We are not legally separated. I have a pension that is paid monthly . Am I legally bound to hand over half ?

We are not legally separated. Am I required to give her half of my pension?

No, not if there is no divorce, separation, or other court order in place.

We are not legally separated. Am I required to give her half of my pension?

Would this be a pay me now or pay me later situation? She is entitled if it goes to something legal. It is affordable and there are no children, just the house that I am living in.

Would this be a pay me now or pay me later situation? She is entitled if it goes to something legal [?]

Possibly. If for example, she files for divorce and asks for a share of the pension, a QDRO (https://en.wikipedia.org/wiki/QDRO) would probably be ordered.

Did the marriage exist the entire time you were accumilating your pension ? That is the question as to how much she may be awarded in a courtroom.