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In this talk, two different cosmological scenarios associated with gravitational waves produced from binaries of black holes will be discussed. In the first part of the talk, I shall present the investigation of the stochastic gravitational wave (GW) background produced by primordial black hole (PBH)-binaries during their early inspiral stage, while accreting high-density radiation surrounding them in the early radiation-dominated Universe. In this work, we first calculated the correction terms appearing in the GW amplitude generated from such a PBH-binary due to changing PBH-masses. Then, we showed that the significance of the correction terms persists for the overall stochastic GW background produced from those PBH-binaries. Also, We investigated the detectability of this stochastic background with present and future gravitational wave detectors. In the second part of the talk, I shall discuss the impact of change of masses of black holes due to spherical accretion of k-essence dilatonic ghost-condensate model of dark energy on the evolution of the binaries formed with those black holes. We found that the average power of the emitted GW from these binaries increases significantly faster than the constant-mass case. Furthermore, we estimated the reduction in coalescence time-intervals of the binaries due to the growth of the black hole masses. This work signifies the effect of accretion of similar scalar-field dark energies on the orbital evolution of binaries of black holes of certain mass-ranges, their coalescence time-scales and as a consequence their merging-rates too.