We compute the Bayesian evidence for models considered in the main analysis of Planck cosmic microwave background data. By utilizing carefully defined nearest-neighbor distances in parameter space, we reuse the Monte Carlo Markov chains already produced for parameter inference to compute Bayes factors B for many different model-data set combinations. The standard 6-parameter flat cold dark matter model with a cosmological constant (ΛCDM) is favored over all other models considered, with curvature being mildly favored only when cosmic microwave background lensing is not included. Many alternative models are strongly disfavored by the data, including primordial correlated isocurvature models (lnB=-7.8), nonzero scalar-to-tensor ratio (lnB=-4.3), running of the spectral index (lnB=-4.7), curvature (lnB=-3.6), nonstandard numbers of neutrinos (lnB=-3.1), nonstandard neutrino masses (lnB=-3.2), nonstandard lensing potential (lnB=-4.6), evolving dark energy (lnB=-3.2), sterile neutrinos (lnB=-6.9), and extra sterile neutrinos with a nonzero scalar-to-tensor ratio (lnB=-10.8). Other models are less strongly disfavored with respect to flat ΛCDM. As with all analyses based on Bayesian evidence, the final numbers depend on the widths of the parameter priors. We adopt the priors used in the Planck analysis, while performing a prior sensitivity analysis. Our quantitative conclusion is that extensions beyond the standard cosmological model are disfavored by Planck data. Only when newer Hubble constant measurements are included does ΛCDM become disfavored, and only mildly, compared with a dynamical dark energy model (lnB∼+2).

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Accurate and sensitive measurements of higher order cumulants open up new approaches to pion interferometry. It is now possible to test whether a given theoretical prediction can match cumulants of both second and third order. Our consistency test utilizes a new sampling technique combining theoretically predicted functions with experimentally determined weights in a quasi -Monte Carlo approach. Testing a simplified version of a quantum statistics-based framework of Bose-Einstein correlations with this technique, we find that predictions for third order cumulants differ significantly from UA1 data. This discrepancy may point the way to more detailed dynamical information.[S0031-9007(97)03528-X] PACS numbers: 13.85. Hd, 05.30.Jp, 12.40.Ee, 25.75.Gz Pion interferometry has been a vital part of multiparticle physics for several decades [1]. While traditionally experimental effort in this field has centered around second order correlations, much progress has been made recently in accurately quantifying higher order correlations by means of so-called correlation integrals [2], to the point where these now yield statistically significant conclusions not only for moments but also for higher order cumulants. Because cumulants are so sensitive to details of the dynamics, they represent a stringent testing ground for proposed theoretical models.A number of theoretical predictions for higher orders exist [3][4][5]. In particular, Andreev, Plümer, and Weiner (APW) [6] have suggested a very general quantumstatistical framework, based on the classical source current formalism applied successfully in quantum optics. Its basic assumptions are (1) a Gaussian density functional for the classical random currents and (2) isotropy in isospin space. These two assumptions determine all higher order correlation functions in terms of the basic correlator, independent of the structure of the sources. All further assumptions concern only a more detailed specification of the space-time evolution of the sources. Thus, the APW framework includes as special cases more specific models of Bose-Einstein correlations such as the GKW model [7] and the approach of Biyajima et al. [4]. Because the APW model is so important, we test a simple version of its predictions below. It will also serve as an example to show how our approach works.While higher order cumulant measurements are valuable in their own right, they can be used to even greater effect in consistency checks: once an assumed parametrization is found to fit the second order data, the same set of parameter values ought to fit all predicted higher order correlations as well. Departing from tried and tested ways, we therefore concentrate not so much on numerical values of source parameters, but rather on utilizing their required constancy over cumulants of different orders to test for consistency and ultimately falsifiability of a given theoretical prediction.Pion interferometry measures correlations in terms of pair variables such as three-or four-momentum differences of two particles. In...

We have made a detailed and quantitative study of dilepton production via bremsstrahlung of a virtual photon during collisions of two free pions. Most calculations of electromagnetic radiation from strong interaction processes rely on the soft photon approximation ͑SPA͒. The conditions underlying this approximation are generally violated when dilepton spectra are calculated in terms of their invariant mass, so that an approach going beyond the SPA becomes necessary. Superseding previous derivations, we derive an exact formula for the bremsstrahlung cross section. The resulting formulation is compared to various forms based on the SPA, the two-particle phase space approximation, and Rückl's formula using a relativistic one boson exchange ͑OBE͒ model. Within the OBE approach, we show that approximations to the bremsstrahlung dilepton cross sections often differ greatly from the exact result; discrepancies become greater both with rising temperature and with invariant mass. Integrated dilepton production rates are overestimated by Rückl-based approximations by factors 1.5-8.0. The largest discrepancies occur for the reaction ϩ ϩ → ϩ ϩ l ϩ l Ϫ , where such approximations overestimate the exact rate by factors ranging from 2 to 30 for invariant masses between 10 and 500 MeV. Our findings, combined with recent estimates of the Landau-Pomeranchuk effect, indicate that bremsstrahlung dilepton rates in ultrarelativistic heavy ion collisions should be even more suppressed than had been thought before.