Bayesian analysis of Friedmannless cosmologies

Assuming only a homogeneous and isotropic universe and using both the 'Gold' Supernova Type Ia sample of Riess et al. and the results from the Supernova Legacy Survey, we calculate the Bayesian evidence of a range of different parameterizations of the deceleration parameter. We consider both spatially flat and curved models. Our results show that although there is strong evidence in the data for an accelerating universe, there is little evidence that the deceleration parameter varies with redshift.Comment: 7 pages, 3 figure

Fisher Matrix Preloaded -- Fisher4Cast

The Fisher Matrix is the backbone of modern cosmological forecasting. We describe the Fisher4Cast software: a general-purpose, easy-to-use, Fisher Matrix framework. It is open source, rigorously designed and tested and includes a Graphical User Interface (GUI) with automated LATEX file creation capability and point-and-click Fisher ellipse generation. Fisher4Cast was designed for ease of extension and, although written in Matlab, is easily portable to open-source alternatives such as Octave and Scilab. Here we use Fisher4Cast to present new 3-D and 4-D visualisations of the forecasting landscape and to investigate the effects of growth and curvature on future cosmological surveys. Early releases have been available at http://www.cosmology.org.za since May 2008 with 750 downloads in the first year. Version 2.2 is made public with this paper and includes a Quick Start guide and the code used to produce the figures in this paper, in the hope that it will be useful to the cosmology and wider scientific communities.Comment: 30 Pages, 15 figures. Minor revisions to match published version, with some additional functionality described to match the current version (2.2) of the code. Software available at http://www.cosmology.org.za. Usage, structure and flow of the software, as well as tests performed are described in the accompanying Users' Manua

Gamma Ray Bursts as standard candles to constrain the cosmological parameters

Gamma Ray Bursts (GRBs) are among the most powerful sources in the Universe: they emit up to 10^54 erg in the hard X-ray band in few tens of seconds. The cosmological origin of GRBs has been confirmed by several spectroscopic measurements of their redshifts, distributed in the range 0.1-6.3. These two properties make GRBs very appealing to investigate the far Universe. The energetics implied by the observed fluences and redshifts span at least four orders of magnitudes. Therefore, at first sight, GRBs are all but standard candles. But there are correlations among some observed quantities which allow us to know the total energy or the peak luminosity emitted by a specific burst with a great accuracy. Through these correlations, GRBs become "known" candles to constrain the cosmological parameters. One of these correlation is between the rest frame peak spectral energy E_peak and the total energy emitted in gamma--rays E_gamma, properly corrected for the collimation factor. Another correlation, discovered very recently, relates the total GRB luminosity L_iso, its peak spectral energy E_peak and a characteristic timescale T_0.45, related to the variability of the prompt emission. It is based only on prompt emission properties, it is completely phenomenological, model independent and assumption--free. The constraints found through these correlations on the Omega_M and Omega_Lambda parameters are consistent with the concordance model. The present limited sample of bursts and the lack of low redshift events, necessary to calibrate these correlations, makes the cosmological constraints obtained with GRBs still large compared to those obtained with other cosmological probes (e.g. SNIa or CMB). However, the newly born field of GRB--cosmology is very promising for the future.Comment: 39 pages, 23 figures, 2 tables. Accepted for publication in the New Journal of Physics focus issue, "Focus on Gamma--Ray bursts in the Swift Era" (Eds. D. H. Hartmann, C. D. Dermer, J. Greiner

AIC, BIC, Bayesian evidence against the interacting dark energy model

Recent astronomical observations have indicated that the Universe is in the phase of accelerated expansion. While there are many cosmological models which try to explain this phenomenon, we focus on the interacting $\Lambda$CDM model where the interaction between the dark energy and dark matter sectors takes place. This model is compared to its simpler alternative---the $\Lambda$CDM model. To choose between these models the likelihood ratio test was applied as well as the model comparison methods (employing Occam's principle): the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Bayesian evidence. Using the current astronomical data: SNIa (Union2.1), $h(z)$, BAO, Alcock--Paczynski test and CMB we evaluated both models. The analyses based on the AIC indicated that there is less support for the interacting $\Lambda$CDM model when compared to the $\Lambda$CDM model, while those based on the BIC indicated that there is the strong evidence against it in favor the $\Lambda$CDM model. Given the weak or almost none support for the interacting $\Lambda$CDM model and bearing in mind Occam's razor we are inclined to reject this model.Comment: LaTeX svjour3, 12 pages, 3 figure

Bayesian experimental design and model selection forecasting

Introduction Common applications of Bayesian methods in cosmology involve the computation of model probabilities and of posterior probability distributions for the parameters of those models. However, Bayesian statistics is not limited to applications based on existing data, but can equally well handle questions about expectations for the future performance of planned experiments, based on our current knowledge. This is an important topic, especially with a number of future cosmology experiments and surveys currently being planned. To give a taste, they include: large-scale optical surveys such as Pan-STARRS (Panoramic Survey Telescope and Rapid Response System), DES (the Dark Energy Survey) and LSST (Large Synoptic Survey Telescope), massive spectroscopic surveys such as WFMOS (Wide-Field Fibrefed Multi-Object Spectrograph), satellite missions such as JDEM (the Joint Dark Energy Explorer) and EUCLID, continental-sized radio telescopes such as SKA (the Square Kilometer Array) and future cosmic microwave background experiments such as B-Pol searching for primordial gravitational waves. As the amount of available resources is limited, the question of how to optimize them in order to obtain the greatest possible science return, given present knowledge, will be of increasing importance. In this chapter we address the issue of experimental forecasting and optimization, starting with the general aspects and a simple example. We then discuss the so-called Fisher Matrix approach, which allows one to compute forecasts rapidly, before looking at a real-world application. Finally, we cover forecasts of model comparison outcomes and model selection Figures of Merit