  [Abridged] We investigate the detectability of the gravitational stochastic
background produced by cosmological sources in scenarios of structure
formation. The model considers the coalescences of three kind of binary
systems: double neutron stars, the neutron star-black hole binaries, and the
black hole-black hole systems. We also included the core-collapse supernovae
leaving black holes as compact remnants. We use two different dark-energy
scenarios, cosmological constant and Chaplygin gas, in order to verify their
influence on the cosmic star formation rate, the coalescence rates, and on the
gravitational wave backgrounds. We calculate the gravitational wave signals
separately for each kind of source as well as we determine their collective
contribution for the stochastic background of gravitational waves. Concerning
to the compact binary systems, we verify that these sources produce stochastic
backgrounds with signal-to-noise ratios (S/N) ~ 1.5 (~ 0.90) for NS-NS, ~ 0.50
(~ 0.30) for NS-BH, ~ 0.20 (~ 0.10) for BH-BH for a pair of advanced LIGO
detectors in the cosmological constant (Chaplygin gas) cosmology. Particularly,
the sensitivity of the future third generation of detectors as the Einstein
Telescope (ET) could increase the present signal-to-noise ratios by a
high-factor (~ 300 - 1000) when compared to the (S/N) calculated for advanced
LIGO detectors. Thus, the third generation of gravitational wave detectors
could be used to reconstruct the history of star formation in the Universe as
well as for contributing with the characterization of the dark energy, for
example, identifying if there is evidence for the evolution of the dark energy
equation-of-state parameter w(a).
