Nobody knows for sure how the universe will evolve. It's accepted by almost all cosmologists that the universe is expanding at an increasingly accelerated rate.
Almost all. There are indeed convincing experimental facts (type IA supernovae, the CMBR), but there is also counter-evidence. I think this is not taken too seriously because there were already Nobel prizes awarded for the discovery that the universe is expanding at an accelerated rate.
See for example this paper, containing much math. The link to this paper is made in this article (many more links are included here).
So maybe dark energy (the Nature of which is completely unknown; it's supposed to become non-diluted by the expansion of space) is not necessary after all. The Dutchman Erik Verlinde (who received the Spinoza prize in 2011 for his in the Netherlands so-called revolutionary new theory of gravity, including a premium of 2 million euros...) proposes that dark energy, as well as dark matter, are emergent properties, though I think observations on the Bullet Cluster defuse his theory.
So the situation is far from settled. And who knows what the future in cosmology holds in store?