Observational Constraints on $$\boldsymbol{f(R)}$$ Gravity Model with DESI BAO Data

We derive cosmological constraints for specific $$f(R)$$ gravity models. We focus on two models: the Hu–Sawicki model and the Starobinsky model, introducing a distortion parameter to quantify deviations from the standard $$\Lambda$$ CDM cosmology. Data from the Big Bang nucleosynthesis (BBN), the Dark Energy Spectroscopic Instrument (DESI), baryon acoustic oscillations (BAO), and the most recent Pantheon Plus datasets—which include Cepheid host distances and covariance from SH0ES samples—are all employed in our investigation. A minor but nonzero divergence from $$\Lambda$$ CDM cosmology is slightly preferred, according to the results, which are corroborated by efficient values of the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). This suggests that $$f(R)$$ gravity aligns well with observational data and holds potential as a viable candidate for modified gravity. Additionally, the deceleration parameter for both models remains close to the corresponding value in the $$\Lambda$$ CDM model. The Statefinder diagnostics reveals distinct evolutionary differences between the two models, although their overall evolutionary trajectories are strikingly similar.