Kernel dependence of the Gaussian Process reconstruction of late Universe expansion history

Abstract

In this work, we discuss model-independent reconstruction of the expansion history of the late Universe. We use Gaussian Process Regression (GPR) to reconstruct the evolution of various cosmological parameters such as Hubble parameter $H(z)$ and deceleration parameter $q(z)$ using observational data to train the GPR model. We look at the GP reconstruction of these parameters using stationary and non-stationary kernel functions. We examine the effect of the choice of kernel functions on the reconstructions. We find that using non-stationary kernels such as lower-order polynomial kernels is a better choice for the reconstruction if the training data set is noisy (such as $H(z)$ data) as shown by the log marginal likelihood analysis. We also look at the reconstructions of the derivatives of $H(z)$ and study the kernel dependence on the reconstruction other cosmological parameters such as the $q(z)$ and the redshift of transition to the accelerated expansion. We see that reconstructed evolution of $q(z)$ also indicate that lower-order polynomial kernels are a better choice for the reconstruction compared to the stationary kernels.