Covariant constraints for generic massive gravity and analysis of its characteristics

We perform a covariant constraint analysis of massive gravity valid for its entire parameter space, demonstrating that the model generically propagates five degrees of freedom; this is also verified by a new and streamlined Hamiltonian description. The constraint's covariant expression permits computation of the model's caustics. Although new features such as the dynamical Riemann tensor appear in the characteristic matrix, the model still exhibits the pathologies uncovered in earlier work: superluminality and likely acausalities.Comment: 26 pages LaTeX, references added, version to appear in Phys. Rev.

From k-essence to generalised Galileons

We determine the most general scalar field theories which have an action that depends on derivatives of order two or less, and have equations of motion that stay second order and lower on flat space-time. We show that those theories can all be obtained from linear combinations of Lagrangians made by multiplying a particular form of the Galileon Lagrangian by an arbitrary scalar function of the scalar field and its first derivatives. We also obtain curved space-time extensions of those theories which have second order field equations for both the metric and the scalar field. This provide the most general extension, under the condition that field equations stay second order, of k-essence, Galileons, k-Mouflage as well as of the kinetically braided scalars. It also gives the most general action for a scalar classicalizer, which has second order field equations. We discuss the relation between our construction and the Euler hierachies of Fairlie et al, showing in particular that Euler hierachies allow one to obtain the most general theory when the latter is shift symmetric. As a simple application of our formalism, we give the covariantized version of the conformal Galileon.Comment: 25 page

Non-linear duality invariant partially massless models?

We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Our models mimic Dirac–Born–Infeld theory but it is unclear whether they are Lagrangian

A note on "symmetric" vielbeins in bimetric, massive, perturbative and non perturbative gravities

We consider a manifold endowed with two different vielbeins $E^{A}{}_{\mu}$ and $L^{A}{}_{\mu}$ corresponding to two different metrics $g_{\mu\nu}$ and $f_{\mu\nu}$. Such a situation arises generically in bimetric or massive gravity (including the recently discussed version of de Rham, Gabadadze and Tolley), as well as in perturbative quantum gravity where one vielbein parametrizes the background space-time and the other the dynamical degrees of freedom. We determine the conditions under which the relation $g^{\mu\nu} E^{A}{}_{\mu} L^{B}{}_{\nu} = g^{\mu\nu} E^{B}{}_{\mu} L^{A}{}_{\nu}$ can be imposed (or the "Deser-van Nieuwenhuizen" gauge chosen). We clarify and correct various statements which have been made about this issue.Comment: 20 pages. Section 7, prop. 6 and 7. added. Some results made more precis

Generalizing Galileons

The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a 3+1-dimensional flat brane embedded in a 5-dimensional Minkowski Bulk. These theories have some intriguing properties, including freedom from ghosts and a non-renormalization theorem that hints at possible applications in both particle physics and cosmology. In this brief review article, we will summarize our attempts over the last year to extend the Galileon idea in two important ways. We will discuss the effective field theory construction arising from co-dimension greater than one flat branes embedded in a flat background - the multiGalileons - and we will then describe symmetric covariant versions of the Galileons, more suitable for general cosmological applications. While all these Galileons can be thought of as interesting four-dimensional field theories in their own rights, the work described here may also make it easier to embed them into string theory, with its multiple extra dimensions and more general gravitational backgrounds.Comment: 16 pages; invited brief review article for a special issue of Classical and Quantum Gravity. Submitted to CQ

Propagation peculiarities of mean field massive gravity

Massive gravity (mGR) describes a dynamical “metric” on a fiducial, background one. We investigate fluctuations of the dynamics about mGR solutions, that is about its “mean field theory”. Analyzing mean field massive gravity (m‾GR) propagation characteristics is not only equivalent to studying those of the full non-linear theory, but also in direct correspondence with earlier analyses of charged higher spin systems, the oldest example being the charged, massive spin 3/2 Rarita–Schwinger (RS) theory. The fiducial and mGR mean field background metrics in the m‾GR model correspond to the RS Minkowski metric and external EM field. The common implications in both systems are that hyperbolicity holds only in a weak background-mean-field limit, immediately ruling both theories out as fundamental theories; a situation in stark contrast with general relativity (GR) which is at least a consistent classical theory. Moreover, even though both m‾GR and RS theories can still in principle be considered as predictive effective models in the weak regime, their lower helicities then exhibit superluminal behavior: lower helicity gravitons are superluminal as compared to photons propagating on either the fiducial or background metric. Thus our approach has uncovered a novel, dispersive, “crystal-like” phenomenon of differing helicities having differing propagation speeds. This applies both to m‾GR and mGR, and is a peculiar feature that is also problematic for consistent coupling to matter

Covariant constraints in ghost free massive gravity

25 pages. Published versionWe show that the reformulation of the de Rham-Gabadadze-Tolley massive gravity theory using vielbeins leads to a very simple and covariant way to count constraints, and hence degrees of freedom. Our method singles out a subset of theories, in the de Rham-Gabadadze-Tolley family, where an extra constraint, needed to eliminate the Boulware Deser ghost, is easily seen to appear. As a side result, we also introduce a new method, different from the Stuckelberg trick, to extract kinetic terms for the polarizations propagating in addition to those of the massless graviton

Self-calibration: an efficient method to control systematic effects in bolometric interferometry

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