Authorship of PI and/or other advisor on independent work? I'm a graduate student in a biological sciences lab. About 6 months ago I started an after-hours (does such a thing exist?) project with a fellow graduate student in a different lab doing computational physics. We principally work on the weekends and late at night, and I like to think that the time we use would otherwise have been spent playing video games, drinking, etc (not doing lab work), but who really knows?

Our collaboration has been extraordinarily fruitful and we have one paper ~90% written, and a follow up ~50% written. Both are highly theoretical, and have no direct relation to our respective theses work. Also, both our PIs know and are supportive of us pursuing this project, and neither has so much as even hinted at wanting authorship. And neither is an expert (or even an amateur..) in physics.

1) Should we include our PIs? They could potentially contribute to editing and big picture, but are not able to even assess the validity of what we've accomplished. As an "experienced" graduate student I know they shouldn't be authors, but they are also making it possible for us spend our time thinking, and they've supported our endeavor at least in spirit.

2) Suppose our PIs are not included. We're just two graduate students. Is it even possible to get a fair review with neither of us having the requisite degrees? How do we pay for publication ($1000-5000)? I'm interested in the "meta" discussion as much, or more, than the ethical discussion. For example, there is a third faculty member in this area who we've had some discussion of the science with, and who is a computational physicist. Should we include him on the manuscript as a signature of credibility? Should he be last author or a middle author, if so? If there are any physicists perusing, I'd be particularly interested in your thoughts, as my experience in publishing has been solely in the biomedical journals so far.

Thanks for considering my dilemma.
There have been a number of discussions on this site about authorship, and looking at the authorship tag will reveal them. 

Ultimately, the conclusion of all those discussions has been that conventions on authorship are field-dependent and define "contribution" in different ways for different areas. In your case, it sounds like your advisors have both encouraged you to work together and have not requested authorship. Since the usual response to questions like yours would be 'ask your advisor', it sounds like they've answered, by saying that you don't need to include them. But I'd check with them anyway.

The remaining part of your question deals with purely tactical considerations: to whit, 


  Can augmenting the author list increase chances of the paper being accepted for publication ? 


I think the consensus on this site, and in general, is that misrepresenting or exaggerating contributions for any reason would be considered quite unethical (where again contributions must be evaluated in a field-specific manner). 

The work must stand or fall on its own merit, and be reviewed accordingly. It might be rare in your community for graduate students to author papers without PIs, but there's always a first time (and in my community it's quite common). 

On the more mundane issue of paying for publication (I assume you're thinking of one of the open access journals that charge such an amount), that's a discussion for you to have with your advisor(s) before submission. They might suggest alternate journals, or even be willing to pay the fees (again, the equivalent would be a PI in my field paying for a student to attend a conference and present a paper not co-authored by the PI: this is also quite common)