A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom à la Galileon models, which allows for the Vainshtein screening mechanism. We investigate this effect on subhorizon scales in a cosmological background, based on the most general second-order scalar-tensor theory. Our analysis takes into account all the relevant nonlinear terms and the effect of metric perturbations consistently. We derive an explicit form of Newton's constant, which in general is time-dependent and hence is constrained from observations, as suggested earlier. It is argued that in the most general case the inverse-square law cannot be reproduced on the smallest scales. Some applications of our results are also presented. 1 In the course of the preparation of this manuscript, we became aware of the very recent paper by De Felice, Kase, and Tsujikawa [11], in which the metric under the influence of the Vainshtein mechanism is obtained for a static and spherically symmetric configuration in a subclass of the most general theory.

Abstract. Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-tensor theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless tensor modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.arXiv:1608.07066v4 [gr-qc]

Abstract. 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 (ΛCDM 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 ΛCDM model for n = ∞. 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 ΛCDM 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.

The cross-correlation between the integrated Sachs-Wolfe (ISW) effect and the large scale structure (LSS) is a powerful tool to constrain dark energy and alternative theories of gravity. In this paper, we obtain observational constraints on kinetic gravity braiding from the ISW-LSS cross-correlation. We find that the late-time ISW effect in the kinetic gravity braiding model anti-correlates with large scale structures in a wide range of parameters, which clearly demonstrates how one can distinguish modified gravity theories from the ΛCDM model using the ISW effect. In addition to the analysis based on a concrete model, we investigate a future prospect of the ISW-LSS cross-correlation by using a phenomenological parametrization of modified gravity models.PACS numbers: 98.80.-k, 04.50. Kd, 95.36.+x

Abstract. In this paper, we scrutinize very closely the cosmology in the proxy theory to massive gravity obtained in Phys. Rev. D84 (2011) 043503. This proxy theory was constructed by covariantizing the decoupling limit Lagrangian of massive gravity and represents a subclass of Horndeski scalar-tensor theory. Thus, this covariantization unifies two important classes of modified gravity theories, namely massive gravity and Horndeski theories. We go beyond the regime which was studied in Phys. Rev. D84 (2011) 043503 and show that the theory does not admit any homogeneous and isotropic self-accelerated solutions. We illustrate that the only attractor solution is flat Minkowski solution, hence this theory is less appealing as a dark energy model. We also show that the absence of de Sitter solutions is tightly related to the presence of shift symmetry breaking interactions.