Eur. Phys. J. C (2024) 84: 402
https://doi.org/10.1140/epjc/s10052-024-12774-x

Regular Article - Theoretical Physics

Analytical Gaussian process cosmography: unveiling insights into matter-energy density parameter at present

¹ Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, 741246, Nadia, West Bengal, India
² Department of Physics and Astronomy, University of the Western Cape, 7535, Cape Town, South Africa

^a bikashd18@gmail.com

Received: 13 February 2024
Accepted: 7 April 2024
Published online: 18 April 2024

Abstract

In this study, we introduce a novel analytical Gaussian Process (GP) cosmography methodology, leveraging the differentiable properties of GPs to derive key cosmological quantities analytically. Our approach combines cosmic chronometer (CC) Hubble parameter data with growth rate (f) observations to constrain the ${\mathrm{\Omega }}_{\text{m0}}$ parameter, offering insights into the underlying dynamics of the Universe. By formulating a consistency relation independent of specific cosmological models, we analyze under a flat FLRW metric and first-order Newtonian perturbation theory framework. Our analytical approach simplifies the process of Gaussian Process regression (GPR), providing a more efficient means of handling large datasets while offering deeper interpretability of results. We demonstrate the effectiveness of our methodology by deriving precise constraints on ${\mathrm{\Omega }}_{\text{m0}}{h}^2$, revealing ${\mathrm{\Omega }}_{\text{m0}}{h}^2=0.139\pm 0.017$. Moreover, leveraging $H_0$ observations, we further constrain ${\mathrm{\Omega }}_{\text{m0}}$, uncovering an inverse correlation between mean $H_0$ and ${\mathrm{\Omega }}_{\text{m0}}$. Our investigation offers a proof of concept for analytical GP cosmography, highlighting the advantages of analytical methods in cosmological parameter estimation.