Abstract: Statistical inference of the fundamental parameters of supersymmetric theories is a challenging and active endeavor. Several sophisticated algorithms have been employed to this end. While Markov-Chain Monte Carlo (MCMC) and nested sampling techniques are geared towards Bayesian inference, they have also been used to estimate frequentist confidence intervals based on the profile likelihood ratio. We investigate the performance and appropriate configuration of MULTINEST, a nested sampling based algorithm, when used for profile likelihood-based analyses both on toy models and on the parameter space of the Constrained MSSM. We find that while the standard configuration previously used in the literarture is appropriate for an accurate reconstruction of the Bayesian posterior, the profile likelihood is poorly approximated. We identify a more appropriate MULTINEST configuration for profile likelihood analyses, which gives an excellent exploration of the profile likelihood (albeit at a larger computational cost), including the identification of the global maximum likelihood value. We conclude that with the appropriate configuration MULTINEST is a suitable tool for profile likelihood studies, indicating previous claims to the contrary are not well founded.

Abstract: We derive the effects of a nonzero cosmological constant Lambda on gravitational wave propagation in the linearized approximation of general relativity. In this approximation, we consider the situation where the metric can be written as g(mu nu) = eta(mu nu) + h(mu nu)(Lambda) + h(mu nu)(W), h(mu nu)(Lambda,W) << 1, where h(mu nu)(Lambda) is the background perturbation and h(mu nu)(W) is a modification interpretable as a gravitational wave. For Lambda not equal 0, this linearization of Einstein equations is self-consistent only in certain coordinate systems. The cosmological Friedmann-Robertson-Walker coordinates do not belong to this class and the derived linearized solutions have to be reinterpreted in a coordinate system that is homogeneous and isotropic to make contact with observations. Plane waves in the linear theory acquire modifications of order root Lambda, both in the amplitude and the phase, when considered in Friedmann-Robertson-Walker coordinates. In the linearization process for h(mu nu), we have also included terms of order O(Lambda h(mu nu)). For the background perturbation h(mu nu)(Lambda), the difference is very small, but when the term h(mu nu)(W)Lambda is retained the equations of motion can be interpreted as describing massive spin-2 particles. However, the extra degrees of freedom can be approximately gauged away, coupling to matter sources with a strength proportional to the cosmological constant itself. Finally, we discuss the viability of detecting the modifications caused by the cosmological constant on the amplitude and phase of gravitational waves. In some cases, the distortion with respect to gravitational waves propagating in Minkowski space-time is considerable. The effect of Lambda could have a detectable impact on pulsar timing arrays.