I don't have a pointer to the equations on the Web. You might want to look at
Re: Gravitational Energy Conservation, or do a
Google groups search on "total energy of the universe" with Baez as author. There's a hand-waving argument that I recently posted in another thread.
There's some reason for assigning potential energy (which can be measured relative to any position) the value 0 when everything is an infinite distance apart. If you do that, and you already know that the act of separating things increases gravitational potential energy (becasue the potential energy is the force times the distance between them), it follows that the gravitational potential energy of the Universe that we see is negative. In fact, it's not terrifically different, as such things go, from the negative of the amount of other positive energy we see ... and maybe they're exactly equal in magnitude but opposite in sign, and exactly cancel each other out. Maybe.
you would think that if a certain amount of mass gives off a gravitational field that cancels out it's energy, then an arbitrarily sized mass could appear via hiesenberg's uncertainty priciple.
Yup. If the energy of the Universe is indeed exactly (or
really really close to exactly zero) then the entire Universe
might be a quantum fluctuation, allowed to be so long-lived because its energy is so low. This is a serious theory. We're probably fairly far away from refuting or corroborating it.