About the Power Spectrum Of Primordial Gravitational Waves

The primordial gravitational waves (PGW) have been generated by inflationary amplification of the primordial (quantum) fluctuations. It is true that they have not been recorded directly so far, but their spectrum can help a lot in solving the basic puzzles of the early universe as Inflation (high) energy scale. In the present work, we give a straightforward method to calculate the spectral energy density (SED) of the relic gravitons different from that used in e.g. Jinno et al. JCAP 1, 41 (2014), Boyle and Steinhardt, Phys. Rev. D 77, 063504 (2008) and Watanabe and Komatsu, Phys. Rev. D 73, 123515 (2006). In our approach, the evolution equations are in terms of the scale factor (instead of conformal time) through the Lagrange formalism (instead of the transfer function). The presence of the Hubble parameter allows to calculate the power spectrum in the different dynamical regimes.