https://insu.hal.science/insu-03644870Vitenti, S. D. P.S. D. P.VitentiIAP - Institut d'Astrophysique de Paris - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche ScientifiquePenna-Lima, M.M.Penna-LimaAPC (UMR_7164) - AstroParticule et Cosmologie - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - IN2P3 - Institut National de Physique Nucléaire et de Physique des Particules du CNRS - Observatoire de Paris - PSL - Université Paris sciences et lettres - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche ScientifiqueA general reconstruction of the recent expansion history of the universeHAL CCSD2015Astrophysics - Cosmology and Nongalactic AstrophysicsGeneral Relativity and Quantum Cosmology[SDU] Sciences of the Universe [physics]Sorbonne Université, Gestionnaire HAL 42022-04-19 14:40:302023-06-02 15:36:272022-04-19 14:40:30enJournal articles10.1088/1475-7516/2015/09/0451Distance 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 10<SUP>4</SUP> catalogs in a total of about 5× 10<SUP>5</SUP>. 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 H<SUB>0</SUB> and the sound horizon r<SUB>s</SUB>(z<SUB>d</SUB>) 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 3σ 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.