Nonparametric reconstruction of dynamical dark energy via observational Hubble parameter data

We study the power of current and future observational Hubble parameter data (OHD) on nonparametric estimations of the dark energy equation of state (EoS), $w(z)$. We propose a new method by conjunction of principal component analysis and the goodness of fit criterion to reconstruct $w(z)$, ensuring the sensitivity and reliability of the extraction of features in the EoS. We also give a new error model to simulate future OHD data, to forecast the power of future OHD on the EoS reconstruction. The result shows that current OHD, despite their lesser quantity, give not only a similar power of reconstruction of dark energy compared to the result given by type Ia supernovae, but also extend the constraint on $w(z)$ up to redshift $z\simeq 2$. Additionally, a reasonable forecast of future data in greater quantity and better quality greatly enhances the reconstruction of dark energy.

Figure 1

Left: Relative error distribution for OHD. The purple and green histograms show the relative errors of unbinned 28 OHD and binned 15 OHD, and the red and blue curves are their best fits with an $m$ distribution. Their counterpart CDF and fitted CDF are shown in the inset. Right: Binned OHD and their reconstructions on $H(z)$ (top) and $w(z)$ (bottom). The shaded orange areas show the $1\sigma$ error regions if we assume a $\Lambda \mathrm{CDM}$ model. Dashed blue lines are the results from binned OHD.

Figure 2

Top left: Reconstruction of $w(z)$ by OHD’s redshift and error configurations, but assuming model 1. Also shown as the blue dashed line is the reconstruction of the OHD set, which is obviously inconsistent with model 1. The remaining three panels show the reconstruction of $w(z)$ from simulated future data, with the underlying models being $\Lambda \mathrm{CDM}$, model 1, and model 2.