The almost-scale-invariant spectrum for the stochastic background wave (in primordial Universe) is a firm prediction of inflationary scenarios. In this work, to study of primordial Gravitational Waves, one-dimensional toy model in generalizations of the Einstein– Hilbert frame, described by second-order curvature invariant (called pure Quadratic Gravity) is considered. Solutions to the primordial perturbations are more varied than Einstein–Hilbert frame and include simple incoming and outcoming waves. By examining the spectrum diagram of the perturbation solutions, it can be seen that the oscillating solutions are ruled out due to not having the necessary spectral power, but the solutions as damping exponential have the ability to produce a scale-invariant spectrum (confirmed by CMB data).
