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The detection and characterization of the Stochastic Gravitational WaveBackground (SGWB) is one of the main goals of Gravitational Wave (GW)experiments. The observed SGWB will be the combination of GWs from cosmological(as predicted by many models describing the physics of the early Universe) andastrophysical origins, which will arise from the superposition of GWs fromunresolved sources whose signal is too faint to be detected. Therefore, it isimportant to have a proper modeling of the astrophysical SGWB (ASGWB) in orderto disentangle the two signals; moreover, this will provide additionalinformation on astrophysical properties of compact objects. Applying the CosmicRulers formalism, we compute the observed ASGWB angular power spectrum, henceusing gauge invariant quantities, accounting for all effects interveningbetween the source and the observer. These are the so-called projectioneffects, which include Kaiser, Doppler and gravitational potentials effect. Ourresults show that these projection effects are the most important at thelargest scales, and they contribute to up to tens of percent of the angularpower spectrum amplitude, with the Kaiser term being the largest at all scales.While the exact impact of these results will depend on instrumental andastrophysical details, a precise theoretical modeling of the ASGWB willnecessarily need to include all these projection effects.

Projection effects on the observed angular spectrum of the astrophysical stochastic gravitational wave background