Topics in theoretical particle physics and cosmology beyond the standard model

Abstract

We review our understanding of spin-1 and spin-2 massless particles as mediators of long-range forces. We discuss how a quantum description of such particles that is compatible with Lorentz covariance leads to gauge invariance, a mathematical redundancy in the description of the physics. We discuss the Weinberg-Witten theorem, which underlines the need for gauge invariance in relativistic theories with massless mediators of higher spin. This leads us to consider a class of models in which long-range interactions are mediated by the Goldstone bosons of spontaneous Lorentz violation. Since the Lorentz symmetry is realized non-linearly in the Goldstones, these models could evade the Weinberg-Witten theorem and the need for gauge invariance. In the case of gravity, the broken symmetry would protect the theory from having non-zero cosmological constant, while the compositeness of the graviton could provide a solution to the perturbative non-renormalizability of gravity. Next we consider the phenomenology of spontaneous Lorentz violation and the experimental limits thereon. We find the general low-energy effective action of the Goldstones of this kind of symmetry breaking minimally coupled to gravity. We compare this effective theory to the ghost condensate that has been proposed in the literature as a model for gravity in a Higgs phase. We compute the modification to Newton's law from this mechanism and discuss observational limits on this kind of Lorentz violation from solar system tests of gravity and from gravitational Cherenkov radiation of cosmic rays. We then summarize the cosmological constant problems and show that models in which a scalar field causes super-acceleration of the universe generally exhibit instabilities connected to violation of the null-energy condition. We discuss how the equation of state evolves in a universe where the dark energy is caused by a ghost condensate. We comment on the anthropic argument for a small cosmological constant and how it is weakened if the inflaton self-coupling varies over the landscape of possible universes. Finally, we discuss the reverse sprinkler, a problem in elementary fluid mechanics that had eluded a definitive treatment for decades.