  One of the predictions from simple inflation models is stochastic background
of gravitational waves (or literally what is called the Primordial
Gravitational Waves (\textbf{PGW})) with a nearly scale-invariant spectrum. To
discuss a possible direct detection of PGW, the quantity so-called Spectral
Energy Density (\textbf{SED}) has crucial role. In this work, we consider PGW
amplified by inflation and generated by perturbing the Anisotropic
(\emph{Bianchi type-I}) metric. We focus on the SED quantity of these gravity
waves. The intended frameworks are the Einstein's and modified (pure quadratic
\emph{Ricci} scalar) gravities. The spectral graphs for SED shows that in
Einstein's gravity, the anisotropic model has the ability to adapt to the
observational data (BBN bounds) and in the modified gravity, in addition to
observational constraint adaptation, the scale-invariant character of the
spectrum is much more pronounced.
