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In this work, we will be testing four different general  f(R) -gravity models, two of which are the more realistic models (namely the Starobinsky and the Hu–Sawicki models), to determine if they are viable alternative models to pursue a more vigorous constraining test upon them. For the testing of these models, we use 359 low- and intermediate-redshift Supernovae Type 1A data obtained from the SDSS-II/SNLS2 Joint Light-curve Analysis (JLA). We develop a Markov Chain Monte Carlo (MCMC) simulation to find a best-fitting function within reasonable ranges for each  f(R) -gravity model, as well as for the Lambda Cold Dark Matter (   $$\varLambda $$   Λ    CDM) model. For simplicity, we assume a flat universe with a negligible radiation density distribution. Therefore, the only difference between the accepted    $$\varLambda $$   Λ    CDM model and the  f(R) -gravity models will be the dark energy term and the arbitrary free parameters. By doing a statistical analysis and using the    $$\varLambda $$   Λ    CDM model as our “true model”, we can obtain an indication whether or not a certain  f(R) -gravity model shows promise and requires a more in-depth view in future studies. In our results, we found that the Starobinsky model obtained a larger likelihood function value than the    $$\varLambda $$   Λ    CDM model, while still obtaining the cosmological parameters to be    $$\varOmega _{m} = 0.268^{+0.027}_{-0.024}$$Ω  m   =  0  .   268   -  0.024    +  0.027for the matter density distribution and    $${\bar{h}} = 0.690^{+0.005}_{-0.005}$$h    ¯    =  0  .   690   -  0.005    +  0.005for the Hubble uncertainty parameter. We also found a reduced Starobinsky model that are able to explain the data, as well as being statistically significant.

Viability tests of f(R)-gravity models with Supernovae Type 1A data