@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 abr. 2024"
}