The Phase of the Cosmological Wavefunction

The principles of symmetry, unitarity, and locality form a vital foundation for our descriptions of fundamental physics. Their implications for particle physics are well established, through, for instance, the spin–statistics theorem, the optical theorem, and the CPT theorem. In contrast, their role in quantum interactions in curved spacetimes is only now being systematically explored. This is essential for understanding the inflationary universe, where spacetime is approximately de Sitter. This thesis investigates how such principles constrain cosmological correlators and the wavefunction of the universe (also referred to as the cosmological wavefunction) in inflationary spacetimes. Using the Effective Field Theory of Inflation (EFToI), the first part of the thesis classifies all parity-even graviton bispectra from local interactions to all orders in derivatives. We identify a minimal set of operators contributing to tree-level bispectra and show how diffeomorphism invariance links contact and exchange terms. Despite the complexity of bulk interactions, the resulting boundary correlators have a remarkably simple analytic structure, with poles only in the total energy. These results provide a complete description of graviton non-Gaussianities in single-clock inflation and new tools for interpreting upcoming cosmic microwave background and large-scale structure data. The second part establishes a non-perturbative framework for understanding CPT symmetry in cosmology. We show that in both flat and de Sitter space, CRT arises from a \mathbb{Z}₂ \times \mathbb{Z}₂ group structure relating discrete rotations (from Lorentz invariance), reflection reality (implied by unitarity), and CRT. In inflationary de Sitter, these must be understood as local Lagrangian symmetries. This leads to the discovery of a novel Cosmological CPT theorem, linking discrete scale invariance and reflection reality, to derive a non-perturbative unitarity constraint in a single Poincaré patch. Applying this to the boundary wavefunction yields universal constraints valid to all loop orders. Finally, we apply these constraints to establish a cosmological analogue of Furry’s theorem and a no-go theorem for parity violation: in single-field inflation with a Bunch–Davies vacuum and scale-invariant operators, late-time parity-odd correlators vanish. This rules out parity-violating signals, such as chiral gravitational waves, for a broad class of inflationary models. Together, these results provide a symmetry-based foundation for understanding the quantum structure of the early universe, answering long-standing questions by establishing non-perturbative constraints on the wavefunction of the universe derived from bulk unitarity. In doing so, they pave the way for identifying viable dS/CFT candidates in holographic cosmology.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2025

Author dc:creator

• Thavanesan, Ayngaran

Advisor dc:contributor.advisor

• Wall, Aron

• Cosmology
• Holography
• Quantum Field Theory
• Quantum Gravity
• Wavefunction

Licence

• https://www.repository.cam.ac.uk/bitstreams/b3bde166-a4ca-4643-bb78-5a38a15a32f0/download
• http://purl.org/NET/rdflicense/allrightsreserved

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.119586

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/386295