Abstract:
We consider the possibility of the existence of a stable massive charged particle by a minimal extension of the standard model particle content. Absolute stability in the case of singly charged particle is not possible if the usual doublet Higgs exists, unless a discrete symmetry is imposed.But a doubly charged particle is absolutely stable.

Abstract:
The ratio between the proton and electron masses was shown to be close to the ratio between the shortest lifetimes of particles, decaying by the electromagnetic and strong interactions. The inherent property of each fundamental interaction is defined, namely the Minimal lifetime of the interaction (MLTI). The rest mass of the Lightest free massive stable particle (LFMSP), acted upon by a particular interaction, is shown to be inversely proportional to MLTI. The found mass relation unifies the masses of four stable particles of completely different kinds (proton, electron, electron neutrino and graviton) and covers an extremely wide range of values, exceeding 40 orders of magnitude. On the basis of this mass relation, the electron neutrino and graviton masses have been approximately estimated to 6.5x10^(-4) eV/c^2 and H*h_bar/c^2 = 1.5x10^(-33) eV/c^2, respectively. Besides, the last value has been obtained independently by dimensional analysis by means of the fundamental parameters speed of light (c), reduced Planck constant (h_bar) and Hubble distance (H). It was shown that the equivalent energy of LFMSP, acted upon by a particular interaction, is close to Breit-Wigner's energy width of the shortest living state, decaying by the respective interaction.

Abstract:
Stable massive neutral particles emitted by astrophysical sources undergo deflection under the gravitational potential of our own galaxy. The deflection angle depends on the particle velocity and therefore non-relativistic particles will be deflected more than relativistic ones. If these particles can be detected through neutrino telescopes, cosmic ray detectors or directional dark matter detectors, their arrival directions would appear aligned on the sky along the source-lens direction. On top of this deflection, the arrival direction of non-relativistic particles is displaced with respect to the relativistic counterpart also due to the relative motion of the source with respect to the observer; this induces an alignment of detections along the sky projection of the source trajectory. The final alignment will be given by a combination of the directions induced by lensing and source proper motion. We derive the deflection-velocity relation for the Milky Way halo and suggest that searching for alignments on detection maps of particle telescopes could be a way to find new particles or new astrophysical phenomena.

Abstract:
In this paper, we consider the spatial gauge symmetries spontaneously break down in GR, and graviton becomes massive on this spatial condensate background. Such model can be considered as a simplest example of massive gravity. We then apply our massive gravity theory to inflation, the graviton mass removes the IR divergence of the inflationary loop diagram.

Abstract:
No-hair theorems exclude the existence of nontrivial scalar and massive vector hair outside four-dimensional, static, asymptotically flat black-hole spacetimes. We show, by explicitly building nonlinear solutions, that black holes can support massive graviton hair in theories of massive gravity. These hairy solutions are, most likely, the generic end state of the recently discovered monopole instability of Schwarzschild black holes in massive graviton theories.

Abstract:
We construct a consistent model of gravity where the tensor graviton mode is massive, while linearized equations for scalar and vector metric perturbations are not modified. The Friedmann equation acquires an extra dark-energy component leading to accelerated expansion. The mass of the graviton can be as large as $\sim (10^{15}{cm})^{-1}$, being constrained by the pulsar timing measurements. We argue that non-relativistic gravitational waves can comprise the cold dark matter and may be detected by the future gravitational wave searches.

Abstract:
It was suggested that observations of the solar system exclude massive gravity, in the sense that the graviton mass must be rigorously zero. This is because there is a discontinuity in the linearized gravity theory at graviton mass equal to zero. The linearized Schwarzschild metric is not recovered for infinitesimal graviton mass, contradicting observations on light deviation by the Sun and Mercury perihelion advance. It was then argued that non-perturbative effects make the massive gravity theory continuous in the graviton mass. Both the original suggestion and its refutation were based on a non-covariant and linearized action, and the physical interpretation of these results remained questionable. Here we use a covariant quasi-massive gravity theory that is known to be discontinuous in the graviton mass in the linear approximation. We show that non-perturbative effects do restore the continuity; the weak-field Schwarzschild solution is recovered in the limit of small graviton mass. We also show that weak-field Schwarzschild with matter is recovered for infinitesimal graviton mass. Thus: Observations of the solar system only put an upper limit on the graviton mass (in the context of the gravity theory that we use, inverse graviton mass, as measured at distances of order inverse graviton mass, is $\gtrsim 100$ Mpc). But graviton can be massive, with a cosmologically interesting mass.

Abstract:
We investigate the massive graviton stability of the BTZ black hole obtained from three dimensional massive gravities which are classified into the parity-even and parity-odd gravity theories. In the parity-even gravity theory, we perform the $s$-mode stability analysis by using the BTZ black string perturbations, which gives two Schr\"odinger equations with frequency-dependent potentials. The $s$-mode stability is consistent with the generalized Breitenlohner-Freedman bound for spin-2 field. It seems that for the parity-odd massive gravity theory, the BTZ black hole is stable when the imaginary part of quasinormal frequencies of massive graviton is positive. However, this condition is not consistent with the $s$-mode stability based on the second-order equation obtained after squaring the first-order equation. Finally we explore the black hole stability connection between the parity-odd and parity-even massive gravity theories.

Abstract:
Nonlinear, ghost-free massive gravity has two tensor fields; when both are dynamical, the mass of the graviton can lead to cosmic acceleration that agrees with background data, even in the absence of a cosmological constant. Here the question of the stability of linear perturbations in this bimetric theory is examined. Instabilities are presented for several classes of models, and simple criteria for the cosmological stability of massive bigravity are derived. In this way, we identify a particular self-accelerating bigravity model, infinite-branch bigravity (IBB), which exhibits both viable background evolution and stable linear perturbations. We discuss the modified gravity parameters for IBB, which do not reduce to the standard $\Lambda$CDM result at early times, and compute the combined likelihood from measured growth data and type Ia supernovae. IBB predicts a present matter density $\Omega_{m0}=0.18$ and an equation of state $w(z)=-0.79+0.21z/(1+z)$. The growth rate of structure is well-approximated at late times by $f(z)\approx\Omega_{m}^{0.47}[1+0.21z/(1+z)]$. The implications of the linear instability for other bigravity models are discussed: the instability does not necessarily rule these models out, but rather presents interesting questions about how to extract observables from them when linear perturbation theory does not hold.

Abstract:
It is shown that the extremal Reissner-Nordstr\"{o}m black hole, the non-extremal one with multiple scattering particles, and the Schwarzschild black hole with radial head-on particles are stable under the collision of the particles near the horizon, if the back-reaction effect and the effect generated by gravity of particles are involved. Moreover, the collision near Reissner-Nordstr\"{o}m black holes with astrophysically typical mass can not generate the Planck-scale center-of-mass energy. However, the head-on collision near the typical primordial black hole could just occur at the Planck-energy scale.