  We present a complete analysis of the imprint of tensor anisotropies on the
Cosmic Microwave Background for a class of f(R) gravity theories within the
PPF-CAMB framework. We derive the equations, both for the cosmological
background and gravitational wave perturbations, required to obtain the
standard temperature and polarization power spectra, taking care to include all
effects which arise from f(R) modifications of both the background and the
perturbation equations. For R^n gravity, we show that for n different from 2,
the initial conditions in the radiation dominated era are the same as those
found in General Relativity. We also find that by doing simulations which
involve either modifying the background evolution while keeping the
perturbation equations fixed or fixing the background to be the Lambda-CDM
model and modifying the perturbation equations, the dominant contribution to
deviations from General Relativity in the temperature and polarization spectra
can be attributed to modifications in the background. This demonstrates the
importance of using the correct background in perturbative studies of f(R)
gravity. Finally an enhancement in the B-modes power spectra is observed which
may allow for lower inflationary energy scales.
