Electromagnetic and Gravitational Waves on a de Sitter background

One of the longstanding problems of modern gravitational physics is the detection of gravitational waves, for which the standard theoretical analysis relies upon the split of the space-time metric g into background plus perturbations. However, the background isn't necessarily Minkowskian in several cases of physical interest. As a consequence, we investigate in more detail what happens if the background space-time has a non-vanishing Riemann curvature. In particular, we want to perform an analysis of electromagnetic and gravitational waves in the de Sitter space-time. Achieving solutions in this maximally symmetric background could constitute the paradigm to investigate any curved space-time by the same techniques and could have interesting cosmological applications. It is by now well known that the problem of solving vector and tensor wave equations in curved space-time is in general a challenge even for the modern computational resources. Within this framework, a striking problem is the coupled nature of the set of hyperbolic equations one arrives at. The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space-time studied in static spherical coordinates. This method is extended to the tensor wave equation of metric perturbations on a de Sitter background and a numerical analysis of solutions is performed. This approach is a step towards a general discussion of gravitational waves in any curved background and might assume relevance in cosmology in order to study the stochastic background emerging from inflation.