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

TL;DR

The study jointly constrains dynamical dark energy and $f(R)$ gravity using diverse distance probes, including FRBs, SNe Ia, BAO, CC, and CMB. It employs a CPL form $w(z)=w_0+w_a(1-a)$ for the $w_0w_a$CDM model and a perturbative $f(R)$ framework with three viable realizations (Hu-Sawicki, Starobinsky, ArcTanh) governed by the deviation parameter $b$. The resulting constraints yield $w_0=-0.866\,\pm\,0.060$ and $w_a=-0.37^{+0.27}_{-0.25}$; for the $f(R)$ models, $b=0.199\pm0.082$ (Hu-Sawicki), $b=0.690^{+0.200}_{-0.130}$ (Starobinsky), and $b=0.193\pm0.080$ (ArcTanh). The analysis reveals that SN Ia and BAO dataset choices significantly affect model preferences, with DESY5 and DESI favoring $w_0w_a$CDM and $f(R)$, while PantheonPlus and BOSS prefer ΛCDM, underscoring the importance of dataset selection for cosmological model discrimination and highlighting FRBs as a powerful distance probe.

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 $Λ$CDM model.

Figures (2)

• Figure 1: The $\mathrm{DM}_{\mathrm{IGM}}$ as a function of redshift for the localized FRBs. The orange points correspond to the 112 selected FRBs from the 125 localized FRBs, while the 13 purple points represent those excluded due to not satisfying the selection criteria. The blue curve denotes the theoretical calculation from the results of Planck 2018 2020AA...641A...6P assuming the flat $\Lambda$CDM cosmology.
• Figure 2: The Hubble parameter $H(z)$ as a function of redshift $z$ based on the cosmic chronometer data we use. The error bars represent the $1\sigma$ CL, which include contributions from both systematic and statistical uncertainties. The blue curve denote the theoretical predictions from Planck 2018 2020AA...641A...6P.