Unfortunately, the new evidence is that some phenomenon we call Dark Energy is expanding the Universe at ever higher rates. So it won't collapse in a big crunch (or gnab gib). And you'd think that without a big crunch, you don't get a new Universe. And even if you had a big crunch, you wouldn't have the same kind of Universe the next time around. And, there's no evidence of a previous Universe - though we'd expect some.
But all cosmologies seem to have an open door to eventually have a new Universe. Before Dark Energy, it was thought that in a flat Universe (which we certainly have) the energy state of the Universe would get so low that a new Universe might eventually spontaneously happen - perhaps due to quantum fluctuations. And with Dark Energy, the new idea of the Big Rip gets us to a low energy state much faster. And String Theorists suggest that every trillion years or so, we get a new Universe from interaction between branes.
But though String Theory is based on evidence, none of it's unique predictions have been tested. That may come soon. And there may not be a Big Rip. We may simply not know enough about how Dark Energy works. I don't think we have much confidence in any predictions for a next Universe.
Matter can be converted to energy, and back. But this matter/energy thing is conserved. It can't be created or destroyed. So where did the matter/energy of the current Universe come from? The answer seems to be that the matter + energy sum of the Universe is zero. Potential energy is negative. Matter is positive. So the Universe is the ultimate free lunch.