Born-Infeld gravity sits at the sweet spot of two quantum extensions

When physicists add 'natural' corrections to quantum mechanics — such as the generalized uncertainty principle — or to gravity, both changes ultimately reshape the same flat cosmological equations. This paper maps the two modifications onto each other through the Friedmann equations, revealing that a simple tweak in one framework can produce unwieldy, unnatural complexity in the other. Scanning across possible models, Born-Infeld-type theories emerge as the unique class that remains elegantly simple on both the quantum-uncertainty and the modified-gravity sides of the correspondence.