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

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 of other cosmological parameters such as the q ( z ) and the redshift of transition to the accelerated expansion. We see that the reconstructed evolution of q ( z ) also indicates that lower-order polynomial kernels are a better choice for the reconstruction compared to the stationary kernels.