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Roberto Trotta

Publications and source records attributed to Roberto Trotta.

86 records · Page 5Linked to original sources
arXiv2007

Forecasting the Bayes factor of a future observation

I present a new procedure to forecast the Bayes factor of a future observation by computing the Predictive Posterior Odds Distribution (PPOD). This can assess the power of future experiments to answer model selection questions and the probability of the outcome, and can be helpful in the context of experiment design. As an illustration, I consider a central quantity for our understanding of the cosmological concordance model, namely the scalar spectral index of primordial perturbations, n_S. I show that the Planck satellite has over 90% probability of gathering strong evidence against n_S = 1, thus conclusively disproving a scale-invariant spectrum. This result is robust with respect to a wide range of choices for the prior on n_S.

astro-ph↗
arXiv2007

Comment on `Tainted evidence: cosmological model selection versus fitting', by Eric V. Linder and Ramon Miquel (astro-ph/0702542v2)

In astro-ph/0702542v2, Linder and Miquel seek to criticize the use of Bayesian model selection for data analysis and for survey forecasting and design. Their discussion is based on three serious misunderstandings of the conceptual underpinnings and application of model-level Bayesian inference, which invalidate all their main conclusions. Their paper includes numerous further inaccuracies, including an erroneous calculation of the Bayesian Information Criterion. Here we seek to set the record straight.

astro-ph↗
arXiv2007

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.

astro-ph↗
arXiv2006

Why anthropic reasoning cannot predict Lambda

We revisit anthropic arguments purporting to explain the measured value of the cosmological constant. We argue that different ways of assigning probabilities to candidate universes lead to totally different anthropic predictions. As an explicit example, we show that weighting different universes by the total number of possible observations leads to an extremely small probability for observing a value of Lambda equal to or greater than what we now measure. We conclude that anthropic reasoning within the framework of probability as frequency is ill-defined and that in the absence of a fundamental motivation for selecting one weighting scheme over another the anthropic principle cannot be used to explain the value of Lambda, nor, likely, any other physical parameters.

astro-ph↗
arXiv2006

What's the trouble with anthropic reasoning?

Selection effects in cosmology are often invoked to "explain" why some of the fundamental constant of Nature, and in particular the cosmological constant, take on the value they do in our Universe. We briefly review this probabilistic "anthropic reasoning" and we argue that different (equally plausible) ways of assigning probabilities to candidate universes lead to totally different anthropic predictions, presenting an explicit example based on the total number of possible observations observers can carry out. We conclude that in absence of a fundamental motivation for selecting one weighting scheme over another the anthropic principle cannot be used to explain the value of Lambda. .

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arXiv2006

A Markov Chain Monte Carlo Analysis of the CMSSM

We perform a comprehensive exploration of the Constrained MSSM parameters using a Markov Chain Monte Carlo technique and a Bayesian analysis. We compute superpartner masses and other collider observables as well as a cold dark matter abundance, and compare them with experimental data. We include uncertainties arising from theoretical approximations as well as from residual experimental errors on relevant SM parameters. We delineate probability distributions of the CMSSM parameters, the collider and cosmological observables as well as a dark matter direct detection cross section. The 68% probability intervals of the CMSSM parameters are: 0.52 TeV < m_{1/2} < 1.26 TeV, m_0 <2.10 TeV, -0.34 TeV < A_0 < 2.41 TeV and 38.5< tan(beta) <54.6. Generally, large fractions of high probability ranges of the superpartner masses will be probed at the LHC. We highlight a complementarity between LHC and WIMP dark matter searches in exploring the CMSSM parameter space. We further expose a number of correlations among the observables, in particular between BR(B_s \to μ^+ μ^-) and BR({\bar B}\to X_sγ) or sigma_p^{SI}. Once SUSY is discovered, this and other correlations may prove helpful in distinguishing the CMSSM from other supersymmetric models. The robustness of our results is investigated in terms of the assumed ranges of CMSSM parameters and the effect of the (g-2)_mu anomaly which shows some tension with the other observables. We find that the results for m_0, and the observables which strongly depend on it, are sensitive to our assumptions, while our conclusions for the other variables are robust.

hep-ph↗
arXiv2006

Prospects for direct dark matter detection in the Constrained MSSM

We outline the WIMP dark matter parameter space in the Constrained MSSM by performing a comprehensive statistical analysis that compares with experimental data predicted superpartner masses and other collider observables as well as a cold dark matter abundance. We include uncertainties arising from theoretical approximations as well as from residual experimental errors on relevant Standard Model parameters. We present high-probability regions for neutralino dark matter direct detection cross section, and we find that 10^-10 pb < sigma_p^SI < 10^-8 for direct WIMP detection (with details slightly dependent on the assumptions made). We highlight a complementarity between LHC and WIMP dark matter searches in exploring the CMSSM parameter space. We conclude that most of the 95% probability region for the cross section will be explored by future one-tonne detectors, that will therefore cover most of the currently favoured region of parameter space.

astro-ph↗
arXiv2006

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.

astro-ph↗
arXiv2006

Surveying the dark side

We examine the prospects for the next generation of surveys aimed at elucidating the nature of dark energy. We review the methods that can be used to determine the redshift evolution of the dark energy equation of state parameter w, highlighting their respective strengths and potential weaknesses. All of the attractive methods require surveys covering more than 5-10,000 square degrees of the sky. We examine the accuracy that each method is likely to deliver within a decade, and discuss the difficulties arising from systematic uncertainties associated with the techniques. We conclude that the proposed photometric and redshift surveys have the potential of delivering measurements of w with percent accuracy at several redshifts out to z ~ 3 . Of particular interest will be the combination of weak lensing and baryonic acoustic oscillations measurements. This exquisite precision is likely to have a fundamental impact on our understanding of the nature of dark energy, providing the necessary guidance for its theoretical explanation.

astro-ph↗
arXiv2006

Measuring the effective complexity of cosmological models

We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly non-informative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a non-zero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the Lambda-CDM concordance cosmology.

astro-ph↗
arXiv2004

Cosmic Microwave Background Anisotropies: Beyond Standard Parameters

In the first part of this work, I review the theoretical framework of cosmological perturbation theory necessary to understand the generation and evolution of cosmic microwave background (CMB) anisotropies. Using analytical and numerical techniques, in the second part I describe the impact on the CMB power spectra of the standard cosmological parameters (such as the matter-energy budget of the Universe, its curvature, the amplitude and spectral properties of the primordial fluctuations, etc.). I introduce the most general type of initial conditions for the primordial perturbations, deriving a new analytical approximation for the neutrino isocurvature modes. In the third part, I discuss the issue of extracting constraints on the parameters of interest from the recent, high-quality CMB measurements, presenting the relevant statistical tools and focusing on the Fisher matrix analysis as a technique to produce reliable forecasts for the performance of future observations. I then apply those tools to the study of several possible extensions of the (currently) standard Lambda CDM model: the presence of extra relativistic particles, possible time variations of the fine structure constant, and the value of the primordial Helium mass fraction. I also use the CMB as a tool to study the very early Universe, via its dependence on the type of initial conditions: I relax the assumption of purely adiabatic initial conditions and discuss the observational consequences and constraints on the presence of general isocurvature modes.

astro-ph↗
arXiv2003

Constraining the helium abundance with CMB

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.

astro-ph↗
arXiv2003

The cosmological constant and the paradigm of adiabaticity

We discuss the value of the cosmological constant as recovered from CMB and LSS data and the robustness of the results when general isocurvature initial conditions are allowed for, as opposed to purely adiabatic perturbations. The Bayesian and frequentist statistical approaches are compared. It is shown that pre-WMAP CMB and LSS data tend to be incompatible with a non-zero cosmological constant, regardless of the type of initial conditions and of the statistical approach. The non-adiabatic contribution is constrained to be < 40% (2sigma c.l.).

astro-ph↗