Three-manifold invariants and their relation with the fundamental group

We consider the 3-manifold invariant I(M) which is defined by means of the Chern-Simons quantum field theory and which coincides with the Reshetikhin-Turaev invariant. We present some arguments and numerical results supporting the conjecture that, for nonvanishing I(M), the absolute value | I(M) | only depends on the fundamental group \pi_1 (M) of the manifold M. For lens spaces, the conjecture is proved when the gauge group is SU(2). In the case in which the gauge group is SU(3), we present numerical computations confirming the conjecture.Comment: 22 pages, Latex document, two eps figure

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

Disformal invariance of continuous media with linear equation of state

We show that the effective theory describing single component continuous media with a linear and constant equation of state of the form $p=w\rho$ is invariant under a 1-parameter family of continuous disformal transformations. In the special case of $w=1/3$ (ultrarelativistic gas), such a family reduces to conformal transformations. As examples, perfect fluids, homogeneous and isotropic solids are discussed.Comment: latex, 7 page

The Fate of the Radion in Models with Metastable Graviton

We clarify some general issues in models where gravity is localized at intermediate distances. We introduce the radion mode, which is usually neglected, and we point out that its role in the model is crucial. We show that the brane bending effects discussed in the literature can be obtained in a formalism where the physical origin is manifest. The model violates positivity of energy due to a negative tension brane, which induces a negative kinetic term for the radion. The very same effect that violates positivity is responsible for the recovery of conventional Einstein gravity at intermediate distances.Comment: Latex file, 13 page

Graviton loops and brane observables

We discuss how to consistently perform effective Lagrangian computations in quantum gravity with branes in compact extra dimensions. A reparametrization invariant and infrared finite result is obtained in a non trivial way. It is crucial to properly account for brane fluctuations and to correctly identify physical observables. Our results correct some confusing claims in the literature. We discuss the implications of graviton loops on electroweak precision observables and on the muon g-2 in models with large extra dimensions. We model the leading effects, not controlled by effective field theory, by introducing a hard momentum cut-off.Comment: 9 pages + 4 eps figures, JHEP style latex document. The paper is composed by a theoretical part, followed (after page 21) by a phenomenological part. v2: version published in JHEP, few typos corrected. v3: few additional typos corrected in the Appendi

Living with ghosts in Horava-Lifshitz gravity

We consider the branch of the projectable Horava-Lifshitz model which exhibits ghost instabilities in the low energy limit. It turns out that, due to the Lorentz violating structure of the model and to the presence of a finite strong coupling scale, the vacuum decay rate into photons is tiny in a wide range of phenomenologically acceptable parameters. The strong coupling scale, understood as a cutoff on ghosts' spatial momenta, can be raised up to $\Lambda \sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared ($10^{-42}\lesssim$) $c^2_s \lesssim 10^{-20}$, that could be a promising candidate for the Dark Matter. Despite these advantages, the unavoidable presence of the strong coupling obscures the implementation of the original Horava's proposal on quantum gravity. Apart from the Horava-Lifshitz model, conclusions of the present work hold also for the mimetic matter scenario, where the analogue of the projectability condition is achieved by a non-invertible conformal transformation of the metric.Comment: 33 pages, 1 figure. The proof of an equivalence between the IR limit of the projectable Horava-Lifshitz gravity and the mimetic matter scenario is given in Appendix A. Version accepted for publication in JHE