The Standard siren tests of viable $f(R)$ cosmologies

TL;DR

This paper assesses whether viable $f(R)$ gravity models, specifically Hu–Sawicki and Starobinsky, can be distinguished from ΛCDM using standard sirens (SS) in addition to electromagnetic (EM) data. By constraining the models with EM datasets (PP+CC, Planck distance priors, DESI2 BAO) and then generating mock ET SS catalogs based on the EM best-fit fiducials, the authors quantify how the GW propagation friction term modifies the SS distance–redshift relation through $\beta_T(z)=\sqrt{(1+F_R0)/(1+F_R(z))}$. They find that SS data provide complementary sensitivity to the modified GW friction, improving discrimination between $f(R)$ gravity and ΛCDM, but the inferred Hubble tension remains dominated by the fiducial cosmology chosen for the SS simulations. For Hu–Sawicki, several EM+SS combinations prefer $F_{RR0}<0$, hinting at potential instabilities and rendering the model less favored; for Starobinsky, EM constraints are nearly symmetric across branches, while SS introduce mild asymmetries and DESI2 data strongly distinguish Starobinsky from ΛCDM. Overall, future independent SS observations will be crucial for a definitive assessment of $f(R)$ gravity as an alternative to ΛCDM.

Abstract

We constrain the Hu-Sawicki and Starobinsky $f(R)$ gravity models utilizing current electromagnetic (PP+CC, Planck and DESI2) datasets and simulate standard siren catalogs based on the resulting best-fit parameters. We demonstrate that the simulated SS data provide complementary sensitivity to the modified gravitational wave propagation friction term, thereby enhancing the discriminating power between $f(R)$ gravity and the $Λ$CDM model. However, we note that standard sirens do not offer a viable resolution to the Hubble tension in this analysis, as the inferred constraints are predominantly driven by the fiducial cosmologies adopted in the simulations. Regarding the specific models, we find that for the Hu-Sawicki scenario, several data combinations favor $F_{RR0}<0$, implying potential theoretical instabilities. And, for the Starobinsky model, while EM-only constraints are nearly symmetric between the two parameter branches ($b<0$ and $b>0$), the inclusion of SS constraints introduces mild asymmetries, revealing the sensitivity of SS observables to the curvature dependence of the theory. Future truly independent standard siren observations would be crucial for a definitive assessment of $f(R)$ gravity as an alternative to $Λ$CDM.

Figures (4)

• Figure 1: Left: Comparison between luminosity-distance measurements from real and simulated datasets. The cyan points with error bars correspond to the PantheonPlus sample (real SNe Ia data). The gray/orange/blue points with error bars show the simulated standard siren datasets $\mathrm{SS}_{\rm DESI2}/\mathrm{SS}_{\rm PP+CC}/\mathrm{SS}_{\rm Planck}$, respectively. The gray/orange/blue solid curves represent the corresponding fiducial luminosity-distance relations used to generate the mock catalogs. Right: One and two dimensional marginalized posteriors (with $1\sigma$ and $2\sigma$ confidence regions) for the parameters of $\Lambda$CDM and the Hu-Sawicki model. The simulated datasets $\Lambda$CDM:$\mathrm{SS}_{\rm DESI2}$/$\Lambda$CDM:$\mathrm{SS}_{\rm PP+CC}$/$\Lambda$CDM:$\mathrm{SS}_{\rm Planck}$ are generated assuming $\Lambda$CDM with the EM best-fit fiducial parameters $(\Omega_{m0}^{\rm fid},H_0^{\rm fid})=(0.348,72.99)/(0.298,69.50)/(0.300,67.89)$. For the Hu-Sawicki simulations, we adopt $(\Omega_{m0}^{\rm fid},H_0^{\rm fid},b^{\rm fid})=(0.348,72.99,0)$, $(0.296,69.37,-0.06\times 10^{-3})$, and $(0.301,67.95,0.15\times 10^{-3})$ for HS:$\mathrm{SS}_{\rm PP+CC}$, HS:$\mathrm{SS}_{\rm DESI2}$, and HS:$\mathrm{SS}_{\rm Planck}$, respectively.
• Figure 2: Same as Fig. \ref{['fr1tri']}, but for the Starobinsky1 ($b<0$) and Starobinsky2 ($b>0$) models. For the corresponding standard siren simulations, the EM best-fit values from PP+CC/Planck/DESI2 are adopted as fiducial (baseline) parameters. Specifically, the mock catalogs Star1:$\mathrm{SS}_{\rm PP+CC}$, Star1:$\mathrm{SS}_{\rm DESI2}$, and Star1:$\mathrm{SS}_{\rm Planck}$ are generated using $(\Omega_{m0}^{\rm fid},H_0^{\rm fid},b^{\rm fid})=(0.293,73.05,-1.05\times10^{-3})$, $(0.325,64.32,-0.99\times10^{-3})$, and $(0.301,67.97,-0.53\times10^{-3})$, respectively. Likewise, the mock catalogs Star2:$\mathrm{SS}_{\rm PP+CC}$, Star2:$\mathrm{SS}_{\rm DESI2}$, and Star2:$\mathrm{SS}_{\rm Planck}$ are generated using $(\Omega_{m0}^{\rm fid},H_0^{\rm fid},b^{\rm fid})=(0.293,73.08,1.05\times10^{-3})$, $(0.325,64.32,0.99\times10^{-3})$, and $(0.301,67.97,0.53\times10^{-3})$, respectively.
• Figure 3: The evolutions of $w_{\rm eff}$ for the Hu-Sawicki (left), Starobinsky1 (middle) and Starobinsky2 (right) models, which are based on the the $1\sigma$ regimes of PP+CC+SS$_{\rm \Lambda CDM:PP+CC}$/PP+CC+SS$_{\rm PP+CC}$, DESI2+SS$_{\rm DESI2}$ and Planck+SS$_{\rm Planck}$ constraining results.
• Figure 4: The evolutions of $F_{R}$, $F_{RR}$, $r$, and $m$ for the Hu-Sawicki (upper), Starobinsky1 (middle) and Starobinsky2 (bottom) models, which are based on the the $1\sigma$ regimes of PP+CC+SS$_{\rm \Lambda CDM:PP+CC}$/PP+CC+SS$_{\rm PP+CC}$, DESI2+SS$_{\rm DESI2}$ and Planck+SS$_{\rm Planck}$ constraining results.