The paper by Juan Maldacena focuses on computing the three-point correlation functions for primordial scalar and tensor fluctuations in single-field inflationary models. The author provides explicit expressions for these correlation functions in the slow roll approximation, where the answers are expressed in terms of the two usual slow roll parameters. In a specific limit, the three-point functions are determined entirely by the tilt of the two-point function spectrum. The paper also discusses the relation between these computations and the dS/CFT and AdS/CFT correspondences, emphasizing that these correspondences can be viewed as statements about the wavefunction of the universe.
The author starts by reviewing the standard results from the quadratic approximation, which predict a Gaussian spectrum of primordial fluctuations. The non-Gaussian corrections are expected to be small and are estimated in previous works. The paper then expands the action to third order to compute the cubic terms in the Lagrangian, which lead to changes in the ground state of the quantum field and non-linearities in the evolution.
The scalar fluctuations are parameterized by $\zeta$, and the tensor (or gravity wave) fluctuations by $\gamma$. The three-point correlation functions for these fluctuations are derived, and the dependence on the slow roll parameters is analyzed. In the limit where one of the momenta is much smaller than the others, the three-point functions are determined by the two-point function spectrum. The paper also discusses the behavior when all momenta are of similar order and provides a detailed computation of the cubic terms in the Lagrangian in two different gauges.
The author concludes by summarizing the results and their implications, noting that the computations can be used to investigate the dS/CFT and AdS/CFT correspondences, which are seen as statements about the wavefunction of the universe.The paper by Juan Maldacena focuses on computing the three-point correlation functions for primordial scalar and tensor fluctuations in single-field inflationary models. The author provides explicit expressions for these correlation functions in the slow roll approximation, where the answers are expressed in terms of the two usual slow roll parameters. In a specific limit, the three-point functions are determined entirely by the tilt of the two-point function spectrum. The paper also discusses the relation between these computations and the dS/CFT and AdS/CFT correspondences, emphasizing that these correspondences can be viewed as statements about the wavefunction of the universe.
The author starts by reviewing the standard results from the quadratic approximation, which predict a Gaussian spectrum of primordial fluctuations. The non-Gaussian corrections are expected to be small and are estimated in previous works. The paper then expands the action to third order to compute the cubic terms in the Lagrangian, which lead to changes in the ground state of the quantum field and non-linearities in the evolution.
The scalar fluctuations are parameterized by $\zeta$, and the tensor (or gravity wave) fluctuations by $\gamma$. The three-point correlation functions for these fluctuations are derived, and the dependence on the slow roll parameters is analyzed. In the limit where one of the momenta is much smaller than the others, the three-point functions are determined by the two-point function spectrum. The paper also discusses the behavior when all momenta are of similar order and provides a detailed computation of the cubic terms in the Lagrangian in two different gauges.
The author concludes by summarizing the results and their implications, noting that the computations can be used to investigate the dS/CFT and AdS/CFT correspondences, which are seen as statements about the wavefunction of the universe.