One of the predictions from simple inflation models is a stochastic
background of gravitational waves (or literally what is called the Primordial
Gravitational Waves (\textbf{PGW})) with a nearly scale--invariant spectrum. In
this work, we consider these waves arising from perturbing the Anisotropic
background (Bianchi type--I) metric by focus on their power spectrums.The
intended frameworks are the Einstein's and modified gravity frames. The
investigations indicate that in the modified gravity context, the results have
more ability to adapt to physical conditions or constraints. Especially, the
scale--invariant character of the spectrum is much more pronounced in the
modified framework.Comment: This paper is same with the paper to Identifier arXiv:2007.0669