Comparison of piecewise-constant methods for dark energy

Abstract

We compare four different methods that can be used to analyze the type Ia supernovae (SnIa) data, ie to use piecewise-constant functions in terms of: the dark energy equation of state $w(z)$, the deceleration parameter $q(z)$, the Hubble parameter $H(z)$ and finally the luminosity distance $d_L$. These four quantities cover all aspects of the accelerating Universe, ie the phenomenological properties of dark energy, the expansion rate (first and second derivatives) of the Universe and the observations themselves. For the first two cases we also perform principal component analysis (PCA) so as to decorrelate the parameters, while for the last two cases we use novel analytic expressions to find the best-fit parameters. In order to test the methods we create mock SnIa data (2000 points, uniform in redshift $z\in [0,1.5]$) for three fiducial cosmologies: the cosmological constant model ($\Lambda$CDM), a linear expansion of the dark energy equation of state parameter $w(a)=w_0+w_a(1-a)$ and the Hu-Sawicki $f(R)$ model. We find that if we focus on the two mainstream approaches for the PCA, i.e. $w(z)$ and $q(z)$, then the best piecewise-constant scheme is always $w(z)$. Finally, to our knowledge the piecewise-constant method for $H(z)$ is new in the literature, while for the rest three methods we present several new analytic expressions.

arXiv comment23 pages, 3 figures, 8 tables. Changes match published version

References in corpus (15)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Uncorrelated Estimates of Dark Energy Evolution
• Parameterization of Dark-Energy Properties: a Principal-Component Approach
• Measuring Baryon Acoustic Oscillations along the line of sight with photometric redshifs: the PAU survey
• Is the Jeffreys' scale a reliable tool for Bayesian model comparison in cosmology?
• Observational constraints on viable f(R) parametrizations with geometrical and dynamical probes
• Curvature vs Distances: testing the FLRW cosmology
• Cosmological tests of General Relativity: a principal component analysis
• Precise photometric redshifts with a narrow-band filter set: The PAU Survey at the William Herschel Telescope
• Dark Energy in Practice
• Comparative analysis of model-independent methods for exploring the nature of dark energy
• Testable dark energy predictions from current data
• Observational constraints on dark energy with a fast varying equation of state
• To Bin or Not To Bin: Decorrelating the Cosmic Equation of State

Cited by in corpus (6)

• A Comparison of Thawing and Freezing Dark Energy Parametrizations
• Conjoined constraints on modified gravity from the expansion history and cosmic growth
• Gaussian processes reconstruction of dark energy from observational data
• How does the cosmic large-scale structure bias the Hubble diagram?
• Model-independent curvature determination with 21cm intensity mapping experiments
• Euclid: Forecast constraints on consistency tests of the $\Lambda$CDM model