A Clustering Bound for Dark Energy in the Fifth-Coordinate Picture: Sound Speed and the Clustering Length

Whether dark energy clusters depends on its sound speed. This paper converts the sound speed of a fifth-coordinate dark-energy component into a clustering length, the distance below which the component can fall into potential wells, and compares that length with the scales on which the cosmic web is observed to be smooth in the dark sector. A sound speed near the speed of light gives a clustering length near the Hubble radius and a component that stays smooth everywhere inside it. Only sound speeds below about three thousandths of the speed of light would let the component cluster on ten-megaparsec scales. The fifth-coordinate picture, whose natural sound speed is of order unity, therefore predicts unclustered dark energy, and any detected dark-energy clustering would require its sound speed to be far from the natural value. Headline values are: Hubble radius Mpc = 4.451e+03, cs for 10Mpc clustering = 2.247e-03, length at c Mpc = 4.451e+03. This study is simulated and computed from stated assumptions; it is not a measurement.