Early-Universe Bulk Viscosity in the Era of Precision Large-Scale Structure Cosmology

Precision cosmology increasingly tests not only the parameters of Lambda-CDM, but also the assumption that the early universe can be treated as an ideal relativistic fluid. We develop a controlled imperfect-fluid extension in which the standard radiation component is supplemented by a density-dependent bulk-viscous pressure, Pi = -3 zeta(rho) H_phys, with zeta(rho) = zeta_0 (rho/rho_ref)^m. The two parameters describe the amplitude and local density scaling of the low-frequency dissipative response of a near-equilibrium relativistic plasma. We motivate this parametrization from standard microphysical considerations, including Kubo relations for the trace of the stress-energy tensor, kinetic-theory relaxation of nonconformal pressure modes, and enhanced bulk viscosity in nonconformal or strongly coupled plasmas. Working in the perturbative Navier-Stokes limit, we derive the background and linear scalar-perturbation equations in Newtonian gauge, retaining both the bulk-viscous pressure Pi and its perturbation delta Pi. The resulting system modifies the effective radiation equation of state and introduces a non-adiabatic pressure source capable of producing controlled evolution of the comoving curvature perturbation. The framework is formulated in a Boltzmann-code-ready form suitable for implementation in CLASS or related solvers. Consistency requires the viscous pressure and its perturbation to remain small compared with the total energy density, ensuring preservation of the standard thermal history and the validity of linear perturbation theory. Within this controlled regime, the expected observational signatures are modest but correlated: mild scale-dependent damping of scalar perturbations, changes to the matter transfer function, and associated tensor-sector attenuation arising from the same viscosity history. Recent CMB and DESI-era large-scale-structure measurements sharpen the need to distinguish late-time dark-energy evolution from early-time modifications of radiation dynamics and transfer functions. The model developed here does not claim that current data require bulk viscosity; rather, it provides a minimal, falsifiable two-parameter baseline for constraining imperfect-fluid effects in the early universe and for separating them from other beyond-Lambda-CDM extensions.