Quadratic f(R) Gravity Confronts Cosmology: A No-Go Result for Evolving Dark Energy and High-Redshift Anomalies

We revisit quadratic f(R) gravity of the form f(R) = R+αR2, motivated by recent observational tensions such as evolving dark energy hints from DESI and the early formation of massive galaxies observed by JWST. Using the auxiliary field formalism, we derive field equations, analyze stability, and confront the model with cosmological datasets. Our rigorous numerical and statistical analysis shows that solar system and cosmological constraints limit α < 10−30 Mpc2, forcing the model to be observationally indistinguishable from ΛCDM. We demonstrate that quadratic corrections cannot account for evolving dark energy (|wa| ≲ 0.01 versus DESI’s |wa| ∼ 0.3–0.5) nor the abundance of high-redshift galaxies. This establishes a no-go result: while theoretically consistent and ghost-free, quadratic f(R) gravity lacks cosmological viability. Our analysis highlights the importance of ruling out simple models and motivates the exploration of more sophisticated f(R) functions and extended modified gravity frameworks.