In this work, we first discuss the possibility that dark energy models with negative energy density values in the past can alleviate the $H_0$ tension, as well as the discrepancy with the baryon acoustic oscillation (BAO) Lyman-$\alpha$ data, both which prevail within the $\mathrm{\Lambda }\mathrm{CDM}$ model. We then investigate whether two minimal extensions of the $\mathrm{\Lambda }\mathrm{CDM}$ model, together or separately, can successfully realize such a scenario: (i) the spatial curvature, which, in the case of spatially closed universe, mimics a negative density source and (ii) simple-graduated dark energy (gDE), which promotes the null inertial mass density of the usual vacuum energy to an arbitrary constant—if negative, the corresponding energy density decreases with redshift similar to the phantom models, but unlike them crosses below zero at a certain redshift. We find that, when the Planck data are not included in the observational analysis, the models with simple-gDE predict interesting and some significant deviations from the $\mathrm{\Lambda }\mathrm{CDM}$ model. In particular, a spatially closed universe along with a simple-gDE of positive inertial mass density, which work in contrast to each other, results in minor improvement to the $H_0$ tension. The joint dataset, including the Planck data, presents no evidence for a deviation from spatial flatness but almost the same evidence for a cosmological constant and the simple-gDE with an inertial mass density of order $\mathcal{O}({10}^{-12}){\mathrm{eV}}^4$. The latter case predicts almost no deviation from the $\mathrm{\Lambda }\mathrm{CDM}$ model up until today—so that it results in no improvement regarding the BAO Ly-$\alpha$ data—except that it slightly aggravates the $H_0$ tension. We also study via dynamical analysis the history of the Universe in the models, as the simple-gDE results in futures different than the de Sitter future of the $\mathrm{\Lambda }\mathrm{CDM}$ model.

In the context of dark energy solutions, we consider a Friedmann—Robertson—Walker spacetime filled with a noninteracting mixture of dust and a viscous fluid, for which the bulk viscosity is governed by the nonlinear model proposed in [R. Maartens and V. Méndez, Phys. Rev. D 55, 1937 (1997)]. Through a phase-space analysis of the equivalent dynamical system, the existence and stability of critical solutions are established, and the respective scale factors are computed. The results point toward the possibility of describing the current accelerated expansion of the Universe by means of the above-mentioned nonlinear model for viscosity.

Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of the classical or quantum gravity of quantum fields in curved space or of other high-energy scenarios on lower-energy corresponding systems. The “reverse way” consists in building fundamental physical theories, for instance, quantum gravity models, inspired by the lower-energy corresponding systems. Here, we present the case of graphene and other Dirac materials.

Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein, and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa’s thermofield dynamics. We then evaluate the von Neumann black hole-environment entropy and noticeably obtain a Page-like evolution. We finally show that this is a consequence of a duality between our model and a quantum dissipativelike fermionic system.