Project III 2023-24


Wavefunction of the Universe

Arthur Lipstein

Description

The holographic principle postulates that quantum gravity can be described by quantum field theory in one lower dimension. This correspondence is best understood in a background with negative comological constant, known as Anti-de Sitter space (AdS). In this case, the holographic description is provided by a conformal field theory (CFT) in the boundary. On the other hand, cosmological observations suggest that the early Universe can be approximately described by de Sitter space (dS), which has positive cosmological constant. In this case, a holographic description is more subtle because time should be emergent. The goal of this project will be to adapt AdS/CFT techniques to compute cosomological correlation functions, which are naturally encoded in an object known as the wavefunction of the Universe. In more detail, students will:

  • learn some basics about cosmology and inflation (sections 1 and 2 of 0907.5424)
  • quantize a free scalar field in de Sitter space and compute 2-point functions (section 2 of these online notes)
  • learn about the wavefunction of the Universe and its symmetries (section 2 of 2005.04234)
  • derive 2-point and 3-point scalar wavefunction coefficients from conformal Ward identities and interpret them in terms of bulk Feynman diagrams (sections 2-4 of 1510.08442)
  • If time permits, students will have the opportunity to explore other related directions such as 4-point wavefuntion coefficients.

    Suggested Pre-requisites

    Mathematical Physics II

    Special Relativity & Electromagnetism II

    Suggested Co-requisites

    Quantum Mechanics III