In this paper we explore the different types of singularities that arise in the $\mathrm{\Lambda }\mathrm{CDM}$ model when dissipative processes are considered, in the framework of the Eckart’s theory. In particular, we study the late-time behavior of $\mathrm{\Lambda }\mathrm{CDM}$ model with viscous cold dark matter (CDM) and an early-time viscous radiation domination era with cosmological constant (CC). The fluids are described by the barotropic equation of state (EoS) $p=(\gamma -1)\rho$, where $p$ is the equilibrium pressure of the fluid, $\rho$ their energy density, and $\gamma$ is the barotropic index. We explore two particular cases for the bulk viscosity $\xi$, a constant bulk viscosity $\xi ={\xi }_0$, and a bulk viscosity proportional to the energy density of the fluid $\xi ={\xi }_0\rho$. Due to some previous investigations that have explored how to describe the behavior of the Universe with a negative CC, we extend our analysis to this case. We found that future singularities like Big Rip are allowed but without having a phantom EoS associated with the DE fluid. Big Crunch singularities also appears when a negative CC is present, but also de Sitter and even Big Rip types are allowed due to the negative pressure of the viscosity, which opens the possibility of an accelerated expansion in anti–de Sitter (AdS) cosmologies. We also discuss a very particular solution without Big Bang singularity that arises in the early-time radiation dominant era of our model known as soft-Big Bang.

Extensions to a $\mathsf{\Lambda }$DM model have been explored in order to face current tensions that occur within its framework, which encompasses broadening the nature of the dark matter (DM) component to include warmness and a non-perfect fluid description. In this paper, we investigated the late-time cosmological evolution of an exact solution recently found in the literature, which describes a viscous warm $\mathsf{\Lambda }$DM model ($\mathsf{\Lambda }$WDM) with a DM component that obeys a polytropic equation of state (EoS), which experiences dissipative effects with a bulk viscosity proportional to its energy density, with proportionality constant ${\xi }_0$. This solution has the particularity of having a very similar behavior to the $\mathsf{\Lambda }$CDM model for small values of ${\xi }_0$, evolving also to a de Sitter type expansion in the very far future. We explore firstly the thermodynamic consistences of this solution in the framework of Eckart’s theory of non-perfect fluids, focusing on the fulfillment of the two following conditions: (i) the near-equilibrium condition and (ii) the positiveness of the entropy production. We explore the range of parameters of the model that allow to fulfill these two conditions at the same time, finding that a viscous WDM component is compatible with both ones, being in this sense, a viable model from the thermodynamic point of view. Furthermore, we constrained the free parameters of the model with the observational data coming from supernovae Ia (SNe Ia) and the observational Hubble parameter data (OHD), using these thermodynamics analyses to define the best priors for the cosmological parameters related to the warmness and the dissipation of the DM, showing that this viscous $\mathsf{\Lambda }$WDM model can describe the combined SNe Ia+OHD data in the same way as the $\mathsf{\Lambda }$CDM model. The cosmological constraint at $3\sigma$ CL gives us an upper limit on the bulk viscous constant of order ${\xi }_0\sim {10}^6$ Pa·s, which is in agreement with some previous investigations. Our results support that the inclusion of a dissipative WDM, as an extension of the standard cosmological model, leads to a both thermodynamically consistent and properly fitted cosmological evolution.

In this paper, we study the thermodynamical and mathematical consistencies for a non-singular early-time viscous cosmological model known as soft-Big Bang, which was previously found in [N. Cruz, E. Gonz\'alez, and J. Jovel, Phys. Rev. D \textbf{105}, 024047 (2022)]. This model represents a flat homogeneous and isotropic universe filled with a dissipative radiation fluid and a cosmological constant $\Lambda$, which is small but not negligible, in the framework of Eckart's theory. In particular, we discuss the capability of the solution in the fulfillment of the three following conditions: (i) the near equilibrium condition, which is assumed in Eckart's theory of non-perfect fluids, (ii) the mathematical stability of the solution under small perturbations, and (iii) the positiveness of the entropy production. We have found that this viscous model can describe the radiation domination era of the $\Lambda$CDM model and, at the same time, fulfill the three conditions mentioned by the fulfillment of a single constraint on the bulk viscous coefficient $\xi_{0}$, finding also that this non-singular model has a positive energy density in the infinity past which is infinity hotter with a constant entropy.

In this paper we explore the different types of singularities that arise in the $\Lambda$CDM model when dissipative processes are considered, in the framework of the Eckart's theory. In particular, we study the late-time behavior of $\Lambda$CDM model with viscous cold dark matter (CDM) and an early-time viscous radiation domination era with cosmological constant (CC). The fluids are described by the barotropic equation of state (EoS) $p=(\gamma-1)\rho$, where $p$ is the equilibrium pressure of the fluid, $\rho$ their energy density, and $\gamma$ is the barotropic index. We explore two particular cases for the bulk viscosity $\xi$, a constant bulk viscosity $\xi=\xi_{0}$, and a bulk viscosity proportional to the energy density of the fluid $\xi=\xi_{0}\rho$. Due to some previous investigations that have explored to describe the behavior of the universe with a negative CC, we extend our analysis to this case. We found that future singularities like Big-Rip are allowed but without having a phantom EoS associated to the DE fluid. Big-Crunch singularities also appears when a negative CC is present, but also de Sitter and even Big-Rip types are allowed due to the negative pressure of the viscosity, which opens the possibility of an accelerated expansion in AdS cosmologies. We also discuss a very particular solution without Big Bang singularity that arises in the early-time radiation dominant era of our model known as Soft-Big Bang.

Extensions to a $\Lambda$DM model have been explored to face current tensions that occur within its framework, which encompasses broadening the nature of the dark matter (DM) component to include warmness and a non-perfect fluid description. In this paper, we investigated the late-time cosmological evolution of an exact solution recently found in [N. Cruz, E. Gonz\'alez, and J. Jovel, Phys. Rev. D \textbf{105}, 024047 (2022)], which describe a viscous warm $\Lambda$DM model ($\Lambda$WDM) with a DM component that obeys a polytropic equation of state (EoS), which experience dissipative effects with a bulk viscosity proportional to its energy density, with proportionality constant $\xi_{0}$. This solution has the particularity of having a very similar behavior to the $\Lambda$CDM model for small values of $\xi_{0}$, evolving also to a de Sitter type expansion in the very far future. We explore firstly the thermodynamic consistences of this solution in the framework of the Eckart's theory of non-perfect fluids, focusing on the fulfillment of the two following conditions: (i) the near equilibrium condition and (ii) the positiveness of the entropy production. We explore the range of parameters of the model that allow to fulfilling these two conditions at the same time, finding that a viscous WDM component is compatible with both ones, being in this sense, a viable model from the thermodynamic point of view. Besides, we constraint the free parameters of the model with the observational data coming form supernovae Ia (SNe Ia) and the observational Hubble parameter data (OHD).(Abridged)