A new test of $f(R)$ gravity with the cosmological standard rulers in radio quasars

Understand

As an important candidate gravity theory alternative to dark energy, a class of $f(R)$ modified gravity, which introduces a perturbation of the Ricci scalar $R$ in the Einstein-Hilbert action, has been extensively applied to cosmology to explain the acceleration of the universe.

• In this paper, we focus on the recently-released VLBI observations of the compact structure in intermediate-luminosity quasars combined with the angular-diameter-distance measurements from galaxy clusters, which consists of 145 data points performing as individual cosmological standard rulers in the redshift range $0.023\le z\le 2.80$, to investigate observational constraints on two viable models in $f(R)$ theories within the Palatini formalism: $f_1(R)=R-\frac{a}{R^b}$ and $f_2(R)=R-\frac{aR}{R+ab}$.
• We also combine the individual standard ruler data with the observations of CMB and BAO, which provides stringent constraints.
• Furthermore, two model diagnostics, $Om(z)$ and statefinder, are also applied to distinguish the two $f(R)$ models and $\Lambda$CDM model.