As a side note, assuming the current model of an acceleration of the expansion of the universe, or even just the expansion at a constant rate, and the curvature of spacetime being flat, then eventually all matter/energy will dissipate due to entropy, and even all subatomic particles will become so far apart from each other that none of the fundamental forces of physics will be able to act upon them. This means that none of the particles will be able to interact with one another (this is sometimes described as "heat death"). Without such interactions, there can be no such thing as time. Therefore, time will literally cease to exist, the universe will be frozen, and it will effectively die. The universe as we know it will be no more.
Bleak, yes, but that is what will happen based on the data we have observed at the present time and the laws of physics that we believe to be true presently, and the assumption (a good one, and one we have no reason to doubt) that the laws of physics are uniform throughout the universe (except at singularities like black holes). Of course, without a doubt our understanding of the laws of physics will change over time as we make newer observations, and our model of the universe will change with them.
Still, it is doubtful based on present observations that the universe will ever do anything but continue to expand indefinitely. Such expansion means an eventual heat death.
This should take more than hundreds of a trillion trillion trillion years, or even much longer to occur, so we need not worry much about it. The earth will long cease to exist before that, as our sun will vaporize it when the sun eventually burns all of its hydrogen fuel and begins its inevitable death. This should occur within approximately five billion years or so, if not sooner.
AS