There are two misconceptions that I have been noticing on infinity in astronomy. The first is that the universe cannot be infinite and the second is that it will definitely collapse back upon itself.

The universe can be infinite without there being an infinite amount of light and thus energy. The problem of the universe being infinite with a limited amount of energy visible is known as Olbers' Paradox.

The problem is solved when you consider two things together: a) even though the universe may be infinite its age is taken to be finite because the universe is expanding and b) the speed of light is finite at 299,792,458 m/s. This means that light can only be received from a distance in light-years equal to the age of the universe (around 10 to 15 billion years depending on the value used for the Hubbell constant which at this time is uncertain). Therefore the universe may very well be infinite, but since we cannot see beyond somewhere between 10 and 15 light-years away we cannot know.


The universe will not necessarily collapse back onto itself in a big crunch. The fate of the universe fits into three categories (assuming a cosmological constant of zero): expansion approaches zero, the universe collapses, or it expands forever. This depends on the amount of mass in the universe which is very uncertain, but the best guesses at this point put the universe's mass is under the critical value needed for a big crunch. As a result the best estimate is that it will expand forever becoming nothing more than infrared radiation.