In this work, we consider four $f(R)$ gravity models—the Hu-Sawicki, Starobinsky, Exponential and Tsujikawa models—and use a range of cosmological data, together with Markov Chain Monte Carlo sampling techniques, to constrain the associated model parameters. Our main aim is to compare the results we get when ${\mathrm{\Omega }}_{k,0}$ is treated as a free parameter with their counterparts in a spatially flat scenario. The bounds we obtain for ${\mathrm{\Omega }}_{k,0}$ in the former case are compatible with a flat geometry. It appears, however, that a higher value of the Hubble constant $H_0$ allows for more curvature. Indeed, upon including in our analysis a Gaussian likelihood constructed from the local measurement of $H_0$, we find that the results favor an open universe at a little over $1\sigma$. This is perhaps not statistically significant, but it underlines the important implications of the Hubble tension for the assumptions commonly made about spatial curvature. We note that the late-time deviation of the Hubble parameter from its $\mathrm{\Lambda }\mathrm{CDM}$ equivalent is comparable across all four models, especially in the nonflat case. When ${\mathrm{\Omega }}_{k,0}=0$, the Hu-Sawicki model admits a smaller mean value for ${\mathrm{\Omega }}_{\mathrm{cdm},0}{h}^2$, which increases the said deviation at redshifts higher than unity. We also study the effect of a change in scale by evaluating the growth rate at two different wave numbers $k_{†}$. Any changes are, on the whole, negligible, although a smaller $k_{†}$ does result in a slightly larger average value for the deviation parameter $b$.

• Received 8 June 2021
• Accepted 22 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.123503