It is not easy to get a clear concept of what space is. We think of space as the space in our room. We put our things in that space, but the cosmic aspect of space is not like that at all.
Before the primordial matter was created (came into being if you want it that way) there was no space and there was no time. Wherever matter is space is.
The space is not infinite. Whatever causes the evolution of the universe (and of life) whether you call it dark energy or GOD is infinite. Being infinite it can go on pushing the universe apart.
Long before that expansion begins to slow down or stop, life on earth would have disappeared and there will be no one to worry about it. So let us stop worrying about that.
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