I don't have the up to date knowledge to say whether this has really "proved" the case (how indeed could you prove something in the future?), but the majority of experts in the field have long been convinced that this is the most likely patten of the cosmic future. The Universe continues to expand indefinitely, in the process dissipating the available energy, until eventually it approaches the point where energy flow is no longer possible. This is where it gets a bit mind-bending, but although the Universe continues to exist, without energy flow there can be no heat or light, no life, no movement, not even any time. All is reduced to a point of inertia. All will die.
Although depressing, this event is sufficiently far off not to trouble most people on a day-to-day basis (perhaps 10100 years from now). But it is a strong challenge to a Christian worldview. Most Christian believe that, whatever evil and chaos we endure in this present time, there is a direction to history and that God has it under control. Anyone whose theology is shaped by the Bible has the very strong conviction that not just human history, but the history of creation, is moving towards a point in the future, the point which Jesus calls "the coming of the Kingdom".
But science now begs to differ. According to Physics, there is no eschatology and no eternity. The future is not a direction, it is merely what lies ahead of us, and is demonstrably finite. One day, all this will come to an end. As the Physicist Steven Weinberg memorably put it, "the more the Universe seems comprehensible, the more it also seems pointless".
I can think of two possible Christian reponses to this (not mutually exclusive). The first is the creed. "He will come again to judge the living and the dead" is not an easy statement of moral piety. It is a conviction that God will, at some point in the future, intervene in the natural order of things. He will bring the flight of time's arrow to a sudden halt, reversing even death itself and starting something new.
The problem is (if you call it a problem), there is no dialogue at this point between faith and science. Science says impossible, faith says possible. You have to take your pick. But let's say you find it too difficult to believe in the second coming - you can only see that the Physics is correct, and the Universe is dying imperceptibly, minute by slow minute. Remember then, that the fate of the Universe is no different from the fate of all creatures, including you and me. We are all treading slowly towards inevitable death, as our energy dissipates and we reach the point where our system no longer works. But Christians believe that God will bring us back. How, we don't know, but just that he can. Beyond death, lies life for us. And as for us, so for the Universe. "God who gives life to the dead, and calls things that are not as though they were" [Romans 4:17] will raise his creation from the dust and breathe new life into it.
Science predicts the end of the Universe based on the available data. Faith and hope tell us that God will provide some new evidence which will completely change the way the future looks.