Must co-founders live together?

My co-founder and I both live in the SF Bay Area about 30 minutes away from each other. We are both eager to start a startup and we are planning on applying for the winter program. We are good friends and we would have no problem living together during the startup's early period. However, this decision has become more complicated for me because a few months ago I moved in with my girlfriend. Although she's 100% supportive of my starting a startup and working crazy hours (as long as we get to see each other once in a while), she's unhappy about my potentially moving out and living with my co-founder. She's worried it would set back our relationship, and she doesn't want to have to find another roommate (which I understand). Plus, she's not convinced (and neither am I, actually) that this new living situation would only last 3 month, during the initial phase of the YCombinator program.

Is living together with your co-founder critical for the success of a startup? If YCombinator accepts our application, will I have to choose between joining the program and continuing to live with my girlfriend? Will YCombinator reject us if my co-founder and I don't commit to living together?

Thanks in advance for clarifying this.