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It is perhaps easy to accept the statement that the universe is expanding. It is just some strange physics indicating that, as time goes on, galaxies (星系) get further away from each other just like two cars racing away from each other.

I personally don't like it and prefer the balloon analogy. In this situation, there are dots all over a balloon. When we blow it up in real life, the dots would increase in size. In this analogy, let's assume they don't. What we are interested in is how the distance between the dots on the surface of the balloon grows as we put more air into it.

The balloon analogy relies somewhat on our geometric sensibilities which refer to our sense of shapes and how they change over time. At its core, what we are trying to develop a sense for is how we measure distances. This concept is also the fundamental goal of general relativity, Einstein's theory of gravity. In general relativity, the most important piece of information is what we call the metric, an equation that describes how distances are measured, and therefore also tells us about the shape space-time is taking.

The whole idea that space-time is expanding was first noticed as a mathematical consequence of general relativity by Georges Lemaitre in 1927, when he solved Einstein's equation and found a solution for the metric showing that distances grow with time. His work provided a theoretical explanation: the standard for measuring cosmic (宇宙的) distance was itself changing with time.

What is delightful is that it means we can quite reasonably say that universe's expansion is a gravitational effect. I enjoy this because it is so deeply counterintuitive to our usual understanding of gravity, which teaches us that it is a force that always draws things together. But in this case where gravity is a geometric effect, we are offered a broader range of gravitational possibilities.

It is worth noting that the geometric explanation of general relativity hasn't been universally popular. The late physicist Steven Weinberg wrote that the geometric explanation of the theory of gravitation has been reduced to a mere analogy, but is otherwise not very useful. Another challenge with the balloon analogy and our reliance on geometric explanation is to explain why gravity seems to pull things together in many situations, while universe is expanding. This difference is resolved by acknowledging that local gravitational effects due to massive objects dominate over large-scale expansion effects, leading to the formation of structures like stars, galaxies and, eventually us.

In fact, the analogy where universe is only expanding and this is the only gravitational effect at play is a very idealized situation where matter was initially spread out perfectly evenly across the universe.