Which part of the electrochemical cell allows the back-and-forth passage of ions from the cathode to the anode? the half cell the voltmeter the electrode the salt bridge

Answer is "The salt Bridge"

Explanation:
                   During the spontaneous reaction in Voltaic Cell, the balance of ions get disturb due to increase in concentration of negative charge in one half cell and positive charge in another. In order to keep balance the charges in cell,  concentration of ions on both sides and overall neutrality of the system, a U-shape tube filled with inert electrolyte is connected to both half cells. The electrolyte migrates in such a way that the charges of solution in cells keep constant.