In this work we explore a new cosmological solution for an universe filled with one dissipative fluid, described by a barotropic equation of state (EoS) $p=\omega \rho$, in the framework of the full Israel-Stewart theory. The form of the bulk viscosity has been assumed of the form $\xi ={\xi }_0{\rho }^{1/2}$. The relaxation time is taken to be a function of the EoS, the bulk viscosity and the speed of bulk viscous perturbations, $c_b$. The solution presents an initial singularity, where the curvature scalar diverges as the scale factor goes to zero. Depending on the values for $\omega$, ${\xi }_0$, $c_b$ accelerated and decelerated cosmic expansion can be obtained. In the case of accelerated expansion, the viscosity drives the effective EoS to be of quintessence type, for the single fluid with positive pressure. Nevertheless, we show that only the solution with decelerated expansion satisfies the thermodynamics conditions $dS/dt>0$ (growth of the entropy) and $d^{2}S/d{t}^2<0$ (convexity condition). We show that an exact stiff matter EoS is not allowed in the framework of the full causal thermodynamic approach; and in the case of a EoS very close to the stiff matter regime, we found that dissipative effects becomes negligible so the entropy remains constant. Finally, we show numerically that the solution is stable under small perturbations.

Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration constant. Recently, it has been shown that energy diffusion that may arise in quantum gravity and in theories with spontaneous collapse is compatible with this framework by virtue of its restricted diffeomorphism invariance. New studies suggest that this phenomenon could lead to higher-order equations in the context of homogeneous and isotropic Universe, affecting the well-posedness of their Cauchy initial-value problem. In this work, we show that this issue can be circumvented by assuming an equation of state that relates the energy density to the function that characterizes diffusion. As an application, we solve the field equations analytically for an isotropic and homogeneous universe in a barotropic model and in the mass-proportional continuous spontaneous localization (CSL) scenario, assuming that only dark matter develops energy diffusion. Different solutions possessing phase transition from decelerated to accelerated expansion are found. We use cosmological data of type Ia supernovae and observational Hubble data to constrain the free parameters of both models. It is found that very small but nontrivial energy nonconservation is compatible with the barotropic model. However, for the CSL model, we find that the best-fit values are not compatible with previous laboratory experiments. We comment on this fact and propose future directions to explore energy diffusion in cosmology.

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.