Constraints On Cosmological Parameters By MCMC Methods In F(R) Gravity Theory

In 1998,the precise measurements of the redshift-apparent magnitude relation of high-redshift supernovae led to the discovery of the accelerated expansion of the Universe.This discovery was later confirmed by other observations,such as the cosmic microwave background,and these observational results suggest the existence of unknown energy,called dark energy,in our Universe.The cosmological constant of theΛCDM model in general relativity provides a simple way to account for dark energy,which is in good agreement with the observations.However,it also suffers from several theoretical difficulties.Despite many successes of standard cosmology,dark energy is still one of the biggest mysteries in modern physics.Modified gravity is one way to explain the accelerated expansion of the Universe without using the dark energy hypothesis.f（R）gravity is one of the modified gravity theories,and we extend the Einstein-Hilbert action of general relativity to the function of the Ricci scalar.The earlier works have proposed cosmological models of f（R）gravity.In this thesis,we investigate the constraints on parameters of the Hu-Sawicki model,which is one of the viable models of f（R）gravity,based on the FLRW space-time.To estimate the model parameters,we perform the Markov Chain Monte Carlo method,combining the measurements of Cosmic Chronometer,type Ia supernovae,baryon acoustic oscillations,quasars,and gamma-ray bursts.The dataset we use contains measurements of a large number of high-redshift quasars,and we consider a relation between the X-ray and UV luminosities of quasars,which allows us to constrain cosmological models in the high-redshift range.At the same time,we also investigate two cases,flat FLRW（Ω_k=0）and non-flat FLRW（Ω_k≠0）,to compare the effects of the non-zero spatial curvature on the constraint of cosmological param-eters.Moreover,we introduce a parameter b,which characterizes the deviation from theΛCDM model,and establish a formulation applicable to other models of f（R）gravity.The result of this thesis shows that under the flat FLRW metric,the Hub-ble constant and matter density parameter in Hu-Sawicki model,are H₀=68.8_-0.⁺¹.₉⁵,Ω_m=0.294_-0.⁺⁰.₀₁₅⁰⁶⁴at 68%confidence level.In flat FLRW and non-flat FLRW,the distortion parameter b in 1σis 0.060_-0⁺⁰..₀₅₃¹⁰⁸and 0.160_-0.⁺⁰.₁₁₃⁴⁰⁴.Finally,analysis of and analysis of the Akaike Information Criterion and Bayesian Information Criterion sug-gests that theΛCDM model is still the most supported model by the measurement result.