  A cosmological gravitational wave background resulting from space-time
quantum perturbations at energy scales of $\sim 10^{15}$GeV is expected as a
consequence of the general relativity theory in the context of the standard
cosmological model. Initial conditions %for the problem are determined during
the inflationary (de Sitter) era, at $z \gtrsim 10^{25} $. A semi-analytic
method was developed to evolve the system up to the present with no need of
simplifying approximations as the thin-horizon (super-adiabatic) or the
instantaneous transitions between the successive phases of domain of the
different cosmic fluids. The accuracy of such assumptions, broadly employed in
the literature, is put in check. Since the physical nature of the fluid (known
as dark energy) leading to the accelerated expansion observed in the recent
Universe is still uncertain, four categories of models were analyzed:
cosmological constant, X-fluid (phantom or not), generalized Chaplygin gas and
(a parametric form of) quintessence. The results are conclusive with respect to
the insensitivity of gravitational waves to dark energy, due to the recentness
of its phase of domain ($z \sim 1 $). The empirical counterparts of the
gravitational wave forecasts are still nonexistent for the noise levels and
operational frequencies of the experiments already built are inadequate to
detect those relics. Perspectives are more promising for space detectors
(planned to be sensitive to amplitudes of $\sim 10^{-23}$ at $10^{-3}-1$Hz).
The cosmic microwave background is also discussed as an alternative of indirect
detection and the energy density scale of inflation is constrained to be
smaller than $10^{-10}$ in the analysis here presented.
