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Constraints on Non-Flat Starobinsky f(R) Dark Energy Model

Authors:	Chao-Qiang Geng Yan-Ting Hsu Jhih-Rong Lu

Affiliation:	1.School of Science, Chongqing University of Posts & Telecommunications, Chongqing 400065, China;2.Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwan; (Y.-T.H.); (J.-R.L.);3.Synergetic Innovation Center for Quantum Effects and Applications (SICQEA), Hunan Normal University, Changsha 410081, China

Abstract:	We study the viable Starobinsky $f (R)$ dark energy model in spatially non-flat FLRW backgrounds, where $f (R) = R - λ R_{c h} [1 - {(1 + R^{2} / R_{c h}^{2})}^{- 1}]$ with $R_{c h}$ and $λ$ representing the characteristic curvature scale and model parameter, respectively. We modify CAMB and CosmoMC packages with the recent observational data to constrain Starobinsky $f (R)$ gravity and the density parameter of curvature $Ω_{K}$ . In particular, we find the model and density parameters to be $λ^{- 1} < 0.283$ at 68% C.L. and $Ω_{K} = - 0 . 00099_{- 0.0042}^{+ 0.0044}$ at 95% C.L., respectively. The best $χ^{2}$ fitting result shows that $χ_{f (R)}^{2} ≲ χ_{Λ C D M}^{2}$ , indicating that the viable $f (R)$ gravity model is consistent with $Λ$ CDM when $Ω_{K}$ is set as a free parameter. We also evaluate the values of AIC, BIC and DIC for the best fitting results of $f (R)$ and $Λ$ CDM models in the non-flat universe.

Keywords:	modified gravitational theory non-flat spacetime