Complete Decoupling Limit of Ghost-free Massive Gravity

We present the complete form of the decoupling limit of ghost-free massive gravity with a Minkowski reference metric, including the full interactions of the helicity-1 and helicity-0 modes of the massive spin-2 field. While in the metric language the square root structure of the mass terms makes it difficult to find a simple way to write down the interactions, we show that using the vierbein formulation of massive gravity, including Stueckelberg fields for both diffeomorphism and local Lorentz symmetries, we can find an explicitly resummed expression for the helicity-1 field interactions. We clarify the equations of motion for the Lorentz Stueckelberg fields and how these generate the symmetric vierbein condition which guarantees equivalence between the vierbein and metric formulations of massive gravity.Comment: 20 pages, typos corrected, references adde

On Black Holes in Massive Gravity

In massive gravity the so-far-found black hole solutions on Minkowski space happen to convert horizons into a certain type of singularities. Here we explore whether these singularities can be avoided if space-time is not asymptotically Minkowskian. We find an exact analytic black hole (BH) solution which evades the above problem by a transition at large scales to self-induced de Sitter (dS) space-time, with the curvature scale set by the graviton mass. This solution is similar to the ones discovered by Koyama, Niz and Tasinato, and by Nieuwenhuizen, but differs in detail. The solution demonstrates that in massive GR, in the Schwarzschild coordinate system, a BH metric has to be accompanied by the St\"uckelberg fields with nontrivial backgrounds to prevent the horizons to convert into the singularities. We also find an analogous solution for a Reissner-Nordstr\"om BH on dS space. A limitation of our approach, is that we find the solutions only for specific values of the two free parameters of the theory, for which both the vector and scalar fluctuations loose their kinetic terms, however, we hope our solutions represent a broader class with better behaved perturbations.Comment: 17 LateX page

String Propagation through a Big Crunch/Big Bang Transition

We consider the propagation of classical and quantum strings on cosmological space-times which interpolate from a collapsing phase to an expanding phase. We begin by considering the classical propagation of strings on space-times with isotropic and anisotropic cosmological singularities. We find that cosmological singularities fall into two classes, in the first class the string evolution is well behaved all the way up to the singularity, whilst in the second class it becomes ill-defined. Then assuming the singularities are regulated by string scale corrections, we consider the implications of the propagation through a `bounce'. It is known that as we evolve through a bounce, quantum strings will become excited giving rise to `particle transmutation'. We reconsider this effect, giving qualitative arguments for the amount of excitation for each class. We find that strings whose physical wavelength at the bounce is less that $\sqrt{\alpha'}$ inevitably emerge in highly excited states, and that in this regime there is an interesting correspondence between strings on anisotropic cosmological space-times and plane waves. We argue that long wavelength modes, such as those describing cosmological perturbations, will also emerge in mildly excited string scale mass states. Finally we discuss the relevance of this to the propagation of cosmological perturbations in models such as the ekpyrotic/cyclic universe.Comment: 15 page

All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property

We prove a generalisation of the $\epsilon$-property, namely that for any dimension and signature, a metric which is not characterised by its polynomial scalar curvature invariants, there is a frame such that the components of the curvature tensors can be arbitrary close to a certain "background". This "background" is defined by its curvature tensors: it is characterised by its curvature tensors and has the same polynomial curvature invariants as the original metric.Comment: 6 page

Mind the gaps: investigating the cause of the current range disjunction in the Cape Platanna, Xenopus gilli (Anura: Pipidae)

Low-lying areas of the Cape at Africa’s south-westernmost tip have undergone dramatic marine-remodelling, with regular changes in sea-level following glacial cycles. Species for which marine barriers are impenetrable underwent concomitant radical distribution changes which may account for current range disjunctions. The Cape platanna, Xenopus gilli, is a frog distributed in only three disjunt areas within low-lying regions of the southwestern Cape. We determined the relationship between frogs from these three disjunct areas, by using a combination of morphometric analysis and mtDNA (ND2 and 16S fragments) sequences of 130 frogs from eight ponds. Coalescent analyses on molecular data dated the divergence in two major clades to around 4.6 Mya, a period during which major uplifting on the eastern side of the subcontinent caused climate changes throughout southern Africa. Principal components analysis showed significant morphometric differences between each clade on head and limb measurements. Consistent differences in ventral colouration and patterning were also observed. We report on increased levels of hybridisation with X. laevis throughout the range of X. gilli, which reaches at least 27% hybrids in some ponds. Urgent conservation actions are required to control habitat loss from alien invasive vegetation, and prevent introgression with the domestic-exotic, X. laevis

The cosmic gravitational wave background in a cyclic universe

Inflation predicts a primordial gravitational wave spectrum that is slightly ``red,'' i.e., nearly scale-invariant with slowly increasing power at longer wavelengths. In this paper, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The spectrum is blue and exponentially suppressed compared to inflation on long wavelengths. The strongest observational constraint emerges from the requirement that the energy density in gravitational waves should not exceed around 10 per cent of the energy density at the time of nucleosynthesis.Comment: 4 pages, 3 figuer