic Microwave Background,
as well as in the turnover on the matter power spectrum. All these corrections
may assume positive as well as negative values, depending on the sign of the
NMC parameter $\xi$. We give analytical formulas describing all these effects.
We show that they can be as large as $10 - 30%$ with respect to equivalent
cosmological constant and ordinary tracking Quintessence models, respecting all
the existing experimental constraints on scalar-tensor theories of gravity.
These results demonstrate that the next decade data will provide deep
constraints on the nature of the dark energy in the Universe, as well as the
structure of the theory of gravity.
