Translation invariant time-dependent solutions to massive gravity

Homogeneous time-dependent solutions of massive gravity generalise the plane wave solutions of the linearised Fierz-Pauli equations for a massive spin-two particle, as well as the Kasner solutions of General Relativity. We show that they also allow a clear counting of the degrees of freedom and represent a simplified framework to work out the constraints, the equations of motion and the initial value formulation. We work in the vielbein formulation of massive gravity, find the phase space resulting from the constraints and show that several disconnected sectors of solutions exist some of which are unstable. The initial values determine the sector to which a solution belongs. Classically, the theory is not pathological but quantum mechanically the theory may suffer from instabilities. The latter are not due to an extra ghost-like degree of freedom.Comment: 31 page

Translation invariant time-dependent solutions to massive gravity II

This paper is a sequel to arXiv:1310.6560 [hep-th] and is also devoted to translation-invariant solutions of ghost-free massive gravity in its moving frame formulation. Here we consider a mass term which is linear in the vielbein (corresponding to a $\beta_3$ term in the 4D metric formulation) in addition to the cosmological constant. We determine explicitly the constraints, and from the initial value formulation show that the time-dependent solutions can have singularities at a finite time. Although the constraints give, as in the $\beta_1$ case, the correct number of degrees of freedom for a massive spin two field, we show that the lapse function can change sign at a finite time causing a singular time evolution. This is very different to the $\beta_1$ case where time evolution is always well defined. We conclude that the $\beta_3$ mass term can be pathological and should be treated with care.Comment: 19 pages, 1 figur

On Tachyon kinks from the DBI action

We consider solitonic solutions of the DBI tachyon effective action for a non-BPS brane in the presence of an electric field. We find that for a constant electric field $\tilde E\le 1$, regular solitons compactified on a circle admit a singular and decompactified limit corresponding to Sen's proposal provided the tachyon potential satisfies some restrictions. On the other hand for the critical electric field $\tilde E=1$, regular and finite energy solitons are constructed without any restriction on the potential.Comment: proceedings of the second string phenomenology conference, Durham, 30th July to 4th August 200

Constraints on string networks with junctions

We consider the constraints on string networks with junctions in which the strings may all be different, as may be found for example in a network of $(p,q)$ cosmic superstrings. We concentrate on three aspects of junction dynamics. First we consider the propagation of small amplitude waves across a static three-string junction. Then, generalizing our earlier work, we determine the kinematic constraints on two colliding strings with different tensions. As before, the important conclusion is that strings do not always reconnect with a third string; they can pass straight through one another (or in the case of non-abelian strings become stuck in an X configuration), the constraint depending on the angle at which the strings meet, on their relative velocity, and on the ratios of the string tensions. For example, if the two colliding strings have equal tensions, then for ultra-relativistic initial velocities they pass through one another. However, if their tensions are sufficiently different they can reconnect. Finally, we consider the global properties of junctions and strings in a network. Assuming that, in a network, the incoming waves at a junction are independently randomly distributed, we determine the r.m.s. velocities of strings and calculate the average speed at which a junction moves along each of the three strings from which it is formed. Our findings suggest that junction dynamics may be such as to preferentially remove the heavy strings from the network leaving a network of predominantly light strings. Furthermore the r.m.s. velocity of strings in a network with junctions is smaller than 1/\sqrt{2}, the result for conventional Nambu-Goto strings without junctions in Minkowski spacetime.Comment: 12 pages, 6 figures. Version to appear in PRD. (2 new references and slightly extended discussion in section VII

Statistical mechanics of strings with Y-junctions

We investigate the Hagedorn transitions of string networks with Y-junctions as may occur, for example, with (p,q) cosmic superstrings. In a simplified model with three different types of string, the partition function reduces to three generalised coupled XY models. We calculate the phase diagram and show that, as the system is heated, the lightest strings first undergo the Hagedorn transition despite the junctions. There is then a second, higher, critical temperature above which infinite strings of all tensions, and junctions, exist. Conversely, on cooling to low temperatures, only the lightest strings remain, but they collapse into small loops

Interurban Bus: Time to Raise the Profile

A review of development of interurban bus services in Britain in recent years, including case studies showing the effects of major quality improvements and ridership growth, often filling gaps in the rail network. Policy recommendations

Economies of Scale and Scope in Network Industries: Lessons for the UK water and sewerage sectors

Many studies of the water and sewerage industries place significant importance on the benefits of economies of scale and scope and how these relate to vertically integrated firms. We have re-examined the early literature on scale and scope economies and find that these studies do not implicitly preclude non-integrated firms from fully utilising assets for multi-product activities; they can still reap scope economies through trading in the open market. Further, we demonstrate difficulties in separating these two types of economies when assessing firm performance. Trade-offs between governance and production costs are a key issue in determining the value of vertically integrated firms that may undergo divestiture. We discuss the present policy debate regarding the optimal structure of the water and sewerage markets in England and Wales in the light of this, and recommend avenues of research that will help determine the optimal policy

A new monolithic approach for mid-IR focal plane arrays

Antimonide-based photodetectors have recently been grown on a GaAs substrate by molecular beam epitaxy (MBE) and reported to have comparable performance to the devices grown on more expensive InSb and GaSb substrates. We demonstrated that GaAs, in addition to providing a cost saving substrate for antimonide-based semiconductor growth, can be used as a functional material to fabricate transistors and realize addressing circuits for the heterogeneously grown photodetectors. Based on co-integration of a GaAs MESFET with an InSb photodiode, we recently reported the first demonstration of a switchable and mid-IR sensible photo-pixel on a GaAs substrate that is suitable for large-scale integration into a focal plane array. In this work we report on the fabrication steps that we had to develop to deliver the integrated photo-pixel. Various highly controllable etch processes, both wet and dry etch based, were established for distinct material layers. Moreover, in order to avoid thermally-induced damage to the InSb detectors, a low temperature annealed Ohmic contact was used, and the processing temperature never exceeded 180 °C. Furthermore, since there is a considerable etch step (> 6 μm) that metal must straddle in order to interconnect the fabricated devices, we developed an intermediate step using polyimide to provide a smoothing section between the lower MESFET and upper photodiode regions of the device. This heterogeneous technology creates great potential to realize a new type of monolithic focal plane array of addressable pixels for imaging in the medium wavelength infrared range without the need for flip-chip bonding to a CMOS readout chip