We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a FLRW metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric. The case for both spatially flat and non flat are studied first in the presence of only the scalar field and subsequently with the addition of non interacting perfect fluids. It is verified that this addition does not change the general form of the solution, but only the particular expressions of the scalar field and the potential. The results are applied in the case of parametric dark energy models where we derive the scalar field equivalence solution for some proposed models in the literature. *
Abstract. In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.
Assuming dislocations could be meaningfully described by torsion, we propose here a scenario based on the role of time in the low-energy regime of two-dimensional Dirac materials, for which coupling of the fully antisymmetric component of the torsion with the emergent spinor is not necessarily zero. Appropriate inclusion of time is our proposal to overcome well-known geometrical obstructions to such a program, that stopped further research of this kind. In particular, our approach is based on the realization of an exotic time-loop, that could be seen as oscillating particle-hole pairs. Although this is a theoretical paper, we moved the first steps toward testing the realization of these scenarios, by envisaging Gedankenexperiments on the interplay between an external electromagnetic field (to excite the pair particle-hole and realize the time-loops), and a suitable distribution of dislocations described as torsion (responsible for the measurable holonomy in the time-loop, hence a current). Our general analysis here establishes that we need to move to a nonlinear response regime. We then conclude by pointing to recent results from the interaction lasergraphene that could be used to look for manifestations of the torsion-induced holonomy of the time-loop, e.g., as specific patterns of suppression/generation of higher harmonics. 1 In the following we refer to two dimensional Dirac materials, with hexagonal lattice. Examples are graphene, germanene, silicene [9]. 2 We use Latin indices a; b; … for tangent/flat space and Greek indices μ; ν; … for base curved manifold. We choose the signature η ab ¼ diagðþ; −; −Þ. The Vielbeins are denoted by e a μ and their inverse by E μ a .3 This is due to the reducible, rather than irreducible, representation of the Lorentz group we use. CIAPPINA, IORIO, PAIS, and ZAMPELI PHYS. REV. D 101, 036021 (2020) 036021-2 FIG. 2. Idealized time-loop. At t ¼ 0, the hole (yellow) and the particle (black) start their journey from y ¼ 0, in opposite directions. Evolving forward in time, at t ¼ t à > 0, the hole reaches −y à , while the particle reaches þy à , (blue portion of the circuit). Then they come back to the original position, y ¼ 0, at t ¼ 2t à (red portion of the circuit). This can be repeated indefinitely. On the far right, the equivalent time-loop, where the hole moving forward in time is replaced by a particle moving backward in time.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.