Galileons as Wess-Zumino Terms

We show that the galileons can be thought of as Wess-Zumino terms for the spontaneous breaking of space-time symmetries. Wess-Zumino terms are terms which are not captured by the coset construction for phenomenological Lagrangians with broken symmetries. Rather they are, in d space-time dimensions, d-form potentials for (d+1)-forms which are non-trivial co-cycles in Lie algebra cohomology of the full symmetry group relative to the unbroken symmetry group. We introduce the galileon algebras and construct the non-trivial (d+1)-form co-cycles, showing that the presence of galileons and multi-galileons in all dimensions is counted by the dimensions of particular Lie algebra cohomology groups. We also discuss the DBI and conformal galileons from this point of view, showing that they are not Wess-Zumino terms, with one exception in each case.Comment: 49 pages. v2 minor changes, version appearing in JHE

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

A clinical pathway for total shoulder arthroplasty-a pilot study

BACKGROUND: Appropriate pain management after total shoulder arthroplasty (TSA) facilitates rehabilitation and may improve clinical outcomes.; QUESTIONS/PURPOSES: This prospective, observational study evaluated a multimodal analgesia clinical pathway for TSA.; METHODS: Ten TSA patients received an interscalene nerve block (25cm(3) 0.375% ropivacaine) with intraoperative general anesthesia. Postoperative analgesia included regularly scheduled non-opioid analgesics (meloxicam, acetaminophen, and pregabalin) and opioids on demand (oral oxycodone and intravenous patient-controlled hydromorphone). Patients were evaluated twice daily to assess pain, anterior deltoid strength, handgrip strength, and sensory function.; RESULTS: The nerve block lasted an average of 18h. Patients had minimal pain after surgery; 0 (median score on a 0-10 scale) in the Post-Anesthesia Care Unit (PACU) but increased on postoperative day (POD) 1 to 2.3 (0.0, 3.8; median (25%, 75%)) at rest and 3.8 (2.1, 6.1) with movement. Half of the patients activated the patient-controlled analgesia four or fewer times in the first 24h after surgery. Operative anterior deltoid strength was 0 in the PACU but returned to 68% by POD 1. Operative hand strength was 0 (median) in the PACU, but the third quartile (75%) had normalized strength 49% of preoperative value.; CONCLUSIONS: Patients did well with this multimodal analgesic protocol. Pain scores were low, half of the patients used little or no intravenous opiate, and some patients had good handgrip strength. Future research can focus on increasing duration of analgesia from the nerve block, minimizing motor block, lowering pain scores, and avoiding intravenous opioids

Non-linear Representations of the Conformal Group and Mapping of Galileons

There are two common non-linear realizations of the 4D conformal group: in the first, the dilaton is the conformal factor of the effective metric \eta_{\mu\nu} e^{-2 \pi}; in the second it describes the fluctuations of a brane in AdS_5. The two are related by a complicated field redefinition, found by Bellucci, Ivanov and Krivonos (2002) to all orders in derivatives. We show that this field redefinition can be understood geometrically as a change of coordinates in AdS_5. In one gauge the brane is rigid at a fixed radial coordinate with a conformal factor on the AdS_5 boundary, while in the other one the brane bends in an unperturbed AdS_5. This geometrical picture illuminates some aspects of the mapping between the two representations. We show that the conformal Galileons in the two representations are mapped into each other in a quite non-trivial way: the DBI action, for example, is mapped into a complete linear combination of all the five Galileons in the other representation. We also verify the equivalence of the dilaton S-matrix in the two representations and point out that the aperture of the dilaton light-cone around non-trivial backgrounds is not the same in the two representations.Comment: 16 pages. v2: typos corrected (notably eq 4.5), matches JHEP versio

Large Scale Structures in Kinetic Gravity Braiding Model That Can Be Unbraided

We study cosmological consequences of a kinetic gravity braiding model, which is proposed as an alternative to the dark energy model. The kinetic braiding model we study is characterized by a parameter n, which corresponds to the original galileon cosmological model for n=1. We find that the background expansion of the universe of the kinetic braiding model is the same as the Dvali-Turner's model, which reduces to that of the standard cold dark matter model with a cosmological constant (LCDM model) for n equal to infinity. We also find that the evolution of the linear cosmological perturbation in the kinetic braiding model reduces to that of the LCDM model for n=\infty. Then, we focus our study on the growth history of the linear density perturbation as well as the spherical collapse in the nonlinear regime of the density perturbations, which might be important in order to distinguish between the kinetic braiding model and the LCDM model when n is finite. The theoretical prediction for the large scale structure is confronted with the multipole power spectrum of the luminous red galaxy sample of the Sloan Digital Sky survey. We also discuss future prospects of constraining the kinetic braiding model using a future redshift survey like the WFMOS/SuMIRe PFS survey as well as the cluster redshift distribution in the South Pole Telescope survey.Comment: 41 pages, 20 figures; This version was accepted for publication in JCA

Inequivalence of coset constructions for spacetime symmetries

Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. We analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds. The aperture of the lightcone is in general different in the two representations and in particular a free (luminal) massless scalar is mapped in a Galileon theory which admits superluminal propagation. We show that in this theory, if we consider backgrounds that vanish at infinity, there is no asymptotic effect: the displacement of the trajectory integrates to zero, as can be expected since the S-matrix is trivial. Regarding local measurements, we show that the puzzle is solved taking into account that a local coupling with fixed sources in one theory is mapped into a non-local coupling and we show that this effect compensates the different lightcone. Therefore the two theories have a different notion of locality. The same applies to the different non-linear realizations of the conformal group and we study the particular case of a cosmologically interesting background: the Galilean Genesis scenarios

de Sitter Galileon

We generalize the Galileon symmetry and its relativistic extension to a de Sitter background. This is made possible by studying a probe-brane in a flat five-dimensional bulk using a de Sitter slicing. The generalized Lovelock invariants induced on the probe brane enjoy the induced Poincar\'e symmetry inherited from the bulk, while living on a de Sitter geometry. The non-relativistic limit of these invariants naturally maintain a generalized Galileon symmetry around de Sitter while being free of ghost-like pathologies. We comment briefly on the cosmology of these models and the extension to the AdS symmetry as well as generic FRW backgrounds

Conditions for the cosmological viability of the most general scalar-tensor theories and their applications to extended Galileon dark energy models

In the Horndeski's most general scalar-tensor theories with second-order field equations, we derive the conditions for the avoidance of ghosts and Laplacian instabilities associated with scalar, tensor, and vector perturbations in the presence of two perfect fluids on the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Our general results are useful for the construction of theoretically consistent models of dark energy. We apply our formulas to extended Galileon models in which a tracker solution with an equation of state smaller than -1 is present. We clarify the allowed parameter space in which the ghosts and Laplacian instabilities are absent and we numerically confirm that such models are indeed cosmologically viable.Comment: 18 pages, 6 figure

Cosmological constraints on extended Galileon models

The extended Galileon models possess tracker solutions with de Sitter attractors along which the dark energy equation of state is constant during the matter-dominated epoch, i.e. w_DE = -1-s, where s is a positive constant. Even with this phantom equation of state there are viable parameter spaces in which the ghosts and Laplacian instabilities are absent. Using the observational data of the supernovae type Ia, the cosmic microwave background (CMB), and baryon acoustic oscillations, we place constraints on the tracker solutions at the background level and find that the parameter s is constrained to be s=0.034 (-0.034,+0.327) (95% CL) in the flat Universe. In order to break the degeneracy between the models we also study the evolution of cosmological density perturbations relevant to the large-scale structure (LSS) and the Integrated-Sachs-Wolfe (ISW) effect in CMB. We show that, depending on the model parameters, the LSS and the ISW effect is either positively or negatively correlated. It is then possible to constrain viable parameter spaces further from the observational data of the ISW-LSS cross-correlation as well as from the matter power spectrum.Comment: 17 pages, 9 figures, uses RevTeX4-