Cosmology in General Massive Gravity Theories

We study the cosmology of general massive gravity theories with five propagating degrees of freedom. This large class of theories includes both the case with a residual Lorentz invariance as the cases with simpler rotational invariance. We find that the existence of a nontrivial homogeneous FRW background, in addition to selecting the lorentz-breaking case, implies in general that perturbations around strict Minkowski or dS space are strongly coupled. The result is that dark energy can be naturally accounted for in massive gravity but its equation of state w_eff has to deviate from -1. We find indeed a relation between the strong coupling scale of perturbations and the deviation of w_eff from -1. Taking into account current limits on w_eff and submillimiter tests of the Newton's law as a limit on the possible strong coupling regime, we find that it is still possible to have a weakly coupled theory in a quasi dS background. Future experimental improvements may be used to predict w_eff in a weakly coupled massive gravity theoryComment: 15 page

Weak Massive Gravity

We find a new class of theories of massive gravity with five propagating degrees of freedom where only rotations are preserved. Our results are based on a non-perturbative and background-independent Hamiltonian analysis. In these theories the weak field approximation is well behaved and the static gravitational potential is typically screened \`a la Yukawa at large distances, while at short distances no vDVZ discontinuity is found and there is no need to rely on nonlinear effects to pass the solar system tests. The effective field theory analysis shows that the ultraviolet cutoff is (m M_PL)^1/2 ~ 1/\mu m, the highest possible. Thus, these theories can be studied in weak-field regime at all the phenomenologically interesting scales, and are candidates for a calculable large-distance modified gravity.Comment: 5 page

Present and Future K and B Meson Mixing Constraints on TeV Scale Left-Right Symmetry

We revisit the $\Delta F=2$ transitions in the $K$ and $B_{d,s}$ neutral meson systems in the context of the minimal Left-Right symmetric model. We take into account, in addition to up-to-date phenomenological data, the contributions related to the renormalization of the flavor-changing neutral Higgs tree-level amplitude. These contributions were neglected in recent discussions, albeit formally needed in order to obtain a gauge independent result. Their impact on the minimal LR model is crucial and twofold. First, the effects are relevant in $B$ meson oscillations, for both CP conserving and CP violating observables, so that for the first time these imply constraints on the LR scenario which compete with those of the $K$ sector (plagued by long-distance uncertainties). Second, they sizably contribute to the indirect kaon CP violation parameter $\varepsilon$. We discuss the bounds from $B$ and $K$ mesons in both cases of LR symmetry: generalized parity ($\mathcal P$) and charge conjugation ($\mathcal C$). In the case of $\mathcal P$, the interplay between the CP-violation parameters $\varepsilon$ and $\varepsilon'$ leads us to rule out the regime of very hierarchical bidoublet vacuum expectation values $v_2/v_1<m_b/m_t\simeq 0.02$. In general, by minimizing the scalar field contribution up to the limit of the perturbative regime and by definite values of the relevant CP phases in the charged right-handed currents, we find that a right-handed gauge boson $W_R$ as light as 3 TeV is allowed at the 95% CL. This is well within the reach of direct detection at the next LHC run. If not discovered, within a decade the upgraded LHCb and Super B factories may reach an indirect sensitivity to a Left-Right scale of 8 TeV.Comment: Refs added + comment

A Finite Quantum Symmetry of M(3,C)

The 27-dimensional Hopf algebra A(F), defined by the exact sequence of quantum groups A(SL(2,C))->A(SL_q(2))->A(F), q^3=1, is studied as a finite quantum group symmetry of the matrix algebra M(3,C), describing the color sector of Alain Connes' formulation of the Standard Model. The duality with the Hopf algebra H,investigated in a recent work by Robert Coquereaux, is established and used to define a representation of H on M(3,C) and two commuting representations of H on A(F).Comment: Amslatex, 17 pages, only Reference [DHS] modifie

Finite Energy of Black Holes in Massive Gravity

In GR the static gravitational potential of a self-gravitating body goes as 1/r at large distances and any slower decrease leads to infinity energy. We show that in a class of four-dimensional massive gravity theories there exists spherically symmetric solutions with finite total energy, featuring an asymptotic behavior slower than 1/r and generically of the form $r^\gamma$. This suggests that configurations with nonstandard asymptotics may well turn out to be physical. The effect is due to an extra field coupled only gravitationally, which allows for modifications of the static potential generated by matter, while counterbalancing the apparently infinite energy budget.Comment: 4 page

Left-Right Symmetry at FCC-hh

We study the production of right-handed $W_R$ bosons and heavy neutrinos $N$ at a future 100 TeV high energy hadron collider in the context of Left-Right symmetry, including the effects of $W_L-W_R$ gauge-boson mixing. We estimate the collider reach for up to 3/ab integrated luminosity using a multi-binned sensitivity measure. In the Keung-Senjanovi\'c and missing energy channels, the 3$\sigma$ sensitivity extends up to $M_{W_R}=35$ and 37 TeV, respectively. We further clarify the interplay between the missing energy channel and the (expected) limits from neutrinoless double beta decay searches, Big Bang nucleosynthesis and dark matter.Comment: 19 pages, version to appear in PR