Cosmological Constraints on Non-flat Exponential $f(R)$ Gravity

Abstract

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

arXiv comment16 pages, 3 figures, accepted for publication in the Astrophysical Journal

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