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The anisotropies of the Cosmological Gravitational Wave Background (CGWB)retain information about the primordial mechanisms that source thegravitational waves and about the geometry and the particle content of theuniverse at early times. In this work, we discuss in detail the computation ofthe angular power spectra of CGWB anisotropies and of their cross correlationwith Cosmic Microwave Background (CMB) anisotropies, assuming differentprocesses for the generation of these primordial signals. We present anefficient implementation of our results in a modified version of CLASS whichwill be publicly available. By combining our new code GW_CLASS withMontePython, we forecast the combined sensitivity of future gravitational waveinterferometers and CMB experiments to the cosmological parameters thatcharacterize the cosmological gravitational wave background.

GW_CLASS: Cosmological Gravitational Wave Background in the Cosmic Linear Anisotropy Solving System