Inferences for f(R) Models from Late-Time Megamaser Observational Data

In this work, we study three widely used models of f(R) gravity, namely HuSawicki, Starobinsky and ArcTanh along with the standard cosmology model (CDM). For this, we employ the megamaser angular diameter distance and velocity measurements from the Megamaser Cosmology Project, which provide a purely geometric determination of the Hubble constant. We constrain the parameters using the Markov Chain Monte Carlo method. Our results show that values of the Hubble Constant, H 0, obtained for all four models are in concordance with its value obtained from other late-time observational data such as SNe Ia. The constraints on H 0 in all the models under study are restrictive and the marginalized estimates lie close to 73 km s-1 Mpc-1. The marginalized estimates of the deviation parameter, b, for the three f(R) gravity models lie close to zero. This late-time dataset, thus predicts that f(R) models mimic CDM. However, the matter density, m, remains weakly constrained for all the models with its marginalized estimate close to 0.5. Further, comparison of the four models (f(R) models and CDM) using information criteria such as Akaike Information Criterion and Bayesian Information Criterion shows that within current uncertainties, the dataset finds f(R) models statistically indistinguishable from CDM. This is consistent with the fact that the favoured value of b for each of the f(R) models lies close to zero.