Testing Modified Gravity with Large-Scale Structure Surveys: Probing Dark Matter and Cosmic Acceleration

Abstract

The accelerated expansion of the Universe, first discovered through Type Ia supernova observations, has prompted significant investigations into the underlying physics driving cosmic acceleration. While the standard ΛCDM model explains many cosmological observations, it suffers from theoretical challenges such as the fine-tuning of the cosmological constant and discrepancies in the growth rate of large-scale structures. Modified gravity theories offer an alternative framework to explain the observed acceleration without invoking dark energy as a separate entity. This paper examines how large-scale structure (LSS) surveys—including galaxy clustering, weak gravitational lensing, baryon acoustic oscillations (BAO), and redshift-space distortions (RSD)—provide stringent observational constraints on deviations from General Relativity. By analyzing the signatures predicted by modified gravity models such as f(R)f(R)f(R) gravity, scalar-tensor theories, and massive gravity, we assess their consistency with current data and explore their potential to resolve tensions within the ΛCDM paradigm. The results indicate that future surveys like Euclid, DESI, and LSST will play a crucial role in distinguishing between modified gravity and standard dark energy scenarios, offering insights into the nature of dark matter, structure formation, and fundamental physics governing cosmic acceleration.