  Density perturbations in the cosmic microwave background within general
$f(R,\phi)$ models of gravity are investigated. The general dynamical equations
for the tensor and scalar modes in any $f(R,\phi)$ gravity model are derived.
An application of the equations to the (varying power)-law modified gravity
toy-model is then made. Formulas and numerical values for the tensor-to-scalar
ratio, the scalar tilt and the tensor tilt are all obtained within this
specific model. While the model cannot provide a theoretical reason for the
value of the energy scale at which inflation should occur, it is found, based
on the latest observations of the density perturbations in the sky, that the
model requires inflation to occur at an energy scale less than the GUT-scale;
namely, $\sim10^{14}\,{\rm GeV}$. The different energy intervals examined here
show that the density perturbations recently obtained from observations are
recovered naturally, with very high precision, and without fine tuning the
model's parameters.
