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.

In this work we study some aspects of the Rastall gravity, it being the thermodynamics consistency of the model which the core of this paper; for this purpose we will consider the dynamical equations of Rastall model in a flat FLRW geometry. Under a holographic description it can be seen that this scenario for gravity contributes to the energy density of the fluid with an extra term that can be related to the deceleration parameter, providing a way to estimate the value of the Rastall parameter, termed as , at present time. By adopting a specific Ansatz for the term it is possible to determine that the behaviour of the Hubble parameter in Rastall gravity has a similar aspect to the CDM model at late times, but at thermodynamics level differs from the standard cosmology since the adiabatic behaviour for the entropy depends on the value of the parameter state, . However, the entropy has a positive growth and simultaneously its convexity condition can be guaranteed; when other contributions are considered such as matter production and chemical potential, the adiabatic expansion cannot be achieved, but the theory keeps its thermodynamics consistency. The chemical potential seems to have an interesting role since at the effective level we could have a cosmological constant or phantom expansion in the model.

We perform a study both statistical and theoretical for cosmological models of matter creation and their ability to describe effective phantom models of dark energy. Such models are beyond the $\mathrm{\Lambda }\mathrm{CDM}$ model since the resulting cosmic expansion is not adiabatic. In fact, we show that this approach exhibits transient phantom/quintessence scenarios at present time and tends to the standard cosmological model at some stage of the cosmic evolution. We discuss some generalities of the thermodynamics properties for this type of cosmological model; we emphasize on the behavior of the temperature associated to dark matter, which keeps positive along cosmic evolution together with the entropy. The enrichment of this type of model by means of the incorporation of cosmological constant and dissipative effects in the fluid description to explore their cosmological consequences in the expansion of the Universe is considered. Finally, a generalization for the matter production rate as an inhomogeneous expression of the Hubble parameter and its derivatives is discussed; as in all the cases examined, such election leads to an effective phantom/quintessence behavior.

In this work, we present an analysis of the phantom zone in a causal viscous cosmology from a thermodynamic point of view. In this description, we consider a chemical potential and the approach of irreversible processes. We assume a flat universe filled with a single dissipative fluid described by a barotropic equation of state, $p=\omega \rho$. This model allows us to construct a negative chemical potential for the phantom regime and have positive definite temperature and entropy.

In this work, we study some thermodynamical aspects associated with torsion in a flat FLRW spacetime cosmic evolution. By implementing two Ansatze for the torsion term, we find that the model admits a phantom regime or a quintessence behavior. This scheme differs from the $$\Lambda $$Λ CDM model at the thermodynamical level. The resulting cosmic expansion is not adiabatic, the fulfillment of the second law of thermodynamics requires a positive torsion term, and the temperature of the cosmic fluid is always positive. The entropy of the torsion phantom scenario is negative, but introducing chemical potential solves this issue. For a Dirac-Milne type Universe, the torsion leads to a growing behavior for the temperature of the fluid but has no incidence on the rate of expansion.

In this work we explore under a holographic approach, the dark energy–dark matter interaction in a non-flat Friedmann–Lemaitre–Robertson–Walker spacetime, with a cut-off for the dark energy component given in terms of the Hubble scale. Based on results coming from the use of observational data, we consider a positive interaction Q -term together with a Chevallier–Polarsky–Linder type parametrization for the coincidence parameter, we realize that the model admits a Type III future singularity, in this singular universe we have that for a null value of the curvature parameter its scale factor is a constant value. With the use of some cosmological parameters constrained with observational data, we obtain that the crossing of the phantom divide is possible. Once the singular nature is obtained for the model, its Statefinder diagnosis reveals a behavior that is far from the Λ-CDM model.