Bulk viscosity from early-time thermalization of cosmic fluids in light of DESI DR2 data

Abstract

If nonrelativistic dark matter and radiation are allowed to interact, reaching an approximate thermal equilibrium, this interaction induces a bulk viscous pressure changing the effective one-fluid description of the universe dynamics, permitted by the existence of a common temperature. It has been shown that by modelling such components as perfect fluids, a cosmologically relevant bulk viscous pressure, expressed in terms of the Eckart formalism, emerges for dark matter particle masses in the range of $1\,\text{eV} - 10\,\text{eV}$ keeping thermal equilibrium with the radiation. Such a transient bulk viscosity introduces significant effects in the expansion rate near the matter-radiation equality redshift ($z_\rm{eq}\sim 3400$), impacting also late times leading to a higher inferred value of the Hubble constant $H_0$. Since this mechanism also impacts the sound speed of the baryon-photon fluid, we use the recent DESI DR2 BAO measurements, reported relative to a fiducial $\Lambda$CDM cosmology, to place an upper bound on the logarithm of the free parameter of the model $\tau_\rm{eq}$ which represents the time scale in which each component follows its own internal perfect fluid dynamics until thermalization occurs. Our main result is encoded in the bound $\log_{10}(\tau_\rm{eq}\,[\rm{s}]) \lesssim -9.76$ (2$\sigma$), with the corresponding dimensionless bulk coefficient $\tilde{\xi} H_0/H_\rm{eq}\lesssim5.94\times10^{-4}$ (2$\sigma$). The obtained constraints show that DESI DR2 data do not support such an interaction between radiation and dark matter prior to the recombination epoch, precluding the model from solving the cosmic tensions.