I have been reading several papers on massive gravity. All of them have equations that involve the square of the graviton mass, rather than graviton mass itself. See for example, equations 43 and 44 in
or de Rham's review of massive gravity in https://arxiv.org/abs/1401.4173 .
This makes me wonder if a graviton has a negative mass. Such negative mass gravitons will still obey these equations (because the square of a negative number is a positive number, just like the square of a positive number).
Can anyone in this forum give any reason why gravitons cannot have a negative mass? Of course, general relativity (GR) is compatible only with gravitons having a zero mass. But massive gravity theories are a modification of general relativity. So the question of massive gravitons contradicting GR does not arise.