Time-reversal violation (TRV) interactions between quarks which appear in the standard model (SM) and beyond-SM theories can induce TRV components in the nucleon-nucleon potential. The effects of these components can be studied by measuring the electric dipole moment (EDM) of light nuclei. In this work we present a complete derivation of the TRV nucleon-nucleon and three-nucleon potential up to next-to-next-to leading order (N2LO) in a chiral effective field theory (chi EFT) framework. The TRV interaction is then used to evaluate the EDM of H-2, H-3, and He-3 focusing in particular on the effects of the TRV three-body force and on the calculation of the theoretical errors. In this work we limit our analysis to study the TRV potential contributions to the EDM without including TRV exchange currents, which we plan to add in a future work. Once added these exchange currents, in case of measurements of the EDMs of these nuclei, our results would contribute to the determination of the values of the low energy constants and to the identification of the source of TRV.
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