Shape of the Cosmos

* Judging from popular media, astronomers are developing tools for observing matter and energy near the edge of the universe. Based on that talk, I contemplated special properties of fields and trajectories at the edge of the universe, eg violations of inverse-square rules and bent photon paths. Attempting to discuss these matters with physics experts, I was shut down before getting started. They say that the universe has no edge. It is bent and joined in a fourth dimension, such that no path leads out. This was explained by analogies.
* A straight string has ends which an ant could come to and jump from, but a looped string has no end for such escape. A flat plane has edges which an animal could come to and jump from, but that plane bent into a sphere and fused has no edge for such escape.
* Analogously, if the universe began by expanding into pre-existing cartesian space, then it would have an outer extreme limit beyond which photons and accelerated particles could escape. But (they say) the universe expanded into its own self-generated or self-contained space which is curved/bent on itself such that all trajectories are within its confines. The idea of space outside the universe or existing before the big bang is meaningless. Perhaps time before the bang or outside the material universe is meaningless. This is my attempt to convey the idea they imparted to me.
* With this theory in its simplest form as an axiom, we can postulate some implications:
1. No point in the universe is demonstrably not at the center of the universe. Every point is effectively as much at the center as any other point.
2. If light were fast enough or the universe small enough, the most distant thing that an observer could see would be itself. If our solar system is the point in question, one need not make this conditional on unrealistic light speed or unrealistic universe size, for photons have been leaving our solar system since early in the the universe's history.
3. Accordingly, the observer would see itself smeared over its sight horizon as the inside surface of a sphere enclosing the whole universe.
4. The most distant object an observer could possibly witness is itself.
5. If an observer leaves a larger body and travels in a straight line in any direction, it will be traveling both away from and toward that larger body, and that larger body would appear to be getting smaller (less wide than the sight horizon) rather than bigger as the observer gets closer, up to a point. That is to say, the angle subtended by the body's diameter in the observer's view will get smaller, until a critical distance is reached where getting closer widens the image.
* These corollaries seem paradoxical--hard to swallow. Therefore, I ask: What is the compelling reason to accept this bent/curved-universe theory? Why not imagine a big bang in a pre-existing cartesian-space-time coordinate system.