I know that the universe is 13 billion years old and the fastest anything could be is the speed of light so if the universe is expanding as fast as it could be wouldn’t the universe be 13 billion light years big? But I’ve searched and it’s 93 billion light years big, so is the universe expanding faster than the speed of light?
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It’s expanding at a rate of about 70km/s per megaparsec (which is the same as a frequency of once per 14 billion years, roughly)
If you assume this expansion rate is constant, this gives you a simple differential equation for a fixed position’s distance in terms of time. The details aren’t important, but it basically means that any region of space gets about e times wider (2.718… times wider) every 14 billion years. This is not necessarily a realistic model, because of the assumption, but it illustrates the idea.
On small scales (the size of galaxies) this has no effect, because things can easily move towards each other much faster than the universe can expand them apart. Gravity holds these things together.
On large scales (beyond small galaxy clusters) the rate of expansion wins out, and these distant galaxies are essentially dragged away by the receding space that they only move through so fast. On massive scales, even light moving towards us can no longer beat the expansion of space, giving a limit to how far we can ever see.
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