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We review several cosmological backgrounds of gravitational waves accessibleto direct-detection experiments, with a special emphasis on those backgroundsdue to first-order phase transitions and networks of cosmic (super-)strings.For these two particular sources, we revisit in detail the computation of thegravitational wave background and improve the results of previous works in theliterature. We apply our results to identify the scientific potential of theNGO/eLISA mission of ESA regarding the detectability of cosmologicalbackgrounds.

Cosmological Backgrounds of Gravitational Waves and eLISA/NGO: Phase Transitions, Cosmic Strings and Other Sources