Cosmological constraints on the $$R^2$$ R 2 -corrected Appleby–Battye model

Abstract

Abstract Nowadays, efforts are being devoted to the study of alternative cosmological scenarios, in which, modifications of the General Relativity theory have been proposed to explain the late cosmic acceleration without assuming the existence of the dark energy component. In this scenario, we investigate the $$R^2$$ R 2 -corrected Appleby–Battye model, or $$R^2$$ R 2 -AB model, which consists of an f(R) model with only one extra free parameter b, besides the cosmological parameters of the flat- $$\varLambda $$ Λ CDM model: $$H_0$$ H 0 and $$\varOmega _{m,0}$$ Ω m , 0 . Regarding this model, it was already shown that a positive value for b is required for the model to be consistent with Solar System tests, moreover, the condition for the existence of a de Sitter state requires $$b \ge 1.6$$ b ≥ 1.6 . To impose observational constraints on the $$R^2$$ R 2 -AB model we consider three datasets: 31 H(z) measurements from Cosmic Chronometers (CC), 20 $$[{f\sigma }_{8}](z)$$ [ f σ 8 ] ( z ) measurements from Redshift-Space Distortion (RSD), and the most recent type Ia Supernovae (SNe Ia) sample from Pantheon+. Next, we perform two diferent analyses: we have cosidered only SNe Ia data and the combined likelihood SNe $$+$$ + CC $$+$$ + RSD. The first one has provided $$b=2.28^{+6.52}_{-0.55}$$ b = 2 . 28 - 0.55 + 6.52 , while the second one $$b=2.18^{+5.41}_{-0.55}$$ b = 2 . 18 - 0.55 + 5.41 . In the first case it was necessary to set the absolute magnitude $$M_B = -19.253$$ M B = - 19.253 from SH0ES collaboration, while in the second we did a marginalization over the Hubble constant $$H_0$$ H 0 in the normalized growth function. We have also observed that the $$H_0-M_B$$ H 0 - M B degenerecency was broken by adding CC data to the SNe data. Additionally, we perform illustrative analyses that compare this f(R) model with the flat- $$\varLambda $$ Λ CDM model, considering several values of the parameter b, for diverse cosmological functions like the Hubble function H(z), the equation of state $$w_\textrm{eff}(z)$$ w eff ( z ) , the parametrized growth rate of cosmic structures $$[f \sigma _8](z)$$ [ f σ 8 ] ( z ) , and $$\sigma _8(z)$$ σ 8 ( z ) . From our results, we conclude that the $$R^2$$ R 2 -AB model fits well current observational data, although the model parameter b was not unambiguously constrained in the analyses.