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@Article{VitentiPenn:2015:GeReRe,
               author = "Vitenti, S. D. P. and Penna-Lima, Mariana",
          affiliation = "{Institut d'Astrophysique de Paris} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)}",
                title = "A general reconstruction of the recent expansion history of the 
                         universe",
              journal = "Journal of Cosmology and Astroparticle Physics",
                 year = "2015",
               volume = "2015",
               number = "9",
                pages = "045",
                month = "Sept.",
             keywords = "baryon acoustic oscillations, dark energy theory, supernova type 
                         Ia-standard candles.",
             abstract = "Distance measurements are currently the most powerful tool to 
                         study the expansion history of the universe without specifying its 
                         matter content nor any theory of gravitation. Assuming only an 
                         isotropic, homogeneous and flat universe, in this work we 
                         introduce a model-independent method to reconstruct directly the 
                         deceleration function via a piecewise function. Including a 
                         penalty factor, we are able to vary continuously the complexity of 
                         the deceleration function from a linear case to an arbitrary 
                         (n+1)-knots spline interpolation. We carry out a Monte Carlo (MC) 
                         analysis to determine the best penalty factor, evaluating the 
                         bias-variance trade-off, given the uncertainties of the SDSS-II 
                         and SNLS supernova combined sample (JLA), compilations of baryon 
                         acoustic oscillation (BAO) and H(z) data. The bias-variance 
                         analysis is done for three fiducial models with different features 
                         in the deceleration curve. We perform the MC analysis generating 
                         mock catalogs and computing their best-fit. For each fiducial 
                         model, we test different reconstructions using, in each case, more 
                         than 104 catalogs in a total of about 5 105. This investigation 
                         proved to be essential in determining the best reconstruction to 
                         study these data. We show that, evaluating a single fiducial 
                         model, the conclusions about the bias-variance ratio are 
                         misleading. We determine the reconstruction method in which the 
                         bias represents at most 10% of the total uncertainty. In all 
                         statistical analyses, we fit the coefficients of the deceleration 
                         function along with four nuisance parameters of the supernova 
                         astrophysical model. For the full sample, we also fit H0 and the 
                         sound horizon rs(zd) at the drag redshift. The bias-variance 
                         trade-off analysis shows that, apart from the deceleration 
                         function, all other estimators are unbiased. Finally, we apply the 
                         Ensemble Sampler Markov Chain Monte Carlo (ESMCMC) method to 
                         explore the posterior of the deceleration function up to redshift 
                         1.3 (using only JLA) and 2.3 (JLA+BAO+H(z)). We obtain that the 
                         standard cosmological model agrees within 3\σ level with the 
                         reconstructed results in the whole studied redshift intervals. 
                         Since our method is calibrated to minimize the bias, the error 
                         bars of the reconstructed functions are a good approximation for 
                         the total uncertainty.",
                  doi = "10.1088/1475-7516/2015/09/045",
                  url = "http://dx.doi.org/10.1088/1475-7516/2015/09/045",
                 issn = "1475-7516",
             language = "en",
           targetfile = "2015_vitenti.pdf",
        urlaccessdate = "27 nov. 2020"
}


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