Should I do it? Polygraph test

My boyfriend left me at 5 months pregnant due to his own trust issues. He claims I've cheated (I haven't) and ultimately it was a messy breakup.

We now have a 2 month old daughter. He hasn't seen her and claims to be terrified of being a dad.

After all he's put me through I don't know that I can forgive him. We did however consider a $400 polygraph test (lie detector) to confirm I was faithful. I'd love to clear the air and hopefully show him how awful he has been.

There is no way we can even talk unless we do this test for once and for all.

Is it worth it? Opinions.