Dark energy that tracks matter: an exchange model with no free exchange parameters tested against DESI

We study a cosmological model in which cold dark matter exchanges energy with a vacuum-like component (equation of state w=-1), at a rate Q=b Hρs(ρm-kρs)/(ρm+ρs) that drives the vacuum-like density ρs towards a level set by the matter density ρm. The two constants are fixed in advance rather than fitted: k=2, because the exchange then reverses when the deceleration of the expansion vanishes (exactly if radiation and neutrino pressure are neglected), and b=1, because the vacuum-like density then grows in proportion to the scale factor during matter domination. The model has the same six free parameters as ΛCDM. Fitted to Planck 2018 temperature and polarisation (plik-lite) with a reionisation prior, Planck lensing, DESI DR2 baryon acoustic oscillations and Pantheon+ supernovae, it gives χ²=2012.5, against 2019.8 for ΛCDM; freeing k and b improves the fit by only 0.8. The preference comes from DESI: without it, the two models differ by 0.9 in χ², in favour of ΛCDM. In conditional tests, with the cosmological parameters fixed at the best fits and nuisance parameters profiled, the model gives fits close to those of ΛCDM despite S8=0.73: it fits KiDS-Legacy and DES Y3 cosmic shear and redshift-space growth data about as well as ΛCDM, whereas ΛCDM with the same S8 is strongly disfavoured, because the returned dark matter is smooth. With k and b free, it also eases the tension on the sum of neutrino masses. Predictions for the DESI five-year BAO data, with a pre-specified decision protocol, were deposited before the data. A companion paper presents a separate, explicitly hypothetical interpretation of the exchange law in terms of modes of space.