The reconstruction of dark energy with Ridge Regression Approach

Abstract

It may be determined by non-parametric method if the dark energy evolves with time. We propose a method of combining PCA and biased estimation on the basis of ridge regression analysis to reconstruct parameters, meanwhile we present an interesting principal component selection criterion to avoid the arbitrariness of principal component selections, and use numerical integral by Lagrange interpolation to linearize the luminosity distance integral formula in nearly flat space to avoid instability of derivative for functional data. We get the preliminary test results that shows if $\Delta \overline{w}(z)=\overline{\left|1+w(z)\right|}<=0.05$ included $w(z)=-1$, the probability of making a type I error for $w_{recon}\ne -1$ is almost zero ($1\%$) in the test; otherwise, if $\Delta \overline{w}(z)=\overline{\left|1+w(z)\right|}>0.05$, the probability of making a type I error for $w_{recon}=-1$ is not more than $10\%$. Finally, we use JLA sample to reconstruct $w(z)$, and the results reject $\mathrm{w}(\mathrm{z})\ne -1$, which is agreement with $\Lambda CDM$ model.

References in corpus (10)

• The 2.5 m Telescope of the Sloan Digital Sky Survey
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey
• Reconstructing Dark Energy
• Gaussian Process Cosmography
• The Sloan Digital Sky Survey-II Supernova Survey: Search Algorithm and Follow-up Observations
• Nonparametric Dark Energy Reconstruction from Supernova Data
• Examining the evidence for dynamical dark energy
• Features in Dark Energy Equation of State and Modulations in the Hubble Diagram

Cited by in corpus (4)

• Gaussian-process reconstructions and model building of quintom dark energy from latest cosmological observations
• A cosmological distance measure using radio-loud quasars
• Observational constraint on Dark Energy from Quantum Uncertainty
• Density perturbation and cosmological evolution in the presence of magnetic field in $f(R)$ gravity models