In this paper, we study the gravitational-wave (GW) radiation and radiative behavior of relativistic compact binary systems in the scale-independent energy-momentum squared gravity (EMSG). The field equations of this theory are solved approximately. The gravitational potential of a gravitational source is then obtained by considering two matter Lagrangian densities that both describe a perfect fluid in general relativity (GR). We derive the GW signals emitted from a compact binary system. The results are different from those obtained in general relativity (GR). It is shown that the relevant non-GR corrections modify the wave amplitude and leave the GW polarizations unchanged. Interestingly, this modification depends on the choice of the matter Lagrangian density. This means that for different Lagrangian densities, this theory presents different predictions for the GW radiation. In this case, the system loses energy to modified GWs. This leads to a change in the secular variation of the Keplerian parameters of the binary system. In this work, we investigate the non-GR effects on the radiative parameter, i.e., the first time derivative of the orbital period. Next, applying these results together with GW observations from the relativistic binary systems, we constrain/test the scale-independent EMSG theory in the strong-field regime. After assuming that GR is the valid gravity theory, as a priori expectation, we find that the free parameter of the theory is of the order 10−5 from the direct GW observation, the GW events GW190425 and GW170817, as well as the indirect GW observation, the double pulsar PSR J0737−3039A/B experiment.

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