Theoretical and Observational Developments of Inflation in Cosmology

Abstract

This thesis takes modest steps towards the goal of understanding the earliest period in the history of the universe—inflation. In the first leg, we focus on loop effects in de Sitter space. Therein we explain the physical meaning of anomalous dimensions and demonstrate how to compute them systematically for a broad class of scalar theories. Ultimately focusing on phenomenology, we highlight how otherwise undetectable light scalars can be visible in the cosmological collider signal of sufficiently heavy particles via its anomalous dimension. Moreover, we demonstrate how strong infrared effects in de Sitter lead to an enhancement of this quantity. Then, we focus on a special class of light scalars called axions, or compact scalar fields. Such particles are very theoretically well motivated as they can resolve several problems within the standard model of particle physics, one of which is the strong CP problem. Being field theoretic analogues of the quantum mechanical particle on a circle, we show that the quantization of these scalars crucially depends on their gauge constraint, or periodicity, unlike their behavior in flat-space. We further illustrate that taking care for their quantization, in addition, has phenomenological consequences which could aid their detection through a cosmological collider channel as well. We also point out that strong infrared effects qualitatively change their primordial signal from the naive expectation for a light scalar in inflation. In the process, we organize the primordial bispectrum generated by a broad class of higher-loop processes into a novel and useful form. In the second leg, we turn our focus towards the late universe. We specifically utilize a careful compression of the three-point correlation function, known as the skew-spectrum, in order to efficiently extract the non- Gaussian information in late-universe tracers of the dark matter density. It is well known that tracers of the matter density in the late universe are highly non-Gaussian, and extracting this information using traditional means can quickly become highly expensive. The skew-spectra due to its compressed nature enables access to this non-Gaussian information with a dramatic improvement in speed. We first test the skew-spectra on simulations of lensing and galaxy cross-correlation analyses in order to estimate the galaxy bias parameters. Finally, we apply the skew-spectrum to the SDSS-BOSS galaxy catalog in order to measure $f_{\rm NL}^{\rm equil}$, finding no evidence of primordial non-Gaussianity.