Observational constraints on Starobinsky f(R) cosmology from cosmic expansion and structure growth data
P. F. Bessa, Miguel Elias M. Campista, Armando Bernui
Abstract
Abstract The unknown physical nature of the Dark Energy motivates in cosmology the study of modifications of the gravity theory at large distances. One of these types of modifications is to consider gravity theories, generally termed as f ( R ). In this paper we use observational data to both constrain and test the Starobinsky f ( R ) model (Starobinsky in JETP Lett 86(3):157–163, 2007), using updated measurements from the dynamics of the expansion of the universe, H ( z ); and the growth rate of cosmic structures, $$[f\sigma _8](z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>f</mml:mi> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , where the distinction between the concordance $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model and modified gravity models f ( R ) becomes clearer. We use MCMC likelihood analyses to explore the parameters space of the f ( R ) model using H ( z ) and $$[f\sigma _8](z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>f</mml:mi> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> data, both individually and jointly, and further, examine which of the models best fits the joint data. To further test the Starobinsky model, we use a method proposed by Linder (Astropart Phys 86:41–45, 2017), where the data from the observables is jointly binned in redshift space. This allows one to further explore the model’s parameter that better fits the data in comparison to the $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model. The joint analysis of H ( z ) and $$[f\sigma _8](z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>f</mml:mi> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> show that the $$n=2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> –Starobinsky f ( R ) model fits well the observational data. In the end, we confirm that this joint analysis is able to break the degenerescence between modified gravity models as proposed in the original work (Starobinsky 2007). Our results indicate that the f ( R ) Starobinsky model provides a good fit to the currently available data for a set of values of its parameters, being, therefore, a possible alternative to the $$\varLambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM model.