The quaternionic commutator bracket and its implications

A quaternionic commutator bracket for position and momentum shows that the quaternionic wave function, \emph{viz.} $\widetilde{\psi}=(\frac{i}{c}\,\psi_0\,,\vec{\psi})$, represents a state of a particle with orbital angular momentum, $L=3\,\hbar$, resulting from the internal structure of the particle. This angular momentum can be attributed to spin of the particle. The vector $\vec{\psi}$, points along the direction of $\vec{L}$. When a charged particle is placed in an electromagnetic fields the interaction energy reveals that the magnetic moments interact with the electric and magnetic fields giving rise to terms similar to Aharonov-Bohm and Aharonov-Casher effects.Comment: 8 page

Phase Space description of Nonlocal Teleparallel Gravity

We study cosmological solutions in nonlocal teleparallel gravity or $f(T)$ theory, where $T$ is the torsion scalar in teleparallel gravity. This is a natural extenstion of the usual teleparallel gravity with nonlocal terms. In this work the phase space portrait proposed to describe the dynamics of an arbitrary flat, homogeneous cosmological background with a number of matter contents, both in early and late time epochs. The aim was to convert the system of the equations of the motion to a first order autonomous dynamical system and to find fixed points and attractors using numerical codes. For this purpose, firstly we derive effective forms of cosmological field equations describing the whole cosmic evolution history in a homogeneous and isotropic cosmological background and construct the autonomous system of the first order dynamical equations. In addition, we investigate the local stability in the dynamical systems called "the stable/unstable manifold" by introducing a specific form of the interaction between matter, dark energy, radiation and a scalar field. Furthermore, we explore the exact solutions of the cosmological equations in the case of de Sitter spacetime. In particular, we examine the role of an auxiliary function called "gauge" $\eta$ in the formation of such cosmological solutions and show whether the de Sitter solutions can exist or not. Moreover, we study the stability issue of the de Sitter solutions both in vacuum and non-vacuum spacetimes. It is demonstrated that for nonlocal $f(T)$ gravity, the stable de Sitter solutions can be produced even in vacuum spacetime.Comment: 14 pages, 3 figures, title changed, version accepted for publication in European Physical Journal

Thermal suppression of bubble nucleation at first-order phase transitions in the early Universe

One of the key observables in a gravitational wave power spectrum from a first order phase transition in the early Universe is the mean bubble spacing, which depends on the rate of nucleation of bubbles of the stable phase, as well as the bubble wall speed. When the bubbles expand as deflagrations, it is expected that the heating of the fluid in front of the phase boundary suppresses the nucleation rate. We quantify the effect, showing that it increases the mean bubble separation, and acts to enhance the gravitational wave signal by a factor of up to order 10. The effect is largest for small wall speeds and strong transitions.Peer reviewe