Does the universe allow retrocausal events to happen as long as there are no time paradoxes?
Not as far as we know. There are some solutions to Einstein's field equations of GR that appear to allow for "closed timelike curves" (basically an object would travel through spacetime back to its starting point, allowing for time travel), but it's likely that this cannot actually happen. Just because the math says something is possible doesn't mean it can actually happen in real life.
Note that time travel threads often attract posts with a high probability of violating PF rules, so I'm going to close this thread before I have to hand someone a warning.
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