Higher Derivative Field Theories: Degeneracy Conditions and Classes

We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.Comment: 26 pages, 1 figure. v2: minor changes, references added, matches version published in JHE

FRW Cosmological Perturbations in Massive Bigravity

Cosmological perturbations of FRW solutions in ghost free massive bigravity, including also a second matter sector, are studied in detail. At early time, we find that sub horizon exponential instabilities are unavoidable and they lead to a premature departure from the perturbative regime of cosmological perturbations.Comment: latex, 14 page

Smart Procurement Of Naturally Generated Energy (SPONGE) for PHEV's

In this paper we propose a new engine management system for hybrid vehicles to enable energy providers and car manufacturers to provide new services. Energy forecasts are used to collaboratively orchestrate the behaviour of engine management systems of a fleet of PHEV's to absorb oncoming energy in an smart manner. Cooperative algorithms are suggested to manage the energy absorption in an optimal manner for a fleet of vehicles, and the mobility simulator SUMO is used to show simple simulations to support the efficacy of the proposed idea.Comment: Updated typos with respect to previous versio

Finite Energy of Black Holes in Massive Gravity

In GR the static gravitational potential of a self-gravitating body goes as 1/r at large distances and any slower decrease leads to infinity energy. We show that in a class of four-dimensional massive gravity theories there exists spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1/r and generically of the form $r^\gamma$. This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counterbalancing the apparently infinite energy budget.Comment: 4 page

Spherically Symmetric Solutions in Ghost-Free Massive Gravity

Recently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz invariant and a Lorentz breaking asymptotically flat behaviour and also fall in two branches. In the first branch, all solutions can be found analitycally and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool.Comment: 15 pages. Some change in the reference

An Assessment on the Use of Stationary Vehicles as a Support to Cooperative Positioning

In this paper, we consider the use of stationary vehicles as tools to enhance the localisation capabilities of moving vehicles in a VANET. We examine the idea in terms of its potential benefits, technical requirements, algorithmic design and experimental evaluation. Simulation results are given to illustrate the efficacy of the technique.Comment: This version of the paper is an updated version of the initial submission, where some initial comments of reviewers have been taken into accoun

Smart Procurement of Naturally Generated Energy (SPONGE) for Plug-in Hybrid Electric Buses

We discuss a recently introduced ECO-driving concept known as SPONGE in the context of Plug-in Hybrid Electric Buses (PHEB)'s.Examples are given to illustrate the benefits of this approach to ECO-driving. Finally, distributed algorithms to realise SPONGE are discussed, paying attention to the privacy implications of the underlying optimisation problems.Comment: This paper is recently submitted to the IEEE Transactions on Automation Science and Engineerin

Vainshtein mechanism after GW170817

The almost simultaneous detection of gravitational waves and a short gamma-ray burst from a neutron star merger has put a tight constraint on the difference between the speed of gravity and light. In the four-dimensional scalar-tensor theory with second order equations of motion, the Horndeski theory, this translates into a significant reduction of the viable parameter space of the theory. Recently, extensions of Horndeski theory, which are free from Ostrogradsky ghosts despite the presence of higher order derivatives in the equations of motion, have been identified and classified exploiting the degeneracy criterium. In these new theories, the fifth force mediated by the scalar field must be suppressed in order to evade the stringent Solar System constraints. We study the Vainshtein mechanism in the most general degenerate higher order scalar-tensor theory in which light and gravity propagate at the same speed. We find that the Vainshtein mechanism generally works outside a matter source but it is broken inside matter, similarly to beyond Horndeski theories. This leaves interesting possibilities to test these theories that are compatible with gravitational wave observations using astrophysical objects.Comment: 5 pages, no figure, added references, corrected typos, accepted for publication in Physical Review