Cosmological fluctuations of a random field and radiation fluid

A generalization of the random fluid hydrodynamic fluctuation theory due to Landau and Lifshitz is applied to describe cosmological fluctuations in systems with radiation and scalar fields. The viscous pressures, parametrized in terms of the bulk and shear viscosity coefficients, and the respective random fluctuations in the radiation fluid are combined with the stochastic and dissipative scalar evolution equation. This results in a complete set of equations describing the perturbations in both scalar and radiation fluids. These derived equations are then studied, as an example, in the context of warm inflation. Similar treatments can be done for other cosmological early universe scenarios involving thermal or statistical fluctuations.