Cosmographic Analysis of the Rastall Gravity Model With Recent Baryon Acoustic Oscillations and Supernova Samples

Abstract

We perform a comprehensive cosmographic analysis of the Rastall gravity extension of the standard $\Lambda \mathrm{CDM}$ model within a spatially flat FLRW framework. We employ the latest observational datasets, including the DR2, cosmic chronometers (CC), and Type Ia supernova samples (PP&SH0ES, Union3, DES-5yr, and DES-Dovekie). We constrain the free parameters for the Rastall gravity model using Markov Chain Monte Carlo (MCMC) simulations implemented through the MontePython and CLASS codes, yielding robust and tightly constrained results. Our analysis reveals that the mean value of the Rastall parameter $\epsilon$ is of order ${10}^{-4}$ for the DR2+CC dataset and remains consistent with zero at the $68\%$ confidence level, suggesting that the Rastall gravity reduces to the standard general relativity description. For the DR2+CC+PP&SH0ES dataset, the constraint on $\epsilon$ undergoes a substantial change, reaching the order of ${10}^{-3}$ and exhibiting a significant $3.4\sigma$ departure from general relativity ($\epsilon =0$), also obtain the Hubble constant $H_0=73.10\pm 1.0$ km $s^{-1}$ ${\mathrm{Mpc}}^{-1}$, which shows strong agreement with the SH0ES calibration at the $68\%$ confidence level. The cosmographic parameters tend toward $j_0\approx 1$ and $s_0\approx 0$, consistent with the standard cosmological model, while the deceleration parameter lies within the range for both models, confirming accelerated expansion of the universe.