Publications
118 results found
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.
Roszkowski L, de Austri RR, Trotta R, 2007, Implications for the Constrained MSSM from a new prediction for b→sγ, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479
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- Citations: 123
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: 5
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
Trotta R, 2006, Probing dark energy with future surveys
I review the observational prospects to constrain the equation of stateparameter of dark energy and I discuss the potential of future imaging andredshift surveys. Bayesian model selection is used to address the question of the level ofaccuracy on the equation of state parameter that is required beforeexplanations alternative to a cosmological constant become very implausible. Idiscuss results in the prediction space of dark energy models. If nosignificant departure from w=-1 is detected, a precision on w of order 1% willtranslate into strong evidence against fluid-like dark energy, while decisiveevidence will require a precision of order 10^-3.
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
Trotta R, 2006, Cosmological Bayesian model selection, Pages: 15-18
Bayesian model comparison can be used to decide whether the introduction of a new parameter is warranted by data. I focus on the Savage-Dickey density ratio as a method to compute the Bayes factor of nested models without carrying out a computationally demanding multi-dimensional integration. I present a new procedure (called "PPOD") to forecast the Bayes factor of a future observation. As an illustration, I consider a few central quantities in the current cosmological concordance model. Copyright © 2006 by Imperial College Press.
Trotta R, Starkman GD, 2006, What's the trouble with anthropic reasoning?, 2nd International Conference on the Dark Side of the Universe, Publisher: AMER INST PHYSICS, Pages: 323-+, ISSN: 0094-243X
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- Citations: 2
Trotta R, Durrer R, 2005, Testing the paradigm of adiabaticity, Proceedings of the MG10 Meeting held at Brazilian Center for Research in Physics (CBPF), Publisher: World Scientific, Pages: 1739-1743
We introduce the concepts of adiabatic (curvature) and isocurvature (entropy)cosmological perturbations and present their relevance for parameter estimationfrom cosmic microwave background anisotropies data. We emphasize that, whilepresent-day data are in excellent agreement with pure adiabaticity, subdominantisocurvature contributions cannot be ruled out. We discuss model independentconstraints on the isocurvature contribution. Finally, we argue that the Plancksatellite will be able to do precision cosmology even if the assumption ofadiabaticity is relaxed.
Trotta R, Melchiorri A, 2005, Indication for primordial anisotropies in the neutrino background from the Wilkinson Microwave Anisotropy Probe and the Sloan digital sky survey, Physical Review Letters, Vol: 95, ISSN: 1079-7114
We demonstrate that combining cosmic microwave background anisotropy measurements from the 1st year Wilkinson Microwave Anisotropy Probe observations with clustering data from the Sloan galaxy redshift survey yields an indication for primordial anisotropies in the cosmological neutrino background.
Lazarides G, Ruiz de Austri R, Trotta R, 2004, Constraints on a mixed inflaton and curvaton scenario for the generation of the curvature perturbation, Physical Review D, Vol: 70, ISSN: 1550-7998
We consider a simple supersymmetric grand unified model which naturally solves the strong CP and μ 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 a curvaton. In contrast to the standard curvaton hypothesis, both the inflaton and the curvaton contribute to the total curvature perturbation. The model predicts the existence of an isocurvature perturbation, too, which has mixed correlation with the adiabatic one. The cold dark matter of the Universe is mostly constituted by axions, which are produced at the QCD phase transition, plus a small amount of lightest sparticles. The predictions of the model are confronted with the first-year Wilkinson microwave anisotropy probe and other cosmic microwave background radiation data. We analyze in detail two representative choices of parameters for our model 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 amplitude of the adiabatic perturbation must be smaller than about 67% and the amplitude of the partial curvature perturbation from the curvaton smaller than 43.2×10−5 (both 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 about 50 to 1. For the second choice of parameters examined, 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 about 107 to 1). We conclude that in the present framework the perturbations must be dominated by the adiabatic component from the inflaton.
Rocha G, Trotta R, Martins CJAP, et al., 2004, Measuring α in the early Universe:: cosmic microwave background polarization, re-ionization and the Fisher matrix analysis, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol: 352, Pages: 20-38, ISSN: 0035-8711
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- Citations: 72
Martins CJAP, Melchiorri A, Rocha G, et al., 2004, WMAP constraints on varying α and the promise of reionization, PHYSICS LETTERS B, Vol: 585, Pages: 29-34, ISSN: 0370-2693
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- Citations: 65
Trotta R, Hansen SH, 2004, Constraining the helium abundance with CMB data, Physical Review D, Vol: 69, ISSN: 1550-7998
We consider for the first time the ability of present-day cosmic microwave background (CMB) anisotropies data to determine the primordial helium mass fraction Yp. We find that CMB data alone give the confidence interval 0.160<Yp<0.501 (at 68% C.L.). We analyze 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 Yp 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.
Trotta R, 2003, The cosmological constant and the paradigm of adiabaticity, New Astronomy Reviews, Vol: 47, Pages: 769-774, ISSN: 1872-9630
We discuss the value of the cosmological constant as recovered from cosmic microwave background (CMB) and large scale structure (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% (2σ c.l.).
Rocha G, Trotta R, Martins CJAP, et al., 2003, New constraints on varying α, 2nd CMBNet Workshop on Science and Parameter Extraction, Publisher: ELSEVIER SCI LTD, Pages: 863-869, ISSN: 1387-6473
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- Citations: 27
Trotta R, Riazuelo A, Durrer R, 2003, Cosmological constant and general isocurvature initial conditions, Physical Review D, Vol: 67, ISSN: 0556-2821
We investigate in detail the question of whether a nonvanishing cosmological constant is required by the present-day cosmic microwave background and large scale structure data when general isocurvature initial conditions are taken into account. We also discuss the differences between the usual Bayesian and the frequentist approaches in data analysis. We show that the Cosmic Background Explorer (COBE)-normalized matter power spectrum is dominated by the adiabatic mode and therefore breaks the degeneracy between initial conditions which is present in the cosmic microwave background anisotropies. We find that in a flat universe the Bayesian analysis requires ΩΛ≠0 to more than 3σ, while in the frequentist approach ΩΛ=0 is still within 3σ for a value of h<~0.48. Both conclusions hold regardless of the initial conditions.
Bowen R, Hansen SH, Melchiorri A, et al., 2002, The impact of an extra background of relativistic particles on the cosmological parameters derived from the cosmic microwave background, MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Vol: 334, Pages: 760-768, ISSN: 0035-8711
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- Citations: 86
Martins CJAP, Melchiorri A, Trotta R, et al., 2002, Measuring α in the early universe:: CMB temperature, large-scale structure, and Fisher matrix analysis -: art. no. 023505, PHYSICAL REVIEW D, Vol: 66, ISSN: 0556-2821
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- Citations: 51
Trotta R, Riazuelo A, Durrer R, 2001, Cosmic microwave background anisotropies with mixed isocurvature perturbations, PHYSICAL REVIEW LETTERS, Vol: 87, ISSN: 0031-9007
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- Citations: 60
Trotta R, Riazuelo A, Durrer R, 2001, Cosmic microwave background anisotropies with mixed isocurvature perturbations, Physical Review Letters, Vol: 87, Pages: 2313011-2313014, ISSN: 0031-9007
The estimations of cosmological parameters with regard to the latest high quality data of the cosmic microwave background anisotropies were discussed. Some cosmological parameters were chosen to vary and others were kept fixed to limit the computational effort. The calibration and the beam size uncertainties were taken into account as two additional parameters of the problem. The use of cosmic microwave background (CMB) data along with cosmological parameters which differ from the ones preferred by adiabatic perturbations, was shown. It was also found that the range of cosmological parameters that can fit the CMB anisotropy data, widen to such an extent that they become meaningless by allowing for generic initial conditions.
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