To keep things brisk and simple, let us establish a few key terms from Sparrow’s book and apply them to our understanding of what happens. Sparrow refers to immediate reality as the Primary Universe, where the laws of the space-time continuum function within the norm, but often deviate due to anomalies in the Fourth Dimension. When such an anomaly occurs, a parallel reality or Tangent Universe gets created — this universe is an identical copy of the original but is highly unstable due to its inability to sustain itself, doomed to inevitably collapse upon itself after some time. If the Tangent Universe suffers no further anomalies, the collapse will be a safe one, not affecting causality in the Primary Universe. However, if this is not the case, the volatile collapse of the Tangent Universe will affect the Primary Universe, causing the end of the world as we know it.
To prevent such a catastrophe from occurring, a Living Receiver is chosen from the Tangent Universe to guide this anomaly (known as The Artifact) back to the Primary Universe, ensuring the safe collapse of the former so that the latter remains intact. If we are to apply these rules to the film, then the jet plane engine that collapses in Donnie’s room at the beginning is the anomaly (The Artifact), and Donnie, the Living Receiver, needs to guide it back to the original reality to ensure everyone’s survival. This means that a chunk of “Donnie Darko” takes place in the Tangent Universe, and Donnie’s quest is to trigger a chain of events potent enough to facilitate the time travel back to the OG universe on October 2nd: the day Frank warned Donnie about the end of the world.
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