Cosmological Constraints on Nonflat Exponential f(R) Gravity

Abstract

Abstract We explore the viable f(R) gravity models in FLRW backgrounds with a free spatial curvature parameter Ω K . In our numerical calculation, we concentrate on the exponential f(R) model of f ( R ) = R − λ R ch ( 1 − exp ( − R / R ch ) ) , where R ch is the characteristic curvature scale, which is independent of Ω K , and λ corresponds to the model parameter, while R ch λ = 2Λ with Λ 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 universes, and compare with those for ΛCDM. From the current observational data, we find that λ − 1 = 0.42927 − 0.32927 + 0.39921 at 68% C.L. and Ω K = − 0.00050 − 0.00414 + 0.00420 at 95% C.L. in the exponential f(R) model. By using the Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion, we conclude that there is no strong preference between the exponential f(R) gravity and ΛCDM models in the nonflat universe.