The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical approach to the problem of time, that has the main goal of reproducing quantum field theory on a fixed Wentzel-Kramers-Brillouin (WKB) background accounting also for quantum gravity corrections. We analyze the different choices of the expansion parameter and discuss the problems arising in previous proposals, where a nonunitary evolution emerges as an effect of quantum gravity corrections. In this work, we develop a new approach to solve this problem by performing the WKB expansion with the introduction of the so-called kinematical action as a clock for quantum matter, that allows to recover a unitary dynamics.
In this work, we study the effect of a magnetic field on the growth of cosmological perturbations. We develop a mathematical consistent treatment in which a perfect fluid and a uniform magnetic field evolve together in a Bianchi I universe. We then study the energy density perturbations on this background with particular emphasis on the effect of the background magnetic field. We develop a full relativistic solution which refines previous analysis in the relativistic limit, recovers the known ones in the Newtonian treatment with adiabatic sound speed, and it adds anisotropic effects to the relativistic ones for perturbations with wavelength within the Hubble horizon. This represents a refined approach on the perturbation theory of an isotropic universe in GR, since most of the present studies deal with fully isotropic systems. arXiv:1807.00434v3 [gr-qc]
We analyse the influence that viscous effects can induce on the evolution of primordial perturbations to the isotropic universe in the presence of a weak uniform magnetic field. Previous analyses have shown that the presence of the magnetic field induces an intrinsic anisotropy in the perturbations dynamics, essentially because of the anisotropic character of the perturbed magnetic pressure. This anisotropic effect is of order unity in the perturbation amplitude, although it remains small in the linear theory when the density constraints are considered. The aim of this study is to determine the impact of viscosity, surely present in the early universe, on the growth of the perturbation anisotropy. The main merit of this study consists of demonstrating that a tiny overlapping exists in the parameter space to deal simultaneously with anisotropic features due to the magnetic field and the viscous damping of such density fluctuation. Actually, we demonstrate that the viscosity affects the value of the anisotropy, by smoothing the growing rate of the instability only when structure smaller than about 5000 solar masses are concerned. This result allows us to guarantee that the intrinsic anisotropy of the magnetized universe perturbations is not affected by the viscosity due to friction among inhomogeneous layers or compressive-like effects, and therefore, they remain good candidates for being seeds for filament formation across the universe.
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