Anomalies and Tensions in Cosmology and a Primordial Solution

Tensions between cosmological datasets are discussed with the assumption of a baseline described by flat \(\Lambda \) CDM model with power law form of primordial spectrum. This chapter discusses the possibility of a new physics in the primordial Universe that can address certain anomalies in the Cosmic Microwave Background (CMB) observations and simultaneously helps in ameliorating the tensions between the observations. We demonstrate that, transient oscillations in the primordial power spectrum with a particular frequency of about 300 MegaParsecs can resolve lensing and curvature anomalies in the CMB data. These oscillations fits the CMB data better than the standard model and at the same time, prefers higher values of Hubble constant and lower values of the growth parameter \(S_8\) . They can be parametrized as transient sinusoidal oscillations. We also demonstrate that slow-roll inflation with an intermediate fast-roll period of 0.5 e-folds can produce similar features in the primordial spectrum.