Massive Gravity Illustrated in the Mandelbrot Set

Abstract

The long-range transition to 5-d or higher, seen in DGP gravity, cascading DGP, and some other theories, can be interpreted as a prior epoch or precursor universe.  This transition has therefore been proposed to be a black hole in 5-d ® 4-d white hole and a spacetime bubble that is our cosmos.  The same transition is represented in the Mandelbrot Set at (-0.75,0i), where the cardioid meets the circular disc, mimicking Cartan’s rolling ball analogy for G₂ symmetries – when M is extended into higher dimensions.  We can therefore study this in an archetypical setting, and it suggests a unique exit from a higher-dimensional origin, which conveniently explains the weakness of gravity and accelerating expansion.  Other analogies allow us to discuss graviton properties and phenomenology.  Notably the Misiurewicz point at about (-1.543689,0i) represents the quantum critical point in BEC formation, which has been connected to black hole event horizons.  A consistent model for gravity with higher-dimensional origins is offered.