The energy-momentum tensor of primordial gravitational waves

In this thesis we have studied the energy momentum tensor (EMT) of cosmological gravitational waves generated in the Early Universe and characterized by a power spectrum described by a power-law in Fourier space. We have computed the EMT by considering only the growing mode of GWs when the scale factor is described as a power of the conformal time, i.e. covering different cosmological stages such as radiation or matter or cosmological constant driven. We have independently verified previous calculations and found that the extra term proportional $H h \dot{h} $ in the energy density is not negligible with respect to the standard terms, i.e. the sum of the kinetic term and laplacian term, in particular on large wavelengths down to the Hubble radius and in the integrated EMT. The full EMT as presented in this thesis should be therefore considered in the comparison with observations. We have also presented an original comparison of the calculation with the growing mode with the regularized EMT in de Sitter space-time, finding a good agreement. The results of this thesis increase our confidence in the calculation with only the growing mode for the post-inflationary era and encourage us to compute the phenomenological implication of the full EMT also at the time of Big Bang Nucleosynthesis for any $n_T$.