On the stability and causality of scalar-vector theories
Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations, such models require to introduce non-standard couplings between vector fields on the one hand, and either gravity or scalar fields on the other hand. In this article, we study models involving a vector field coupled to a scalar field. We derive restrictive necessary conditions for these models to be both stable (Hamiltonian bounded by below) and causal (hyperbolic equations of motion).
Abstract: We study the pointwise behavior of the Fourier transform of the spectral measure for discrete one-dimensional Schrödinger operators with sparse potentials. We find a resonance structure which admits a physical interpretation in terms of a simple quasiclassical model. We also present an improved version of known results on the spectrum of such operators.