Constraining and Comparing the Dynamical Dark Energy and f(R) Modified Gravity Models with Cosmological Distance Measurements

Abstract: We constrain and compare the $w_{0}w_{a}$CDM dynamical dark energy model and three $f(R)$ modified gravity models using the current cosmological distance measurements, including 112 high-quality localized FRBs, BAO measurements from the Dark Energy Spectroscopic Instrument Data Release 2 (DESI-DR2) and the Baryon Oscillation Spectroscopic Survey Data Release 12 (BOSS-DR12), SNe Ia from the PantheonPlus compilation and the Dark Energy Survey Year 5 (DESY5) sample, cosmic chronometers (CC), and the angular scale of the first acoustic peak of the cosmic microwave background (CMB) from Planck 2018. These datasets allow us to effectively break parameter degeneracy, obtain stringent cosmological constraint results, and conduct systematic model comparison and selection. By using the FRB+PantheonPlus+DESI+CC+CMB dataset, we constrain the parameters of the dark energy equation of state in the $w_{0}w_{a}$CDM model, obtaining $w_{0} = -0.866 \pm 0.060$ and $w_{a} = -0.37^{+0.27}_{-0.25}$. For the $f(R)$ modified gravity models, the deviation parameter $b$, which characterizes departure from general relativity, is constrained to be $b = 0.199 \pm 0.082$, $b = 0.690^{+0.200}_{-0.130}$, and $b = 0.193 \pm 0.080$ for Hu-Sawicki, Starobinsky, and ArcTanh models, respectively. Besides, we compare the impacts of different SNe Ia datasets (PantheonPlus and DESY5) and BAO datasets (DESI-DR2 and BOSS-DR12) on the constraints of the cosmological models. By employing Bayesian evidence and other model selection criteria, we find that the choice of SNe Ia and BAO datasets can significantly influence the inferred preference for cosmological models. Specifically, the DESY5 and DESI datasets tend to favor $w_{0}w_{a}$CDM and $f(R)$ models, whereas the PantheonPlus and BOSS datasets show a comparatively stronger preference for the $\Lambda$CDM model.