Investigating the properties of gamma ray bursts and gravitational wave standard sirens as high redshift distance indicators

In a discipline commonly faulted for ad hoc assumptions and models with very little discriminating observational evidence, cosmologists are continually trying, and in many cases succeeding, to improve both the data and models. However, the desire to support currently favoured models often dominates research and may lead to a systematic bias being introduced in favour of a model before a strong body of supporting evidence has been accumulated. This is perhaps most evident in literature supporting the viability of Gamma Ray Bursts as cosmological distance indicators, where aside from subjective data-selection, the basic statistical methods are at best questionable and at worst incorrect. To this end, we construct a simple cosmology-independent illustration of the effect that the application of these methods has on parameter estimation and discuss the correct method to apply to current data. We also investigate the constraints potential future Gamma Ray Burst data may place on alternatives to the status quo Concordance Model in the shape of Conformal Gravity and Unified Dark Matter through a widely applicable and transferable Bayesian model comparison technique and the development of a representative mock data set. Finally, we investigate gravitational wave standard sirens as an alternative high-redshift distance indicator. We first illustrate their strong diagnostic potential through a Bayesian model comparison between the standard Unified Dark Matter model and a variant in which the dark component is redshift dependent. By drawing mock data from a known cosmological model, thus fixing the expected values of the model parameters, we find that while 182 Type 1a Supernovae are readily confused between constant and evolving models, just 2 standard sirens are able to successfully identify the correct model. Having established standard sirens as an effective tool in cosmological model comparison, we then address the potential confusion of models with dynamical dark energy and intrinsic curvature. We show that currently used distance indicators - Type 1a Supernovae, Baryon Acoustic Oscillations and the Cosmic Microwave Background Radiation - are not reliable enough to identify a small amount of intrinsic curvature, which partly justifies the common practice of assuming flat space in order to reduce the number of free parameters. However, we show that the addition of even a small number of standard sirens greatly reduces this problem. The addition of just two sirens offers a slight improvement, while adding ten sirens to the aforementioned list of indicators halves the range over which there is uncertainty between models