We propose new massive gravity theories with 5 dynamical degrees of freedom.
We evade uniqueness theorems regarding the form of the kinetic and potential
terms by adopting the "generalized massive gravity" framework, where a global
translation invariance is broken. By exploiting the rotation symmetry in the
field space, we determine two novel classes of theories. The first one is an
extension of generalized massive gravity with a non-minimal coupling. On the
other hand, the second theory produces a mass term that is different from de
Rham, Gabadadze, Tolley construction and trivially has 5 degrees of freedom.
Both theories allows for stable cosmological solutions without infinite strong
coupling, which are free of ghost and gradient instabilities.

In this paper, we fully investigate cosmological scenarios in which dark<br />
matter is non-minimally coupled to an extra scalar degree of freedom. The<br />
interaction is realized by means of conformal and disformal terms in the<br />
transformed gravitational metric. Considering linear perturbation theory, we<br />
show that the growth rate of dark matter differs from the uncoupled case and<br />
that the well-known Kaiser formula undergoes modification. As a result,<br />
redshift space distortion measurements cease to be a direct probe of the linear<br />
growth rate of total matter, since the distortion factor has an extra,<br />
coupling-dependent term. We study the effect of the coupling in three<br />
cosmological models, two conformally and one disformally coupled, and forecast<br />
the constraints on the coupling, and other cosmological parameters, from future<br />
galaxy surveys.

We construct Lorentz-invariant massless/massive spin-2 theories in flat<br />
spacetime. Starting from the most generic action of a rank-2 symmetric tensor<br />
field whose Lagrangian contains up to quadratic in first derivatives of a<br />
field, we investigate the possibility of new theories by using the Hamiltonian<br />
analysis. By imposing the degeneracy of the kinetic matrix and the existence of<br />
subsequent constraints, we classify theories based on the number of degrees of<br />
freedom and constraint structures and obtain a wider class of Fierz-Pauli<br />
theory as well as massless and partially massless theories, whose scalar and/or<br />
vector degrees of freedom are absent. We also discuss the relation between our<br />
theories and known massless and massive spin-2 theories.

We present an impact of coupling between dark matter and a scalar field,<br />
which might be responsible for dark energy, on measurements of redshift-space<br />
distortions. We point out that, in the presence of conformal and/or disformal<br />
coupling, linearized continuity and Euler equations for total matter fluid<br />
significantly deviate from the standard ones even in the sub-horizon scales. In<br />
such a case, a peculiar velocity of total matter field is determined not only<br />
by a logarithmic time derivative of its density perturbation but also by<br />
density perturbations for both dark matter and baryon, leading to a large<br />
modification of the physical interpretation of observed data obtained by<br />
measurements of redshift-space distortions. We reformulate galaxy two-point<br />
correlation function in the redshift space based on the modified continuity and<br />
Euler equations. We conclude from the resultant formula that the true value of<br />
the linear growth rate of large-scale structure cannot be necessarily<br />
constrained by single-redshift measurements of the redshift-space distortions,<br />
unless one observes the actual time-evolution of structure.

We study cosmological applications of extended vector-tensor theories, whose<br />
Lagrangians contain up to two derivatives with respect to metric and vector<br />
field. We derive background equations under the assumption of homogeneous and<br />
isotropic universe and study the nature of cosmological perturbations on top of<br />
the background. We found an example of healthy cosmological solutions in<br />
non-trivial degenerate theory of gravity for the first time, where those<br />
perturbations do not suffer from any instabilities, that is, ghost and gradient<br />
instabilities.

We discuss a covariant extension of interactions between scalar fields and<br />
fermions in a flat space-time. We show, in a covariant theory, how to evade<br />
fermionic ghosts appearing because of the extra degrees of freedom behind a<br />
fermionic nature even in the Lagrangian with first derivatives. We will give a<br />
concrete example of a quadratic theory with up to the first derivative of<br />
multiple scalar fields and a Weyl fermion. We examine not only the maximally<br />
degenerate condition, which makes the number of degrees of freedom correct, but<br />
also a supplementary condition guaranteeing that the time evolution takes place<br />
properly. We also show that proposed derivative interaction terms between<br />
scalar fields and a Weyl fermion cannot be removed by field redefinitions.

We study the coexistence system of both bosonic and fermionic degrees of freedom. Even if a Lagrangian does not include higher derivatives, fermionic ghosts exist. For a Lagrangian with up to first derivatives, we find the fermionic ghost free condition in Hamiltonian analysis, which is found to be the same as requiring that the equations of motion of fermions be first order in Lagrangian formulation. When fermionic degrees of freedom are present, the uniqueness of time evolution is not guaranteed a priori because of the Grassmann property. We confirm that the additional condition, which is introduced to close Hamiltonian analysis, also ensures the uniqueness of the time evolution of the system.

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.

We investigate gravitational Cherenkov radiation in a healthy branch of background solutions in the ghost-free bigravity model. In this model, because of the modification of dispersion relations, each polarization mode can possess subluminal phase velocities, and the gravitational Cherenkov radiation could be potentially emitted from a relativistic particle. In the present paper, we derive conditions for the process of the gravitational Cherenkov radiation to occur and estimate the energy emission rate for each polarization mode. We found that the gravitational Cherenkov radiation emitted even from an ultrahigh energy cosmic ray is sufficiently suppressed for the graviton's effective mass less than 100 eV, and the bigravity model with dark matter coupled to the hidden metric is therefore consistent with observations of high energy cosmic rays.

The Vainshtein mechanism suppresses the fifth force at astrophysical distances, while enabling it to compete with gravity at cosmological scales. Typically, Vainshtein solutions exhibit superluminal perturbations. However, a restricted class of solutions with special boundary conditions was shown to be devoid of the faster-than-light modes. Here we extend this class by finding solutions in a theory of quasidilaton, amended by derivative terms consistent with its symmetries. Solutions with Minkowski asymptotics are not stable, while the ones that exhibit the Vainshtein mechanism by transitioning to cosmological backgrounds are free of ghosts, tachyons, gradient instability, and superluminality, for all propagating modes present in the theory. These solutions require a special choice of the strength and signs of nonlinear terms, as well as a choice of asymptotic cosmological boundary conditions.

It has been shown that the spherically symmetric solutions in a subclass of<br />
quasidilaton theory are stable against all degrees of freedom and does not even<br />
exhibit superluminal propagation. These solutions can be found by switching off<br />
scalar-tensor interactions, which can not be removed by a local transformation.<br />
In this paper, we extend the analysis to quasidilaton theory, including<br />
non-diagonalizable scalar-tensor interactions. We show that all solutions<br />
inside the Vainshtein radius are problematic : the scalar mode in massive<br />
graviton suffers from gradient instabilities, the vector mode are infinitely<br />
strongly coupled vector perturbations, or the Vainshtein mechanism is absent.

Quasidilaton massive gravity is an extension of massive general relativity to a theory with additional scale invariance and approximate internal Galilean symmetry. The theory has a novel self-accelerated solution with the metric indistinguishable (in the decoupling limit) from the de Sitter space, its curvature set by the graviton mass. The spectra of tensor, vector, and scalar perturbations on this solution contain neither ghosts nor gradient instabilities or superluminal modes, for a range of the parameter space. This represents an example of a self-accelerated solution with viable perturbations, attainable within a low-energy effective field theory.

In this paper, we scrutinize very closely the cosmology in the proxy theory to massive gravity obtained in de Rham and Heisenberg [Phys. Rev. D 84, 043503 (2011)]. This proxy theory was constructed by covariantizing the decoupling limit Lagrangian of massive gravity, and it 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 de Rham and Heisenberg [Phys. Rev. D 84, 043503 (2011)] and show that the theory does not admit any homogeneous and isotropic self-accelerated solutions. We illustrate that the only attractor solution is the 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. © 2014 American Physical Society.

In this paper, we scrutinize very closely the cosmology in the proxy theory to massive gravity obtained in de Rham and Heisenberg [Phys. Rev. D 84, 043503 (2011)]. This proxy theory was constructed by covariantizing the decoupling limit Lagrangian of massive gravity, and it 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 de Rham and Heisenberg [Phys. Rev. D 84, 043503 (2011)] and show that the theory does not admit any homogeneous and isotropic self-accelerated solutions. We illustrate that the only attractor solution is the 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.

We investigate the possibility of a new massive gravity theory with derivative interactions as an extension of de Rham-Gabadadze-Tolley massive gravity. We find the most general Lagrangian of derivative interactions using a Riemann tensor whose cutoff energy scale is Lambda(3), which is consistent with de Rham-Gabadadze-Tolley massive gravity. Surprisingly, this infinite number of derivative interactions can be resummed with the same method in de Rham-Gabadadze-Tolley massive gravity, and remaining interactions contain only two parameters. We show that the equations of motion for scalar and tensor modes in the decoupling limit contain fourth derivatives with respect to spacetime, which implies the appearance of ghosts at Lambda(3). We claim that consistent derivative interactions in de Rham-Gabadadze-Tolley massive gravity have a mass scale M, which is much smaller than the Planck mass M-Pl.

We demonstrate that the general second-order scalar-tensor theories, which have attracted attention as possible modified gravity models to explain the late time cosmic acceleration, could be strongly constrained from the argument of the gravitational Cherenkov radiation. To this end, we consider the purely kinetic coupled gravity and the extended galileon model on a cosmological background. In these models, the propagation speed of tensor mode could be less than the speed of light, which puts very strong constraints from the gravitational Cherenkov radiation.

The cross correlation between the integrated Sachs-Wolfe (ISW) effect and the large-scale structure 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-large-scale-structure cross correlation. We find that the late-time ISW effect in the kinetic gravity braiding model anticorrelates with large-scale structures in a wide range of parameters, which clearly demonstrates how one can distinguish modified gravity theories from the lambda cold dark matter model using the ISW effect.

A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom phi a 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.

We investigate the structure of halos in the sDGP (self-accelerating branch of the Dvali-Gavadadze-Porrati braneworld gravity) model and the Galileon modified gravity model on the basis of the static and spherically symmetric solutions of the collisionless Boltzmann equation, which reduce to the singular isothermal sphere model and the King model in the limit of Newtonian gravity. The common feature of these halos is that the density of a halo in the outer region is larger (smaller) in the sDGP (Galileon) model, respectively, in comparison with Newtonian gravity. This comes from the suppression (enhancement) of the effective gravity at large distance in the sDGP (Galileon) model, respectively. However, the difference between these modified gravity models and Newtonian gravity only appears outside the halo due to the Vainshtein mechanism, which makes it difficult to distinguish between them. We also discuss the case in which the halo density profile is fixed independently of the gravity model for comparison between our results and previous work.

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 (Lambda CDM 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 Lambda CDM model for n = 1. 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 Lambda CDM 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.

We investigate the quantum effect on the Larmor radiation from a moving charge in an expanding universe based on the framework of the scalar quantum electrodynamics. A theoretical formula for the radiation energy is derived at the lowest order of the perturbation theory with respect to the coupling constant of the scalar quantum electrodynamics. We evaluate the radiation energy on the background universe so that the Minkowski spacetime transits to the Milne universe, in which the equation of motion for the mode function of the free complex scalar field can be exactly solved in an analytic way. Then, the result is compared with the WKB approach, in which the equation of motion of the mode function is constructed with the WKB approximation which is valid as long as the Compton wavelength is shorter than the Hubble horizon length. This demonstrates that the quantum effect on the Larmor radiation of the order e(2)(h) over bar is determined by a nonlocal integration in time depending on the background expansion. We also compare our result with a recent work by Higuchi and Walker [Phys. Rev. D 80, 105019 (2009)], which investigated the quantum correction to the Larmor radiation from a charged particle in a nonrelativistic motion in a homogeneous electric field.