Generalising the matter coupling in massive gravity: a search for new interactions

Massive gravity theory introduced by de Rham, Gabadadze, Tolley (dRGT) is restricted by several uniqueness theorems that protect the form of the potential and kinetic terms, as well as the matter coupling. These restrictions arise from the requirement that the degrees of freedom match the expectation from Poincar\'e representations of a spin--2 field. Any modification beyond the dRGT form is known to invalidate a constraint that the theory enjoys and revive a dangerous sixth mode. One loophole is to exploit the effective nature of the theory by pushing the sixth mode beyond the strong coupling scale without completely removing it. In this paper, we search for modifications to dRGT action by coupling the matter sector to an arbitrary metric constructed out of the already existing degrees of freedom in the dRGT action. We formulate the conditions that such an extension should satisfy in order to prevent the sixth mode from contaminating the effective theory. Our approach provides a new perspective for the "composite coupling" which emerges as the unique extension up to four-point interactions.Comment: 19 pages; v2: new references added, accepted for publication in PR

Horava-Lifshitz gravity with λ→∞\lambda\to\infty

In the framework of the power-counting renormalizable theory of gravitation, recently proposed by Ho\v{r}ava, we study the limit $\lambda\to\infty$, which is arguably the most natural candidate for the ultraviolet fixed point of the renormalization group flow. In the projectable version with dynamical critical exponent $z=3$, we analyze the Friedmann-Robertson-Walker background driven by the so-called "dark matter as integration constant" and perturbations around it. We show that amplitudes of quantum fluctuations for both scalar and tensor gravitons remain finite in the limit and that the theory is weakly coupled under a certain condition

Stable cosmology in ghost-free quasidilaton theory

We present a novel cosmological solution in the framework of extended quasidilaton theory which underwent scrutiny recently. We only consider terms that do not generate the Boulware-Deser degree of freedom, hence the "ghost-free" quasidilaton theory, and show three new branches of cosmological evolution therein. One of the solutions passes the perturbative stability tests. This new solution exhibits a late time self-acceleration and all graviton polarizations acquire masses that converge to a constant in the asymptotic future. Moreover, all modes propagate at the speed of light. We propose that this solution can be used as a benchmark model for future phenomenological studies.Comment: 12 page

On the viability of bigravity cosmology

We revisit the question of viability of bigravity cosmology as a candidate for dark energy. In the context of the low energy limit model, where matter couples to a single metric, we study linear perturbations around homogeneous and isotropic backgrounds to derive the Poisson's equation for the Newtonian potential. Extending to second order perturbations, we identify the Vainshtein radius below which non-linear scalar self interactions conspire to reproduce GR on local scales. We combine all of these results to determine the parameter space that allows a late time de-Sitter attractor compatible with observations and a successful Vainsthein mechanism. We find that the requirement on having a successful Vainsthein mechanism is not compatible with the existence of cosmological solutions at early times.Comment: Accepted for publication in PR

Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation

We compute the phenomenological signatures of a model (Watanabe et al' 09) of anisotropic inflation driven by a scalar and a vector field. The action for the vector is U(1) invariant, and the model is free of ghost instabilities. A suitable coupling of the scalar to the kinetic term of the vector allows for a slow roll evolution of the vector vev, and hence for a prolonged anisotropic expansion; this provides a counter example to the cosmic no hair conjecture. We compute the nonvanishing two point correlation functions between physical modes of the system, and express them in terms of power spectra with angular dependence. The anisotropy parameter g_* for the scalar-scalar spectrum (defined as in the Ackerman et al '07 parametrization) turns out to be negative in the simplest realization of the model, which, therefore, cannot account for the angular dependence emerged in some analyses of the WMAP data. A g_* of order -0.1 is achieved when the energy of the vector is about 6-7 orders of magnitude smaller than that of the scalar during inflation. For such values of the parameters, the scalar-tensor correlation (which is in principle a distinctive signature of anisotropic spaces) is smaller than the tensor-tensor correlation

Role of matter in extended quasidilaton massive gravity

The extended quasidilaton theory is one of the simplest Lorentz-invariant massive gravity theories which can accommodate a stable self-accelerating vacuum solution. In this paper we revisit this theory and study the effect of matter fields. For a matter sector that couples minimally to the physical metric, we find hints of a Jeans type instability in the IR. In the analogue k-essence field set-up, this instability manifests itself as an IR ghost for the scalar field perturbation, but this can be interpreted as a classical instability that becomes relevant below some momentum scale in terms of matter density perturbations. We also consider the effect of the background evolution influenced by matter on the stability of the gravity sector perturbations. In particular, we address the previous claims of ghost instability in the IR around the late time attractor. We show that, although the matter-induced modification of the evolution potentially brings tension to the stability conditions, one goes beyond the regime of validity of the effective theory well before the solutions become unstable. We also draw attention to the fact that the IR stability conditions are also enforced by the existence requirements of consistent background solutions.Comment: 17 pages, accepted for publication in PR

CMB Anomalies from Relic Anisotropy

Most of the analysis of the Cosmic Microwave Background relies on the assumption of statistical isotropy. However, given some recent evidence pointing against isotropy, as for instance the observed alignment of different multipoles on large scales, it is worth testing this assumption against the increasing amount of available data. As a pivot model, we assume that the spectrum of the primordial perturbations depends also on their directionality (rather than just on the magnitude of their momentum, as in the standard case). We explicitly compute the correlation matrix for the temperature anisotropies in the simpler case in which there is a residual isotropy between two spatial directions. As a concrete example, we consider a different initial expansion rate along one direction, and the following isotropization which takes place during inflation. Depending on the amount of inflation, this can lead to broken statistical isotropy on the largest observable scales.Comment: 6 pages, 2 .ps figure

Massive gravity: nonlinear instability of the homogeneous and isotropic universe

We argue that all homogeneous and isotropic solutions in nonlinear massive gravity are unstable. For this purpose, we study the propagating modes on a Bianchi type--I manifold. We analyze their kinetic terms and dispersion relations as the background manifold approaches the homogeneous and isotropic limit. We show that in this limit, at least one ghost always exists and that its frequency tends to vanish for large scales, meaning that it cannot be integrated out from the low energy effective theory. This ghost mode is interpreted as a leading nonlinear perturbation around a homogeneous and isotropic background.Comment: 4 pages, uses REVTeX4.1; v2: minor update to match the published versio