In my opinion, there are an infinite number of universes that exist relative to this one (the one we are currently in). What does this mean? It means that there are copies of ourselves, and the world, that live a similar life next to ours. There is no way to travel to these universes, for they exist in a different space-time, a different dimension than this.
Have you ever thought about something as simple and classic as flipping a coin? I mean, everyone learned in school what probability means and that there is a fifty-fifty chance of a coin landing on heads or tails, but have you ever wondered why at one particular coin flip, it just happened to land on one side instead of the other? What I think is really happening is that every time someone flips a coin, the same coin (or a copy of it, depending on how you look at it) is being flipped in a parallel universe from this one. In one universe, it lands on heads. In the other, tails. Since we are in one universe at a time, we see only one outcome.
So if the cosmos is composed of infinite parallel universes, then it would be shaped like a tree diagram. The concept of infinity would be difficult to picture, so let's take a look at what just one part of the cosmos might look like. It might have two universes, side by side, each exactly the same except for one tiny detail that is changed. Each splits off, becoming more and more different from the previous, as time goes on in the universes. In the real world this would look like maybe a lost letter that causes someone to never see each other again. Up until the point in time the letter is either lost or found, the two universes are the same. Then the outcome of the letter shapes the future, causing people to go down a different path.