Abstract: Motivated by the apparent discrepancy between cosmic microwave background measurements of the Hubble constant and measurements from Type-la supernovae, we construct a model for dark energy with equation of state w = p/rho < -1, violating the null energy condition. Naive canonical models of so-called “phantom” dark energy require a negative scalar kinetic term, resulting in a Hamiltonian unbounded from below and associated vacuum instability. We construct a scalar field model for dark energy with w < -1, which nonetheless has a Hamiltonian bounded from below in the comoving reference frame, i.e., in the rest frame of the fluid. We demonstrate that the solution is a cosmological attractor, and find that early-time cosmological boundary conditions consist of a “frozen” scalar field, which relaxes to the attractor solution once the dark energy component dominates the cosmological energy density. We consider the model in an arbitrary choice of gauge, and find that, unlike the case of comoving gauge, the fluid Hamiltonian is in fact unbounded from below in the reference frame of a highly boosted observer, corresponding to a nonlinear gradient instability. We discuss this in the context of general NEC-violating perfect fluids, for which this instability is a general property.

Abstract: The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.

Abstract: Our way of describing Nature is based on local relativistic quantum field theories, and then CPT symmetry, a natural consequence of Lorentz invariance, locality and hermiticity of the Hamiltonian, is one of the few if not the only prediction that all of them share. Therefore, testing CPT invariance does not test a particular model but the whole paradigm. Current and future long baseline experiments will assess the status of CPT in the neutrino sector at an unprecedented level and thus its distinction from similar experimental signatures arising from non-standard interactions is imperative. Whether the whole paradigm is at stake or just the standard model of neutrinos crucially depends on that.