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

Abstract

Abstract 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 ( $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM) model. For simplicity, we assume a flat universe with a negligible radiation density distribution. Therefore, the only difference between the accepted $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> 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 $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> 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 $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Λ</mml:mi></mml:math> CDM model, while still obtaining the cosmological parameters to be $$\varOmega _{m} = 0.268^{+0.027}_{-0.024}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ω</mml:mi><mml:mi>m</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>268</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.024</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.027</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> for the matter density distribution and $${\bar{h}} = 0.690^{+0.005}_{-0.005}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover><mml:mo>=</mml:mo><mml:mn>0</mml:mn><mml:mo>.</mml:mo><mml:msubsup><mml:mn>690</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>0.005</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mn>0.005</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math> for the Hubble uncertainty parameter. We also found a reduced Starobinsky model that are able to explain the data, as well as being statistically significant.

Topics & Concepts