Gravitational waves in the presence of a cosmological constant

We derive the effects of a non-zero cosmological constant $\Lambda$ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation we consider the situation where the metric can be written as $g_{\mu\nu}= \eta_{\mu\nu}+ h_{\mu\nu}^\Lambda + h_{\mu\nu}^W$, $h_{\mu\nu}^{\Lambda,W}<< 1$, where $h_{\mu\nu}^{\Lambda}$ is the background perturbation and $h_{\mu\nu}^{W}$ is a modification interpretable as a gravitational wave. For $\Lambda \neq 0$ this linearization of Einstein equations is self-consistent only in certain coordinate systems. The cosmological Friedmann-Robertson-Walker coordinates do not belong to this class and the derived linearized solutions have to be reinterpreted in a coordinate system that is homogeneous and isotropic to make contact with observations. Plane waves in the linear theory acquire modifications of order $\sqrt{\Lambda}$, both in the amplitude and the phase, when considered in FRW coordinates. In the linearization process for $h_{\mu\nu}$, we have also included terms of order $\mathcal{O}(\Lambda h_{\mu\nu})$. For the background perturbation $h_{\mu\nu}^\Lambda$ the difference is very small but when the term $h_{\mu\nu}^{W}\Lambda$ is retained the equations of motion can be interpreted as describing massive spin-2 particles. However, the extra degrees of freedom can be approximately gauged away, coupling to matter sources with a strength proportional to the cosmological constant itself. Finally we discuss the viability of detecting the modifications caused by the cosmological constant on the amplitude and phase of gravitational waves. In some cases the distortion with respect to gravitational waves propagating in Minkowski space-time is considerable. The effect of $\Lambda$ could have a detectable impact on pulsar timing arrays.Comment: 20 pages, 1 figur

Children road safety training with augmented reality (AR) [Demo]

© 2017 International Ambient Media Association (iAMEA). All rights reserved. Children killed or seriously injured through road accidents can be avoided through an appropriate safety training. Through play and engagement children learn and understand hazards at i.e. railway stations, bus stops, crossings, school zones, train stations, footpaths, or while cycling. We developed a rapid prototype of an Augmented Reality (AR) safety training proof-of-concept demonstrator for a scaled real-world model of dangerous road hazards. Two scenarios have been picked to give children the possibility to apply, and acquire knowledge of road safety: 1. handling emergency situations and informing authorities; 2. correct behavior at a bus stop on arrival/departure of a bus. In this paper we discuss our design approach, outline the technical implementation of the system, and give a brief overview of our lessons learned