A220 pilot reported diverting to an alternate airport after experiencing false GPWS terrain warnings in cruise flight. The warnings became continuous and extremely distracting during the diversion; and the aircraft was taken out of service for maintenance.

Narrative

While cruising at FL360; PULL UP warning activated and appeared on both Primary Flight Displays (PFD) screens. There was light chop at that flight level so we requested a decent to FL340 which was reported smooth. The erroneous warnings continued; and became increasingly more frequent. Dispatch and Maintenance was contacted via SATCOM; and the decision was made jointly to divert to ZZZ where Maintenance would be contacted to address the issue on the ground.During diversion; the warning began to appear constantly; and continued all the way to landing; with EICAS messages appearing related to TWAS while on final approach. The workload was high; coordinating the diversion with ATC and programming the FMS. First Officer (FO) flew while Captain handled Comms and aircraft set up. Landing was otherwise made normally.We were met by Maintenance at the gate and advised them of the issue in a much detail as possible.The initial plan of action as we were told by Maintenance on the Ground was to apply MEL X which provided no deactivation of the GPWS system; only acknowledgement of 'heightened pilot awareness' as to the terrain and requirements to closely monitor the flight path. Maintenance was unable to positively identify the cause of the malfunction; and acknowledged that the erroneous warning would likely continue during a subsequent flight until it can be corrected. Phone calls were received by Captain from chief pilot; primarily to gain a greater understanding of what occurred to advise of the possible next steps. Passengers were kept updated with all relevant info received. After some troubleshooting by Maintenance; Captain was advised that they would be attempting to download the aircraft data in an effort to identify the root cause of the problem; and thereby apply a more appropriate MEL to isolate the erroneous warnings so that they did not occur during flight back to maintenance base. This was not achieved as far as the crew was made aware. Captain and FO were contacted by chief pilot; and asked if willing to operated the aircraft as a ferry back to ZZZ1 same evening. Both Captain and FO stated several times that we were not satisfied that the airplane was safe to operate with this malfunction unresolved; as it could no longer assure safe terrain avoidance; as well as the unpredictability of the malfunction related to the flight profile. Further; it was now night; with IMC and snow conditions being reported at ZZZ1 throughout the evening. It was further noted during an earlier phone conversation that the malfunction can cause uncommanded thrust reduction to idle. It was also very distracting to operate with the warning appearing constantly. Chief pilot also asked if crew would be willing to ferry the flight to ZZZ2 for maintenance the following day if VMC conditions. Captain stated that although it would be more comfortable; as I had mentioned in an earlier conversation; I was still not satisfied that the flight could be operated safely due to the nature of the unresolved malfunction. Further; we are not technical pilots; therefore being asked to fly an airplane with a very distracting malfunction of a critical system would have been; in the Captain's opinion; an unnecessary risk to safety. Further; Captain has limited experience on the aircraft type; with approximately 200 hours since upgrade.The airplane was ultimately taken out of service. Another aircraft was dispatched from ZZZ1 to bring pax to ZZZ3; however Captain and FO would have subsequently exceeded flight duty period (FDP) to complete the pairing.