FIMP Dark Matter in bulk viscous non-standard cosmologies

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 $\phi$, which interacts with the radiation component during the early universe. Specifically, we consider an interaction term of the form $\Gamma_{\phi} \rho_{\phi}$, where $\Gamma_{\phi}$ represents the decay rate of the field and $\rho_{\phi}$ denotes its energy density and a bulk viscosity described by $\xi=\xi_{0}\rho_{\phi}^{1/2}$, 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 ($\langle\sigma v\rangle$), as well as a preliminary analysis of the non-constant case. In particular, for certain combinations of the model and Dark Matter parameters, namely ($T_\text{end}$,$\kappa$) and $(m_\chi,\langle\sigma v\rangle)$, where $T_\text{end}$ corresponds to the temperature at which $\phi$ decays, $\kappa$ is the ratio between the initial energy density of $\phi$ 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.
Comment: 17 pages and 23 figures. Sections I, II, and III have been revised, and a new Section III C has been added, specifically addressing the non-constant total thermally averaged DM production cross-section for FIMPs. The rest of the paper remains unchanged