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 $Λ$CDM cosmology, to place an upper bound on the logarithm of the free parameter of the model $τ_\rm{eq}$ 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 $\log_{10}(τ_\rm{eq}\,[\rm{s}]) \lesssim -9.76$ (2$σ$), with the corresponding dimensionless bulk coefficient $\tildeξ H_0/H_\rm{eq}\lesssim5.94\times10^{-4}$ (2$σ$). 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.

Figures (5)

• Figure 1: Percentage difference between the Hubble rate computed with and without a bulk viscous pressure, shown as a function of the redshift for different $\tau_\text{eq}$ values. The benchmark $\Lambda$CDM curve corresponds to the viscous case for $\tau_\text{eq}=0\,\text{s}$. The value $\tau_\text{eq} = 1.64 \times 10^{-8}\,\text{s}$ denotes the theoretical upper bound imposed by the positivity of the sound speed, as will be discussed in \ref{['subsec:sound_speed']}.
• Figure 2: Evolution of the squared sound speed \ref{['eq:fullcs2']}, including the nonadiabatic correction, as a function of the redshift for different $\tau_\text{eq}$ values. In the limit $z\to\infty$, the radiation-dominated behavior $c_s^2=1/3$ is recovered, while at $z=z_\text{d}$, baryons decouple from the photon drag and the acoustic oscillation freeze out, leaving the characteristic BAO imprint. For $\tau_\text{eq}= 1.64 \times10^{-8}\,\text{s}$, the adiabatic contribution is almost completely suppressed by the nonadiabatic component leading to a vanishing $c^2_s$ before $z_\text{eq}$. For $\tau_\text{eq}\sim10^{-10}\,\text{s}$, the nonadiabatic correction is almost negligible.
• Figure 3: Effective bulk viscosity as a function of the normalized scale factor, for different various of $m_\chi$ in the allowed range, at fixed $\tau_\text{eq}$. The upper panel shows the results for the maximum value of $\tau_\text{eq}$, constrained by the positivity of the speed of sound in \ref{['eq:taueq_csbound']}. In the lower one we use the $2\sigma$ upper bound given by DESI DR2 data in \ref{['eq:finalbound']}.
• Figure 4: 1D marginalized posteriors, normalized to their maximum value, for the combination of redshift bins of DESI DR2, in comparison with DES Y3 measurement of the comoving transverse distance.
• Figure 5: 1D marginalized posteriors, normalized to their maximum value, for the single tracers of DESI DR2 dataset.