From what I gather, the observable universe is expanding at the speed of light. In addition, information cannot travel faster than the speed of light. It seems as though these two facts would imply that information cannot leave the observable universe. However, if that is true, it would either mean that the universe started spread apart, or that the observable universe is the entire universe. So, which of these explanations is correct?
Good question! I will need to go into some cosmology to answer it, my main source being Davis & Lineweaver (2003).
Nothing traveling through space should be able to leave the observable universe. However, information can and will inevitably leave our observable universe. How is this possible?
The Universe is expanding.
If we lived in a static universe, no objects would leave our observable universe. However, in our accelerating universe, space is being created between objects, with farther objects drifting away faster than closer ones.
Einstein said nothing can travel through space faster than light. However, space is literally being created between objects, so they can be pushed away from each other faster than light. So while the observable universe is expanding at the speed of light, distant objects are moving away from us even faster.
And the result? Take a look at this image:
This describes how the observable universe will evolve. The Hubble sphere defines the area in which objects are receding from us at or below the speed of light. Beyond this, objects are far enough to recede from us faster than light.
The light cone is the region of the Universe capable of influencing us today. Essentially, it is the observable universe, and its boundary is clearly marked. It is, as you mentioned, growing at the speed of light.
The light cone does not contain the entire Hubble sphere, since photons from many objects receding faster than light cannot reach us yet. Conversely, the Hubble sphere doesn't contain the entire light cone. This is because photons emitted by objects outside of the Hubble sphere can crawl into regions of space that are receding from us a bit slower than the one from which they were emitted. They can then crawl into regions that expand slower than the last one, and so on. Eventually, the photons will reach regions of space that aren't expanding faster than light, and they can reach us.
Now, there is a distance beyond which space expands faster than the light can traverse it. This distance is called the cosmic event horizon. Light from beyond the event horizon will never reach us. Our observable universe grows because more photons come into our view. However, the observable universe will infinitely approach the event horizon, since light from beyond there can never reach us.
Thus, after an incomprehensibly long time, the observable universe would stop growing. At this point, it may finally be possible to travel through space beyond the observable universe.