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A novel, interesting class of scalar-tensor gravity theories is those with alimit on the field motion, where the scalar field either goes to a constantacceleration or stops accelerating and goes to a constant velocity. We combinethese with the ability to dynamically cancel a high energy cosmologicalconstant, e.g. through the well tempered or self tuning approaches. One cansuccessfully have a cosmic expansion history with a matter dominated epoch andlate time acceleration despite a large cosmological constant, although the latetime de Sitter limit may be unstable. Pole models, such as in aDirac-Born-Infeld action, are of particular interest for a cosmic speed limit.

Cosmic Acceleration with and without Limits