Exploring Scalar-Tensor Theories of Gravity in Light of Tensions and Anomalies in Standard Cosmology

Abstract

The $\Lambda$CDM model, the standard model of cosmology, has been highly successful in describing a wide range of cosmological observations. However, in the era of precision cosmology, it faces increasing challenges in the form of persistent tensions—most notably the Hubble and $S_8$ tensions—as well as anomalies in the Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillation (BAO) data. These discrepancies motivate the exploration of extensions to General Relativity. In this thesis, we investigate subclasses of Horndeski gravity, a broad scalar-tensor framework that introduces an additional scalar degree of freedom while maintaining second-order field equations. At early times, we focus on generalised nonminimal derivative couplings during inflation, which generate large-scale oscillatory features in the primordial power spectrum and provide improved fits to CMB anomalies. At late times, we construct a dynamical dark energy model with nonminimal couplings and self-interactions, allowing for phantom crossing and a potential resolution to the Hubble tension. Using Bayesian analyses with CMB, BAO, and Supernova data, we evaluate these models' phenomenology and observational viability. Although $\Lambda$CDM remains statistically preferred in global fits, our results reveal a mild preference for nonzero modifications, underscoring the promise of scalar-tensor theories in addressing current cosmological tensions.