Geodesic completion of big bangs from emergent geometry

A theorem by Borde, Guth, and Vilenkin requires any cosmology that is always expanding to be past-incomplete, similar to a big bang singularity. A non-singular cosmology is thought to require either an asymptotically stationary cosmology or an initially contracting cosmology. There is a third possibility: Einstein-frame cosmic time can be a dynamical quantity that is able to spontaneously reverse direction. This occurs in the presence of phantom Chaplygin gas, whose acoustic cone defines a more fundamental "causal-frame" geometry. The resulting spacetime is geodesically complete even with a local minimum of cosmic time in the Einstein-frame metric where the laps function changes time. This soft "singularity" is dubbed a Big Benjamin Button, as gravity experiences time reversal while the chaplygin gas continues to evolve forward in time. This creates a mismatch between the thermodynamic arrows of time between Chaplygin gas and gravitational waves. The causal-frame geometry created by the Chaplygin gas provides a sensible notion of causality for all degrees of freedom, and predicts a non-singular bounce that is robust against arbitrary additions of any types of matter.