No!
The universe started with a
Big Bang and will not end in a cold, dead whimper!
Astronomers now believe that the expansion of the universe is increasing. They call the cause zero-point energy or Einstein's cosmological constant, or dark energy. It's not well understood, but they assume it will continue this way, always accelerating. So, it's natural to think that our universe will get colder and colder until everything stops moving.
We're not that lucky! There's an idea by Robert Caldwell and his colleagues Marc Kamionkowski and Nevin Weinberg called 'The Big Rip', and it seems much more likely.
To understand this, consider that there's an edge to the universe. It's not an edge like a waterfall. It's called the 'observable universe'- at a certain distance away the expansion of space gets so fast relative to say, the Earth, that not even light can make it from there to the Earth- the space in between is expanding so fast that the distance increases by more than 299,792.458km per second, the speed of light, so the light never makes it.
Now, as the expansion speeds up, the closest distance for the expansion to exceed the speed of light goes down, so the distance to the edge of the observable universe goes down. For all intents and purposes, your personal bit, the bit of the universe that can effect you is shrinking; as the growth rate goes up. So, accelerating expansion leads to a smaller universe! Ironic huh?
Now, the universe is pretty big- at the moment.
But as the expansion rate increases, the size gets ever smaller. Eventually it will be smaller than the distance to the nearest stars, and they would disappear from the Earths point of view, ripped away by the expansion rate of the space. Then smaller than the distance to the Sun, so the Earth gets very dark and is no longer in orbit, because gravity travels at the speed of light and the Earth and Sun are moving apart very, very fast.
But the electromagnetic forces that hold physical objects like the Earth, and you, and me, together travel at the speed of light too. So, a few weeks later, the Earth will just fall apart without any hope of keeping it together, ripped by the ever accelerating expansion. Then the people, then cells, then the the molecules, then atoms fall apart, then the subatomic particle size is reached.
What happens after that, is anyones guess. But we certainly won't be there to find out...
Thirteen billion years you've got and that's it!
"Oh well, just time for a quick bath then; pass the sponge someone!" - Douglas Adams