Probing dark energy with future surveys

I review the observational prospects to constrain the equation of state parameter of dark energy and I discuss the potential of future imaging and redshift surveys. Bayesian model selection is used to address the question of the level of accuracy on the equation of state parameter that is required before explanations alternative to a cosmological constant become very implausible. I discuss results in the prediction space of dark energy models. If no significant departure from w=-1 is detected, a precision on w of order 1% will translate into strong evidence against fluid-like dark energy, while decisive evidence will require a precision of order 10^-3

Testing the paradigm of adiabaticity

We introduce the concepts of adiabatic (curvature) and isocurvature (entropy) cosmological perturbations and present their relevance for parameter estimation from cosmic microwave background anisotropies data. We emphasize that, while present-day data are in excellent agreement with pure adiabaticity, subdominant isocurvature contributions cannot be ruled out. We discuss model independent constraints on the isocurvature contribution. Finally, we argue that the Planck satellite will be able to do precision cosmology even if the assumption of adiabaticity is relaxed.Comment: Proceedings of the 10th Marcel Grossmann Meeting, Rio de Janeiro, July 2003, 5 pages, 2 figure

Applications of Bayesian model selection to cosmological parameters

Bayesian model selection is a tool to decide whether the introduction of a new parameter is warranted by data. I argue that the usual sampling statistic significance tests for a null hypothesis can be misleading, since they do not take into account the information gained through the data, when updating the prior distribution to the posterior. On the contrary, Bayesian model selection offers a quantitative implementation of Occam's razor. I introduce the Savage-Dickey density ratio, a computationally quick method to determine the Bayes factor of two nested models and hence perform model selection. As an illustration, I consider three key parameters for our understanding of the cosmological concordance model. By using WMAP 3-year data complemented by other cosmological measurements, I show that a non-scale invariant spectral index of perturbations is favoured for any sensible choice of prior. It is also found that a flat Universe is favoured with odds of 29:1 over non--flat models, and that there is strong evidence against a CDM isocurvature component to the initial conditions which is totally (anti)correlated with the adiabatic mode (odds of about 2000:1), but that this is strongly dependent on the prior adopted. These results are contrasted with the analysis of WMAP 1-year data, which were not informative enough to allow a conclusion as to the status of the spectral index. In a companion paper, a new technique to forecast the Bayes factor of a future observation is presented.Comment: v2 to v3: minor changes, matches accepted version by MNRAS. v1 to v2: major revision. New results using WMAP 3-yr data, scale-invariant spectrum now disfavoured with moderate evidence. New benchmark test for the accuracy of the method. Bayes factor forecast methodology (PPOD, formerly called ExPO) expanded and now presented in a companion paper (astro-ph/0703063

Statistical Challenges of Global SUSY Fits

We present recent results aiming at assessing the coverage properties of Bayesian and frequentist inference methods, as applied to the reconstruction of supersymmetric parameters from simulated LHC data. We discuss the statistical challenges of the reconstruction procedure, and highlight the algorithmic difficulties of obtaining accurate profile likelihood estimates

Constraining the helium abundance with CMB data

We consider for the first time the ability of present-day cosmic microwave background (CMB) anisotropies data to determine the primordial helium mass fraction, Y_p. We find that CMB data alone gives the confidence interval 0.160 < Y_p < 0.501 (at 68% c.l.). We analyse the impact on the baryon abundance as measured by CMB and discuss the implications for big bang nucleosynthesis. We identify and discuss correlations between the helium mass fraction and both the redshift of reionization and the spectral index. We forecast the precision of future CMB observations, and find that Planck alone will measure Y_p with error-bars of 5%. We point out that the uncertainty in the determination of the helium fraction will have to be taken into account in order to correctly estimate the baryon density from Planck-quality CMB data

Reproducing Cosmic Microwave Background anisotropies with mixed isocurvature perturbations

Recently high quality data of the cosmic microwave background anisotropies have been published. In this work we study to which extent the cosmological parameters determined by using this data depend on assumptions about the initial conditions. We show that for generic initial conditions, not only the best fit values are very different but, and this is our main result, the allowed parameter range enlarges dramatically.Comment: 4 pages, 5 figures, submitted to PRL; Major changes following referees suggestions; the allowed cosmological parameter range enlarges dramaticall

The isocurvature fraction after WMAP 3-year data

I revisit the question of the adiabaticity of initial conditions for cosmological perturbations in view of the 3-year WMAP data. I focus on the simplest alternative to pure adiabatic conditions, namely a superposition of the adiabatic mode and one of the 3 possible isocurvature modes, with the same spectral index as the adiabatic component. I discuss findings in terms of posterior bounds on the isocurvature fraction and Bayesian model selection. The Bayes factor (models likelihood ratio) and the effective Bayesian complexity are computed for several prior ranges for the isocurvature content. I find that the CDM isocurvature fraction is now constrained to be less than about 10%, while the fraction in either the neutrino entropy or velocity mode is below about 20%. Model comparison strongly disfavours mixed models that allow for isocurvature fractions larger than unity, while current data do not allow to distinguish between a purely adiabatic model and models with a moderate (ie, below about 10%) isocurvature contribution. The conclusion is that purely adiabatic conditions are strongly favoured from a model selection perspective. This is expected to apply in even stronger terms to more complicated superpositions of isocurvature contributions.Comment: Expanded discussion of degeneracies, updated references, no change to conclusions. Matches published versio

Constraints on a mixed inflaton and curvaton scenario for the generation of the curvature perturbation

We consider a supersymmetric grand unified model which naturally solves the strong CP and mu problems via a Peccei-Quinn symmetry and leads to the standard realization of hybrid inflation. We show that the Peccei-Quinn field of this model can act as curvaton. In contrast to the standard curvaton hypothesis, both the inflaton and the curvaton contribute to the total curvature perturbation. The model predicts an isocurvature perturbation too which has mixed correlation with the adiabatic one. The cold dark matter of the universe is mostly constituted by axions plus a small amount of lightest sparticles. The predictions of the model are confronted with the Wilkinson microwave anisotropy probe and other cosmic microwave background radiation data. We analyze two representative choices of parameters and derive bounds on the curvaton contribution to the adiabatic perturbation. We find that, for the choice which provides the best fitting of the data, the curvaton contribution to the adiabatic amplitude must be smaller than about 67% (at 95% confidence level). The best-fit power spectra are dominated by the adiabatic part of the inflaton contribution. We use Bayesian model comparison to show that this choice of parameters is disfavored with respect to the pure inflaton scale-invariant case with odds of 50 to 1. For the second choice of parameters, the adiabatic mode is dominated by the curvaton, but this choice is strongly disfavored relative to the pure inflaton scale-invariant case (with odds of 10^7 to 1). We conclude that in the present framework the perturbations must be dominated by the adiabatic component from the inflaton.Comment: 27 pages including 16 figures, uses Revte

Efficient reconstruction of CMSSM parameters from LHC data - A case study

We present an efficient method of reconstructing the parameters of the Constrained MSSM from assumed future LHC data, applied both on their own right and in combination with the cosmological determination of the relic dark matter abundance. Focusing on the ATLAS SU3 benchmark point, we demonstrate that our simple Gaussian approximation can recover the values of its parameters remarkably well. We examine two popular non-informative priors and obtain very similar results, although when we use an informative, naturalness-motivated prior, we find some sizeable differences. We show that a further strong improvement in reconstructing the SU3 parameters can by achieved by applying additional information about the relic abundance at the level of WMAP accuracy, although the expected data from Planck will have only a very limited additional impact. Further external data may be required to break some remaining degeneracies. We argue that the method presented here is applicable to a wide class of low-energy effective supersymmetric models, as it does not require to deal with purely experimental issues, eg, detector performance, and has the additional advantages of computational efficiency. Furthermore, our approach allows one to distinguish the effect of the model's internal structure and of the external data on the final parameters constraints.Comment: 23 pages, 10 figures - moderate revision: includes naturalness prior. Matches published versio

Introducing doubt in Bayesian model comparison

There are things we know, things we know we dont know, and then there are things we dont know we dont know. In this paper we address the latter two issues in a Bayesian framework, introducing the notion of doubt to quantify the degree of (dis)belief in a model given observational data in the absence of explicit alternative models. We demonstrate how a properly calibrated doubt can lead to model discovery when the true model is unknown