# Probing Cosmic Acceleration by Using Model-Independent Parametrizations and Three Kinds of Supernova Statistics Techniques

## TL;DR

This paper investigates the evolution of dark energy's equation of state using model-independent parametrizations and various supernova data analysis techniques, confirming the consistency of the cosmological constant and exploring methodological impacts on constraints.

## Contribution

It introduces and compares three methods for binning redshift data and three supernova statistical techniques, assessing their effects on dark energy parameter constraints.

## Key findings

- Dark energy equation of state remains consistent with -1 at 1σ confidence.
- The 'free Δz' model yields the smallest error bars with magnitude statistics.
- Improved flux statistics suggest a universe with the slowest cosmic acceleration.

## Abstract

In this work, we explore the evolution of the dark energy equation of state {\omega} by using Chevalliear-PolarskiLinder (CPL) parametrization and the binned parametrizations. For binned parametrizations, we adopt three methods to choose the redshift interval: I. Ensure that "{\Delta}z = const", where {\Delta}z is the width of each bin; II.Ensure that "n{\Delta}z = const", where n is the number of SNIa in each bin; III. Treat redshift discontinuity points as models parameters, i.e. "free {\Delta}z". For observational data, we adopt JLA type Ia supernova (SNIa) samples, SDSS DR12 data, and Planck 2015 distance priors. In particular, for JLA SNIa samples, we consider three statistic techniques: I. Magnitude statistics, which is the traditional method; II. Flux statistics, which reduces the systematic uncertainties of SNIa; III. Improve flux statistics, which can reduce the systematic uncertainties and give tighter constrains at the same time. The results are as follows: (1) For all the cases, {\omega} = -1 is always satisfied at 1{\sigma} confidence regions; It means that {\Lambda}CDM is still favored by current observations. (2) For magnitude statistics, "free {\Delta}z" model will give the smallest error bars; this conclusion does not hold true for flux statistics and improved flux statistic. (3) The improved flux statistic yields a largest present fractional density of matter {\Omega}m; in addition, this technique will give a largest current deceleration parameter q0 , which reveals a universe with a slowest cosmic acceleration.