Research Projects

During the period of the fellowship, I intend to study two particular aspects of cosmological observables: loop structure and implications of unitarity. Loop structure: Cosmological/inflationary observables are computed using perturbation theory similar to scattering amplitudes in flat space Quantum Field Theory (QFT). Most of the literature on inflationary cosmology is confined to computing tree-level correlation functions and very little attention has been given to loop computations mostly because of their calculational complexity and weak signal. The analytic structure for two-point function at one-loop was studied in arXiv: 0506236 & 0912.2734. I with my collaborators extended these results to three-point functions at one-loop (arXiv: 2405.10374 & 2503.21880), classifying the possible analytic structures for bubble diagrams (two-site one-loop) derivative interactions. During the period of the fellowship, I would like to develop techniques to compute one-loop higher-site diagrams, e.g., triangle diagrams with three vertices. In particular, I would like to develop a systematic understanding of possible analytic structures at one loop for both derivative and non-derivative interactions. This kind of analysis can prove to be very powerful, e.g., the analytic structure of the S-matrix at loop level was essential in deriving strong positivity bounds for Wilson coefficients in the case of flat space EFTs. Implications of unitarity: Implications of unitarity in the context of cosmology were first studied in arXiv: 2009.02898 & 2103.09832. The authors derived a set of Cutkosky-like cutting rule relations for the cosmological wave function (cosmological correlators can be obtained from the cosmological wave function). The authors crucially assumed that inflation starts in the simplest possible configuration, i.e., the vacuum. These results were extended by me (and collaborators) in arXiv: 2407.06258 & 2502.05630 to excited initial states known as Bogoliubov states. These works also extended the cutting rules to fields of any mass and (integer) spin. Using our cutting rule relations we derived constraints on n-point contact and four-point exchange wave function coefficients. During the period of the fellowship, I would like to develop a general formalism that applies to any initial state. Furthermore, it would be interesting to derive non-perturbative implications of unitarity for cosmological observables. The cutting rules derived until now are perturbative and only apply diagram by diagram. A non-perturbative unitarity relation may in the future be very useful for deriving positivity bounds for cosmological EFTs. Finally, it would be interesting to analyze how violations of unitarity in the data may potentially be used to infer the existence of missing on-shell states in the spectrum. This could be used to probe additional degrees of freedom during inflation.