## Publications

107 results found

Starkman GD, Trotta R, Vaudrevange PM, 2010, The virtues of frugality - why cosmological observers should release their data slowly, *Monthly Notices of the Royal Astronomical Society*, Vol: 401, Pages: L15-L18, ISSN: 1365-2966

Cosmologists will soon be in a unique position. Observational noise will gradually be replaced by cosmic variance as the dominant source of uncertainty in an increasing number of observations. We reflect on the ramifications for the discovery and verification of new models. If there are features in the full data set that call for a new model, there will be no subsequent observations to test that model's predictions. We give specific examples of the problem by discussing the pitfalls of model discovery by prior adjustment in the context of dark energy models and inflationary theories. We show how the gradual release of data can mitigate this difficulty, allowing anomalies to be identified and new models to be proposed and tested. We advocate that observers plan for the frugal release of data from future cosmic-variance-limited observations.

Trotta R, Parkinson DR, Kunz M, et al., 2009, Bayesian Experimental Design and Model Selection Forecasting, Bayesian Methods in Cosmology, Editors: Hobson, Jaffe, Liddle, Mukherjee, Parkinson, Cambridge, Publisher: Cambridge University Press, ISBN: 9780521887946

Strigari LE, Trotta R, 2009, Reconstructing WIMP properties in direct detection experiments including galactic dark matter distribution uncertainties, *Journal of Cosmology and Astroparticle Physics*, Vol: 2009, ISSN: 1475-7516

We present a new method for determining Weakly Interacting Massive Particle(WIMP) properties in future tonne scale direct detection experiments which accounts for uncertainties in the Milky Way (MW) smooth dark matter distribution. Using synthetic data on the kinematics of MW halo stars matching present samples from the Sloan Digital Sky Survey, complemented by local escape velocity constraints, we demonstrate that the local dark matter density can be constrained to ∼ 20% accuracy. For low mass WIMPs, wefind that a factor of two error in the assumed local dark matter density leads to a severely biased reconstruction of the WIMP spin-independent cross section that is incorrect at the 15σ level. We show that this bias may be overcome by marginalizing over parameters that describe the MW potential, and use this formalism to project the accuracy attainable on WIMP properties in future 1 ton Xenon detectors. Our method can be readily applied to different detector technologies and extended to more detailed MW halo models.

Trotta R, Ruiz de Austri R, de los Heros CP, 2009, Prospects for dark matter detection with IceCube in the context of the CMSSM, *Journal of Cosmology and Astroparticle Physics*, Vol: 2009, ISSN: 1475-7516

We study in detail the ability of the nominal configuration of the IceCube neutrinotelescope (with 80 strings) to probe the parameter space of the Constrained MSSM (CMSSM) favoured by current collider and cosmological data. Adopting conservative assumptions about the galactic halo model and the expected experiment performance, we find that IceCube has a probability between 2% and 12% of achieving a 5σ detection of dark matter annihilation in the Sun, depending on the choice of priors for the scalar and gaugino masses and on the astrophysical assumptions. We identify the most important annihilationchannels in the CMSSM parameter space favoured by current constraints, and we demonstrate that assuming that the signal is dominated by a single annihilation channel can lead to large systematic errors in the inferred WIMP annihilation cross section. We demonstrate that ∼ 66% of the CMSSM parameter space violates the equilibrium condition between capture and annihilation in the center of the Sun. By cross-correlating our predictions withdirect detection methods, we conclude that if IceCube does detect a neutrino flux from the Sun at high significance while direct detection experiments do not find a signal above a spinindependent cross section σSIp>∼ 7× 10−9 pb, the CMSSM will be strongly disfavoured, given standard astrophysical assumptions for the WIMP distribution. This result is robust with respect to a change of priors. We argue that the proposed low-energy DeepCore extension ofIceCube will be an ideal instrument to focus on relevant CMSSM areas of parameter space.

Vardanyan M, Trotta R, Silk J, 2009, How flat can you get ? A model comparison perspective on the curvature of the Universe, *Monthly Notices of the Royal Astronomical Society*, Vol: 397, Pages: 431-444, ISSN: 1365-2966

Martinez GD, Bullock JS, Kaplinghat M,
et al., 2009, Indirect dark matter detection from dwarf satellites: joint expectations from astrophysics and supersymmetry, *Joutrnal of Cosmology and Astroparticle Physics*, Vol: 2009, ISSN: 1475-7516

We present a general methodology for determining the gamma-ray flux fromannihilation of dark matter particles in Milky Way satellite galaxies, focusing on two promising satellites as examples: Segue 1 and Draco. We use the SuperBayeS code to explore the best-fitting regions of the Constrained Minimal Supersymmetric Standard Model (CMSSM) parameter space, and an independent MCMC analysis of the dark matter halo properties of the satellites using published radial velocities. We present a formalism for determining the boost from halo substructure in these galaxies and show that its value depends stronglyon the extrapolation of the concentration-mass (c(M)) relation for CDM subhalos down to the minimum possible mass. We show that the preferred region for this minimum halo mass within the CMSSM with neutralino dark matter is ∼ 10−9 − 10−6 M⊙. For the boost model where the observed power-law c(M) relation is extrapolated down to the minimum halo mass we find average boosts of about 20, while the Bullock et al (2001) c(M) model results in boosts of order unity. We estimate that for the power-law c(M) boost model and photonenergies greater than a GeV, the Fermi space-telescope has about 20% chance of detecting a dark matter annihilation signal from Draco with signal-to-noise greater than 3 after about 5 years of observation.

Roszkowski L, de Austri RR, Silk J,
et al., 2009, On prospects for dark matter indirect detection in the Constrained MSSM, *PHYSICS LETTERS B*, Vol: 671, Pages: 10-14, ISSN: 0370-2693

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Hobson MP, Jaffe AH, Liddle AR, et al., 2009, Bayesian methods in cosmology, ISBN: 9780521887946

© Cambridge University Press, 2010. In recent years cosmologists have advanced from largely qualitative models of the Universe to precision modelling using Bayesian methods, in order to determine the properties of the Universe to high accuracy. This timely book is the only comprehensive introduction to the use of Bayesian methods in cosmological studies, and is an essential reference for graduate students and researchers in cosmology, astrophysics and applied statistics. The first part of the book focuses on methodology, setting the basic foundations and giving a detailed description of techniques. It covers topics including the estimation of parameters, Bayesian model comparison, and separation of signals. The second part explores a diverse range of applications, from the detection of astronomical sources (including through gravitational waves), to cosmic microwave background analysis and the quantification and classification of galaxy properties. Contributions from 24 highly regarded cosmologists and statisticians make this an authoritative guide to the subject.

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- Citations: 26

Trotta R, Feroz F, Hobson M,
et al., 2008, The impact of priors and observables on parameter inferences in the constrained MSSM, *Journal of High Energy Physics*, Vol: 2008, ISSN: 1126-6708

We use a newly released version of the SuperBayeS code to analyze the impact of the choice of priors and the influence of various constraints on the statistical conclusions for the preferred values of the parameters of the Constrained MSSM. We assess the effect in a Bayesian framework and compare it with an alternative likelihood-based measure of a profile likelihood. We employ a new scanning algorithm (MultiNest) which increases the computational efficiency by a factor ~ 200 with respect to previously used techniques. We demonstrate that the currently available data are not yet sufficiently constraining to allow one to determine the preferred values of CMSSM parameters in a way that is completely independent of the choice of priors and statistical measures. While B R ({\bar B} → Xsγ) generally favors large m0, this is in some contrast with the preference for low values of m0 and m1/2 that is almost entirely a consequence of a combination of prior effects and a single constraint coming from the anomalous magnetic moment of the muon, which remains somewhat controversial. Using an information-theoretical measure, we find that the cosmological dark matter abundance determination provides at least 80% of the total constraining power of all available observables. Despite the remaining uncertainties, prospects for direct detection in the CMSSM remain excellent, with the spin-independent neutralino-proton cross section almost guaranteed above σSIp 10-10pb, independently of the choice of priors or statistics. Likewise, gluino and lightest Higgs discovery at the LHC remain highly encouraging. While in this work we have used the CMSSM as particle physics model, our formalism and scanning technique can be readily applied to a wider class of models with several free parameters.

Roszkowski L, De Austri RR, Trotta R, 2008, A Bayesian approach to the constrained MSSM, Pages: 163-166

We present a new analysis of the Constrained MSSM in terms of Bayesian statistics. We illustrate our results with the light Higgs boson whose inferred mass range one should be able to exclude at the Tevatron with high confidence.

Roszkowski L, Austri RRD, Silk J,
et al., 2008, On prospects for dark matter indirect detection in the Constrained MSSM, *Physics Letters B*, Vol: 671, Pages: 10-14, ISSN: 0370-2693

In the framework of the Constrained MSSM we derive the most probable rangesof the diffuse gamma radiation flux from the direction of the Galactic centerand of the positron flux from the Galactic halo due to neutralino dark matterannihilation. We find that, for a given halo model, and assuming flat priors,the 68% probability range of the integrated gamma-ray flux spans about oneorder of magnitude, while the 95% probability range can be much larger andextend over four orders of magnitude (even exceeding five for a tiny region atsmall neutralino mass). The detectability of the signal by GLAST dependingprimarily on the cuspiness of the halo profile. The positron flux, on the otherhand, appears to be too small to be detectable by PAMELA, unless the boostfactor is at least of order ten and/or the halo profile is extremely cuspy. Wealso briefly discuss the sensitivity of our results to the choice of priors.

Starkman GD, Trotta R, Vaudrevange PM, 2008, Introducing doubt in Bayesian model comparison

There are things we know, things we know we don't know, and then there are things we don't know we don't 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.

Feroz F, Allanach BC, Hobson M,
et al., 2008, Bayesian selection of sign mu within mSUGRA in global fits including WMAP5 results, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 56

Trotta R, 2008, Bayes in the sky: Bayesian inference and model selection in cosmology, *Contemporary Physics*, Vol: 49, Pages: 71-104, ISSN: 1366-5812

The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more traditional statistical tools, offering the advantage of higher efficiency and of a consistent conceptual basis for dealing with the problem of induction in the presence of uncertainty. This trend is likely to continue in the future, when the way we collect, manipulate and analyse observations and compare them with theoretical models will assume an even more central role in cosmology.This review is an introduction to Bayesian methods in cosmology and astrophysics and recent results in the field. I first present Bayesian probability theory and its conceptual underpinnings, Bayes' Theorem and the role of priors. I discuss the problem of parameter inference and its general solution, along with numerical techniques such as Monte Carlo Markov Chain methods. I then review the theory and application of Bayesian model comparison, discussing the notions of Bayesian evidence and effective model complexity, and how to compute and interpret those quantities. Recent developments in cosmological parameter extraction and Bayesian cosmological model building are summarised, highlighting the challenges that lie ahead.

Kampakoglou M, Trotta R, Silk J, 2008, Monolithic or hierarchical star formation? A new statistical analysis, *Monthly Notices of the Royal Astronomical Society*, Vol: 384, Pages: 1414-1426, ISSN: 1365-2966

We consider an analytic model of cosmic star formation which incorporates supernova feedback, gas accretion and enriched outflows, reproducing the history of cosmic star formation, metallicity, Type II supernova rates and the fraction of baryons allocated to structures. We present a new statistical treatment of the available observational data on the star formation rate and metallicity that accounts for the presence of possible systematics. We then employ a Bayesian Markov Chain Monte Carlo method to compare the predictions of our model with observations and derive constraints on the seven free parameters of the model. We find that the dust-correction scheme one chooses to adopt for the star formation data is critical in determining which scenario is favoured between a hierarchical star formation model, where star formation is prolonged by accretion, infall and merging, and a monolithic scenario, where star formation is rapid and efficient. We distinguish between these modes by defining a characteristic minimum mass, M≳ 1011M⊙, in our fiducial model, for early-type galaxies where star formation occurs efficiently. Our results indicate that the hierarchical star formation model can achieve better agreement with the data, but that this requires a high efficiency of supernova-driven outflows. In a monolithic model, our analysis points to the need for a mechanism that drives metal-poor winds, perhaps in the form of supermassive black hole induced outflows. Furthermore, the relative absence of star formation beyond z∼ 5 in the monolithic scenario requires an alternative mechanism to dwarf galaxies for re-ionizing the universe at z∼ 11, as required by observations of the microwave background. While the monolithic scenario is less favoured in terms of its quality-of-fit, it cannot yet be excluded.

Ballesteros G, Casas JA, Espinosa JR,
et al., 2008, Flat tree-level inflationary potentials in the light of cosmic microwave background and large scale structure data, *JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS*, ISSN: 1475-7516

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- Citations: 12

Gordon C, Trotta R, 2007, Bayesian calibrated significance levels applied to the spectral tilt and hemispherical asymmetry, *MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY*, Vol: 382, Pages: 1859-1863, ISSN: 0035-8711

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- Citations: 43

Zunckel C, Trotta R, 2007, Reconstructing the history of dark energy using maximum entropy, *MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY*, Vol: 380, Pages: 865-876, ISSN: 0035-8711

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- Citations: 24

Roszkowski L, de Austri RR, Trotta R, 2007, Implications for the Constrained MSSM from a new prediction for b -> s gamma, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 122

Trotta R, 2007, Forecasting the Bayes factor of a future observation, *Monthly Notices of the Royal Astronomical Society*, Vol: 378, Pages: 819-824, ISSN: 1365-2966

I present a new procedure to forecast the Bayes factor of a future observation bycomputing the Predictive Posterior Odds Distribution (PPOD). This can assess thepower of future experiments to answer model selection questions and the probabilityof 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 cosmologicalconcordance model, namely the scalar spectral index of primordial perturbations,nS. I show that the Planck satellite has over 90% probability of gatheringstrong evidence againstnS = 1, thus conclusively disproving a scale–invariant spectrum.This result is robust with respect to a wide range of choices for the prior on nS.

Trotta R, 2007, Applications of Bayesian model selection to cosmological parameters, *Monthly Notices of the Royal Astronomical Society*, Vol: 378, Pages: 72-82, ISSN: 1365-2966

Bayesian model selection is a tool for deciding whether the introduction of a new parameter is warranted by the 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. In contrast, 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 Wilkinson Microwave Anisotropy Probe (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 cold dark matter 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.

Roszkowski L, de Austri RR, Trotta R, 2007, On the detectability of the CMSSM light Higgs boson at the Tevatron, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 34

Trotta R, Ruiz de Austri R, Roszkowski L, 2007, Prospects for direct dark matter detection in the constrained MSSM, Francesco Melchiorri Memorial Conference, Publisher: Elsevier, Pages: 316-320, ISSN: 1872-9630

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 pbView the MathML source 10−8 pb 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.

Trotta R, 2007, The isocurvature fraction after WMAP 3-yr data, *Monthly Notices of the Royal Astronomical Society*, Vol: 375, Pages: L26-L30, ISSN: 1365-2966

I revisit the question of the adiabaticity of initial conditions for cosmological perturbations in view of the 3-yr Wilkinson Microwave Anisotropy Probe (WMAP) data. I focus on the simplest alternative to purely adiabatic conditions, namely a superposition of the adiabatic mode and one of the three 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 cold dark matter isocurvature fraction is now constrained to be less than about 10 per cent, while the fraction in either the neutrino entropy or velocity mode is below about 20 per cent. Model comparison strongly disfavours mixed models that allow for isocurvature fractions larger than unity, while current data do not allow one to distinguish between a purely adiabatic model and models with a moderate (i.e. below about 10 per cent) 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.

Trotta R, De Austri RR, Roszkowski L, 2007, Prospects for direct dark matter searches in the constrained mssm, Pages: 81-86

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 find that 10-10pb ≲ σSIp ≲10-8 pb for direct WIMP detection (with details slightly dependent on the assumptions made). We conclude that most of the 95% probability region for the cross section will be explored by future onetonne detectors, that will therefore cover most of the currently favoured region of parameter space.

Trotta R, Ruiz de Austri R, Roszkowski L, 2007, Direct dark matter detection around the corner? Prospects in the Constrained MSSM, TeV Particle Astrophysics II Workshop 2006, Publisher: IOP PUBLISHING LTD, Pages: 259-+, ISSN: 1742-6588

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- Citations: 4

Starkman GD, Trotta R, 2006, Why Anthropic Reasoning Cannot Predict Λ, *Physical Review Letters*, Vol: 97, ISSN: 1079-7114

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 differentanthropic predictions. As an explicit example, we show that weighting different universes by the totalnumber of possible observations leads to an extremely small probability for observing a value of equalto or greater than what we now measure. We conclude that anthropic reasoning within the framework ofprobability as frequency is ill-defined and that in the absence of a fundamental motivation for selectingone weighting scheme over another the anthropic principle cannot be used to explain the value of , nor,likely, any other physical parameters.

Trotta R, Bower R, 2006, Surveying the dark side, *ASTRONOMY & GEOPHYSICS*, Vol: 47, Pages: 20-27, ISSN: 1366-8781

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- Citations: 14

Kunz M, Trotta R, Parkinson DR, 2006, Measuring the effective complexity of cosmological models, *Physical Review D*, Vol: 74, ISSN: 1550-7998

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 noninformative 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 nonzero 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 ΛCDM concordance cosmology.

de Austri RR, Trotta R, Roszkowski L, 2006, A Markov chain Monte Carlo analysis of the CMSSM, *Journal of High Energy Physics*, Vol: 2006, ISSN: 1126-6708

We perform a comprehensive exploration of the Constrained MSSM parameter space employing 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 of relevant Standard Model 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: 0.52TeV < m1/2 < 1.26TeV, m0 < 2.10TeV, −0.34TeV < A0 < 2.41TeV and 38.5 < tan β < 54.6. Generally, large fractions of high probability ranges of the superpartner masses will be probed at the LHC. For example, we find that the probability of mtilde g < 2.7TeV is 78%, of mtilde qR < 2.5TeV is 85% and of mχ1± < 0.8TeV is 65%. As regards the other observables, for example at 68% probability we find 3.5 × 10−9 < BR(Bs→μ+μ−) < 1.7 × 10−8, 1.9 × 10−10 < δaμSUSY < 9.9 × 10−10 and 1 × 10−10 pb < σSIp < 1 × 10−8 pb for direct WIMP detection. 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(Bs→μ+μ−) and BR(bar B→Xsγ) or σSIp. Once SUSY is discovered, this and other correlations may prove helpful in distinguishing the CMSSM from other supersymmetric models. We investigate the robustness of our results in terms of the assumed ranges of CMSSM parameters and the effect of the (g−2)μ anomaly which shows some tension with the other observables. We find that the r

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