Cosmological Constraints on Nonflat Exponential f(R) Gravity

We explore the viable $f(R)$ gravity models in FLRW backgrounds with a free spatial curvature parameter $\Omega_{K}$. In our numerical calculation, we concentrate on exponential model of $f(R) = R - \lambda R_{ch}(1-\exp{(-R/R_{ch}}))$, where $R_{ch}$ is characteristic scale, which independent $\Omega_K$, and $\lambda$ corresponds to parameter, while $R_{ch}\lambda=2\Lambda$ $\Lambda$ cosmological constant. particular, study evolutions dark energy density equation state for open, flat closed universe, compare those $\Lambda$CDM. From current observational data, find that $\lambda^{-1}=0.42927^{+0.39921}_{-0.32927}$ at 68$\%$ C.L $\Omega_K=-0.00050^{+0.00420}_{-0.00414}$ 95$\%$ C.L. model. By using Akaike information criterion (AIC), Bayesian (BIC) Deviance Information Criterion (DIC), conclude there no strong preference between $\Lambda$CDM non-flat universe.