Constraining modified gravity models with cosmological data

Abstract

In this dissertation, we looked at the cosmological constraints of some f(R)-modi ed gravity models, such as f(R) = Rn (our rst toy model), f(R) = R + Rn (our second toy model), and more realistic ones like the Starobinsky and Hu-Sawicki models. We used 236 intermediate-redshift and 123 low-redshift Supernovae Type 1A data obtained from the SDSS-II/SNLS3 Joint Light-curve Analysis (JLA), with absolute magnitudes, for the B- lter, found on the NASA Extragalactic Database (NED). We also developed a Markov Chain Monte-Carlo (MCMC) simulation to find the best- fitting luminosity distance function value for each combination of cosmological parameters, namely the matter density distribution ohm m and the Hubble uncertainty parameter h (fi rstly for the ACDM model and then for the f(R)-gravity models). We then used the ACDM model results to constrain the priors for the f(R)-gravity models. We assumed a flat universe ohm k = 0 and a radiation density distribution ohm r that is negligible to simplify these models. Therefore, the only difference between the ACDM model and f(R)-gravity models are the dark energy component and the arbitrary free parameters. This gave us an indication if there exist viable f(R)-gravity models when we compared them statistically to the results of the ACDM model. Furthermore, we developed a numerical method to solve the models to which we were not able to find an analytical solution, and incorporated it into the MCMC simulation.

We found 2 viable models, namely the Starobinsky model and a reduced version of the Starobinsky model.

Both were able to predict an accelerating universe. We also found a further three models that were able to t the data, but were statistically rejected, namely the second toy model where n is fixed to the parameter values of n = 0 and n = 2, as well as the Hu-Sawicki model. Lastly, we found a further three models that were not able to t the supernova data and as a consequence were statistically rejected, namely the first toy model, and the second toy model for fixed n-values of n = 1/2 and n = 1. Therefore, we were able to constrain the viability of some of the f(R)-gravity models with cosmological data.