Testing logarithmic corrections on $R^2$-exponential gravity by observational data

This paper is devoted to the analysis of a class of $F(R)$ gravity, where additional logarithmic corrections are assumed. The gravitational action includes an exponential term and a $R^2$ inflationary term, both with logarithmic corrections. This model can unify an early time inflationary era and also the late time acceleration of the universe expansion. This model is deeply analysed, confronting with recent observational data coming from the largest Pantheon Type Ia supernovae sample, the latest measurements of the Hubble parameter $H(z)$, manifestations of Baryon Acoustic Oscillations and Cosmic Microwave Background radiation. The viability of the model is studied and the corresponding constraints on the free parameters are obtained, leading to an statistical analysis in comparison to $\Lambda$CDM model. The inflationary era is also analysed within this model and its compatibility with the latest observational data for the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio. Finally, possible corrections on the Newton's law and constraints due to primordial nucleosynthesis are analysed.