Reconstruction of late-time cosmology using Principal Component Analysis

We reconstruct late-time cosmology in a model-independent manner using the technique of Principal Component Analysis (PCA). In particular, we focus on the reconstruction of the dark energy equation of state parameters from two different observational data sets, supernova type Ia data, and the Hubble parameter data. To achieve this reconstruction, we have adopted two different techniques. The first is a derived approach wherein we reconstruct the observable quantities of the data sets, namely the Hubble parameter and the supernova distance modulus from observations using PCA and subsequently reconstruct the allowed equation of state parameter. The other approach is a direct one where dark energy equation of state is reconstructed directly from the data sets. We show that a combination of PCA algorithm and calculation of correlation coefficients can be used as a tool of reconstruction. The derived approach is found to be statistically preferable over the direct approach. We have carried out the analysis with simulated data and observed data sets of Hubble parameter measurements and distance modulus measurements of type Ia supernova. The reconstructed equation of state indicates a slowly varying dark energy equation of state parameter.