The biggest point of confusion in this question is the assumption that in 13.7 billion years the universe could have grown by only 13.7 billion light-years. This assumption is false. When we talk about the universe being a certain age, we mean that the proper time measured by a clock moving with cosmic expansion reads that many years since the Big Bang. If we use coordinates based on Albert Einstein’s special theory of relativity, that assumed clock moving with expansion travels close to the speed of light and thus hardly ticks at all. Thus, the universe can get huge before clocks have measured 13.7 billion years.Astronomy magazine subscribers can read the full answer for free. Just make sure you're registered with the website.