CONSTRAINTS ON MODIFIED GRAVITY THEORIES FROM COSMIC MICROWAVE BACKGROUND AND BARYON ACOUSTIC OSCILLATION DATA

Abstract

Modified gravity (MG) theories have emerged as promising alternatives to dark energy for explaining the observed accelerated expansion of the Universe. While the ΛCDM model remains consistent with a wide range of cosmological probes, deviations from General Relativity (GR) may appear in the growth rate of structure, gravitational potentials, or the propagation of perturbations. This study investigates observational constraints on MG models using Cosmic Microwave Background (CMB) anisotropy measurements and Baryon Acoustic Oscillation (BAO) distance data. We analyze parametrized deviations from GR—including the effective gravitational strength μ(k, a) and gravitational slip parameter η(k, a)—within several representative MG models such as f(R) gravity, scalar-tensor theories, and Horndeski models. Using parameter likelihood analysis, we find that CMB + BAO datasets tightly constrain deviations from GR, with | f R0| ≤ 10⁻⁵ in Hu–Sawicki f(R) gravity and η ≈ 1 within 5–10% precision. Our results support the robustness of GR on cosmological scales and reinforce the consistency of the ΛCDM framework.