In this paper, we explore an extension of the classical non-standard cosmological scenario in which the new field, ϕ, which interacts with the radiation component in the early universe, experiences dissipative processes in the form of a bulk viscosity. Assuming an interaction term given by Γ _ϕ ρ _ϕ , where Γ _ϕ accounts for the decay rate of the field and ρ _ϕ corresponds to its energy density, and a bulk viscosity according to the expression ξ=ξ ₀ ρ _ϕ ϕ^1/2 in the framework of Eckart's theory, we apply this novel non-standard cosmology to study the parameters space for WIMPs Dark Matter candidate production. This parameter space shows deviations from the classical non-standard cosmological scenario, obtaining new regions to search for this candidate. In particular, for certain combinations of the free parameters, we found large regions in which the model can establish the DM and reproduce the current observable relic density.

In this paper, we revisit the extension of the classical non-standard cosmological model in which dissipative processes are considered through a bulk viscous term in the new field $\varphi$, which interacts with the radiation component during the early universe. Specifically, we consider an interaction term of the form ${\Gamma }_{\varphi }{\rho }_{\varphi }$, where ${\Gamma }_{\varphi }$ represents the decay rate of the field and ${\rho }_{\varphi }$ denotes its energy density and a bulk viscosity described by $\xi ={\xi }_0{\rho }_{\varphi }^{1/2}$, within the framework of Eckart’s theory. This extended non-standard cosmology is employed to explore the parameter space for the production of Feebly Interacting Massive Particles (FIMPs) as Dark Matter candidates, assuming a constant thermal averaged Dark Matter production cross-section ($⟨\sigma v⟩$), as well as a preliminary analysis of the non-constant case. In particular, for certain combinations of the model and Dark Matter parameters, namely ($T_{\mathrm{end}}$,$\kappa$) and $(m_{\chi },⟨\sigma v⟩)$, where $T_{\mathrm{end}}$ corresponds to the temperature at which $\varphi$ decays, $\kappa$ is the ratio between the initial energy density of $\varphi$ and radiation, and $m_{\chi }$ is the Dark Matter mass, we identify extensive new parameter regions where Dark Matter can be successfully established while reproducing the currently observed relic density, in contrast to the predictions of $\Lambda$CDM and classical non-standard cosmological scenarios.