A general reconstruction of the recent expansion history of the universe

Abstract

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 biasvariance 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 4 catalogs in a total of about 5 × 10 5 . 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 0 and the sound horizon r s (z d ) 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.

Null test of the cosmic curvature usingH(z)and supernovae data

“…There are many different methodologies to reconstruct functions from the data. For a brief analysis, see [12]. Since we should use a nonparametric approach to smooth the data and to reconstruct the derivative, the so-called Gaussian processes [13][14][15][16] are very suitable for our purpose.…”

Model-independent constraints on dark energy evolution from low-redshift observations

“…Some of the most studied approaches are Principal Component Analysis (PCA) (Huterer & Starkman 2003), Generic Algorithm (GA) (Bogdanos & Nesseris 2009;Nesseris & Shafieloo 2010), Gaussian Processes (GP) (Seikel et al 2012;Shafieloo et al 2012) etc. See (Vitenti & Penn-Lima 2015) for a nice review on different approaches for reconstruction. Cosmographic approach to constrain the background evolution of the Universe is a simple and yet useful approach (Visser et al 2004).…”

Observational constraints on the jerk parameter with the data of the Hubble parameter

“…The kinematic approach is advantageous since it does not need any model specific assumptions like the composition of the universe. It is described by a metric theory of gravity and is assumed that the universe is homogeneous and isotropic at cosmological scales (for review on this topic, see [22][23][24][25][26][27][28][29][30][31]). In the literature, there have been many attempts to constrain the present values of H, q and j by parametrizing q or j [31][32][33][34][35][36][37][38][39][40][41][42].…”