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 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 universes, 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 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 ?CDM models in the nonflat universe.

Automated summary

This study investigates viable f(R) gravity models in FLRW backgrounds with a free spatial curvature parameter Omega(K). Numerical calculations focus on the exponential f(R) model, finding no strong preference between exponential f(R) gravity and ΛCDM models in the nonflat universe.