The unified first law in “cosmic triad” vector field scenario

In this Letter, we try to apply the unified first law to the “cosmic triad” vector field scenario both in the minimal coupling case and in the non-minimal coupling case. After transferring the non-minimally coupling action in the Jordan frame to the Einstein frame, the correct dynamical equation (Friedmann equation) is gotten in a thermal equilibrium process by using the already existing entropy while the entropy in the non-minimal coupled “cosmic triad” scenario has not been derived. And after transferring the variables back to the Jordan frame, the corresponding Friedmann equation is demonstrated to be correct. For complete arguments, we also calculate the related Misner-Sharp energy in the Jordan and Einstein frames.