Constraining f(R) models with cosmic chronometers and the H II galaxy Hubble diagram

We consider several well-known f(R) cosmological models and constrain their parameters, namely the deviation parameter b and the cosmological parameters Ω_m and h. We first obtain analytical approximations for the Hubble rate H(z) and the luminosity distance d_L(z) in terms of these parameters, and then test these against the observational expansion rate derived from cosmic chronometers (CCs) and the distance modulus in the H II galaxy Hubble diagram, obtained in a model-independent way using Gaussian processes. We first optimize the models based solely on the CCs and then repeat this process with a joint analysis using both the CCs and H II galaxies.