A Bound on the Dark-Sector Interaction Rate from Structure Formation

Energy exchange between dark matter and dark energy changes the growth of structure, and published growth measurements therefore bound the exchange rate. This paper converts a coupling parametrised as a fraction of the Hubble rate times the dark-energy density into physical rates at several redshifts, and compares the transferred density over a Hubble time with the matter density that structure formation can tolerate losing or gaining. Couplings at the level sometimes quoted as interesting, a tenth of the Hubble rate, would move a substantial fraction of the matter density over cosmic time and are disfavoured in this simple accounting; couplings below about one hundredth of the Hubble rate move less than a few percent and remain compatible. The bound is stated as a rate in inverse seconds as well as a dimensionless coupling. Headline values are: rate at bound per s = 2.183e-20, coupling approx bound = 1.0e-02, fraction at coupling 0p1 = 2.172e-01, H0 per s = 2.183e-18. This study is simulated and computed from stated assumptions; it is not a measurement.