We reproduce the differential operators and the unifying relations for 1-loop Feynman integrands between the Yang-Mills theory and the Yang-Mills scalar theory by the sewing procedure of the Berends-Giele currents. We also generalize the discussion to the (A)dS case for the scalar theory with a minimal coupling with gluons.

Unifying relations of amplitudes are elegant results in flat spacetime, but the research on these in (A)dS case is not very rich. In this paper, we discuss a type of unifying relation in (A)dS by using Berends-Giele currents. By taking the flat limit, we also get a semi-on-shell way to prove the unifying relations in the flat case. We also discuss the applications of our results in cosmology.

Unifying relations of amplitudes are elegant results in flat spacetime, but the research on these in (A)dS case is not very rich. In this paper, we discuss a type of unifying relations in (A)dS by using Berends-Giele currents. By taking flat limit, we also get a semi-on-shell way to prove the unifying relations in flat case. We also discuss the applications of our results in cosmology.