Narrow Results

The noncommutative Bianchi I curved space–time vierbeins and spin connections are derived. Moreover, the corresponding noncommutative Dirac equation as well as its solutions are presented. As an application within the quantum field theory approach using Bogoliubov transformations, the von Neumann fermion–antifermion pair creation quantum entanglement entropy is studied. It is shown that its behavior is strongly dependent on the value of the noncommutativity $\theta$ parameter, $k_{\perp }$-modes frequencies and the structure of the curved space–time. Various discussions of the obtained features are presented.

In this work, we have examined the behavior of Bianchi-I (axially symmetric) matter-dominated and the anisotropic Universe with the proposed dark energy, Tsallis holographic dark energy (THDE), with the Hubble horizon as infrared cut-off [Tavayef et al., Tsallis holographic dark energy, Phys. Lett. B781 (2018) 195–200]. The Universe evolution from matter-dominated epoch to dark energy dominated epoch is described by our proposed THDE model. The EoS parameter in our THDE model explains the evolution of the Universe according to the value of nonextensive or Tsallis parameter $\delta$, phantom era (${\omega }_T\le -1$) or quintom (phantom line crossing) and the quintessence era (${\omega }_T\ge -1$), before reaching to completely dark energy-dominated era in the future. Additionally, we also plan to reconcile the dark energy by the method of reconstructing the evolution of the scalar field potential. For the analysis, we take into account the quintessence field and phantom scalar field for this reconstruction, which at present shows the accelerated expansion.

In this study, we have investigated homogeneous and anisotropic Marder and Bianchi type I universe models filled with normal and phantom scalar field matter distributions with $\mathrm{\Lambda }$ in $f(R,T)$ gravitation theory (T. Harko et al., Phys. Rev. D84 (2011) 024020). In this model, $R$ is the Ricci scalar and $T$ is the trace of energy–momentum tensor. To obtain exact solutions of modified field equations, we have used anisotropy feature of the universe and different scalar potential models with $f(R,T)=R+2f(T)$ function. Also, we have obtained general relativity (GR) solutions for normal and phantom scalar field matter distributions in Marder and Bianchi type I universes. Additionally, we obtained the same scalar function values by using different scalar field potentials for Marder and Bianchi type I universe models with constant difference in $f(R,T)$ gravity and GR theory. From obtained solutions, we get negative cosmological term value for $V(\varphi )=V_0$ constant scalar potential model with Marder and Bianchi type I universes in GR theory. These results agree with the studies of Maeda and Ohta, Aktaş et al. also Biswas and Mazumdar. Finally, we have discussed and compared our results in gravitation theories.

We analyze the Bianchi I cosmology in the presence of a massless scalar field and describe its dynamics via a semiclassical and quantum polymer approach. We investigate the morphology of the emerging Big Bounce by adopting three different sets of configurational variables: the natural Ashtekar connections, the Universe volume plus two anisotropy coordinates and a set of anisotropic volume-like coordinates (the latter two sets of variables would coincide in the case of an isotropic Universe). In the semiclassical analysis we demonstrate that the Big Bounce emerges in the dynamics for all the three sets of variables. Moreover, when the Universe volume itself is considered as a configurational variable, we have derived the polymer-modified Friedmann equation and demonstrated that the Big Bounce has a universal nature, i.e. the total critical energy density has a maximum value fixed by fundamental constants and the Immirzi parameter only. From a pure quantum point of view, we investigate the Bianchi I dynamics only in terms of the Ashtekar connections. In particular, we apply the Arnowitt–Deser–Misner (ADM) reduction of the variational principle and then we quantize the system. We study the resulting Schrödinger dynamics, stressing that the wave packet peak behavior over time singles out common features with the semiclassical trajectories.