Comparative Cosmological Constraints on Hu–Sawicki f(R), Teleparallel f(T), and Horndeski Gravity Models in the DESI Era

Abstract

The accelerated expansion of the Universe motivates tests of gravitational theories beyond General Relativity and the standard flat ΛCDM model. The Dark Energy Spectroscopic Instrument (DESI) has improved baryon acoustic oscillation (BAO) measurements, creating new opportunities to constrain the background expansion and, when combined with growth-sensitive observations, the gravitational sector. This article develops a comparative framework for three representative modified-gravity classes: Hu–Sawicki f(R) gravity, teleparallel f(T) gravity, and Horndeski scalar–tensor gravity. Their theoretical foundations, potential observational signatures, stability requirements and data needs are compared with emphasis on DESI BAO, Planck cosmic microwave background (CMB) information, Type Ia supernovae, cosmic chronometers, full-shape clustering, lensing and late-time potential evolution. Published studies show that BAO and CMB information provide complementary constraints, while DESI-era analyses of modified gravity generally find allowed deviations consistent with the General Relativity limit for the tested parameterizations. Recent f(T) work also illustrates that late-time-only inferences can shift toward the standard limit when early-Universe CMB information is added. This manuscript is a literature-grounded comparative synthesis and reproducible analysis framework; it does not claim new joint MCMC constraints or original posterior regions. Quantitative values from prior studies are identified as published benchmarks. The framework specifies how a future unified likelihood analysis could test whether the three gravity classes are distinguishable with current and forthcoming cosmological observations.