This paper presents the computation of three-point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. The results are derived in the slow roll limit, where the answer is expressed in terms of the two standard slow roll parameters. The three-point functions are determined by the tilt of the two-point functions' spectra. The paper also discusses the relation of these results to dS/CFT and AdS/CFT correspondences, emphasizing that these dualities can be viewed as statements about the wavefunction of the universe.
The scalar fluctuations are parameterized by ζ, a gauge-invariant variable that remains constant outside the horizon. Tensor fluctuations are denoted by γ. The three-point functions are given by expressions involving the slow roll parameter ε and homogeneous functions of the momenta, with explicit forms provided. In the limit where one momentum is much smaller than the others, the three-point functions are determined by the tilt of the two-point functions. This is shown through a simple argument involving the rescaling of momenta and the violation of scale invariance.
The paper also discusses the behavior of the three-point functions when all momenta are of similar order, requiring a more detailed computation. The results are related to the stress tensor correlators in a dual conformal field theory, where the three-point functions are determined by the behavior of the two-point functions under coordinate rescaling.
The paper is organized into sections reviewing the quadratic computation, expanding the action to third order, computing the three-point functions, and discussing the relationship to dS/CFT and AdS/CFT. The quadratic computation is reviewed, and the action is expanded to third order. The three-point functions are computed, and their dependence on the slow roll parameters is analyzed. The results are related to the dual conformal field theories, and the paper concludes with a discussion of the implications for the wavefunction of the universe.This paper presents the computation of three-point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. The results are derived in the slow roll limit, where the answer is expressed in terms of the two standard slow roll parameters. The three-point functions are determined by the tilt of the two-point functions' spectra. The paper also discusses the relation of these results to dS/CFT and AdS/CFT correspondences, emphasizing that these dualities can be viewed as statements about the wavefunction of the universe.
The scalar fluctuations are parameterized by ζ, a gauge-invariant variable that remains constant outside the horizon. Tensor fluctuations are denoted by γ. The three-point functions are given by expressions involving the slow roll parameter ε and homogeneous functions of the momenta, with explicit forms provided. In the limit where one momentum is much smaller than the others, the three-point functions are determined by the tilt of the two-point functions. This is shown through a simple argument involving the rescaling of momenta and the violation of scale invariance.
The paper also discusses the behavior of the three-point functions when all momenta are of similar order, requiring a more detailed computation. The results are related to the stress tensor correlators in a dual conformal field theory, where the three-point functions are determined by the behavior of the two-point functions under coordinate rescaling.
The paper is organized into sections reviewing the quadratic computation, expanding the action to third order, computing the three-point functions, and discussing the relationship to dS/CFT and AdS/CFT. The quadratic computation is reviewed, and the action is expanded to third order. The three-point functions are computed, and their dependence on the slow roll parameters is analyzed. The results are related to the dual conformal field theories, and the paper concludes with a discussion of the implications for the wavefunction of the universe.