Shadow Formulation of In-in Correlators Enables New Insights into Four Dimensional De Sitter Space

Cosmological observations rely on understanding how particles interact and evolve within the expanding universe, a task that requires precise calculations of fundamental quantities known as in-in correlators. Chandramouli Chowdhury, Arthur Lipstein, Joe Marshall, and Alex Jiayi Zhang, from the Universities of Southampton and Durham, present a new approach to calculating these crucial correlators for a range of particles, including gluons and gravitons, within the complex environment of de Sitter space. Their work introduces a refined method for handling the mathematical challenges inherent in these calculations, and importantly, establishes a link between calculations in de Sitter space and more familiar calculations in Anti-de Sitter space, simplifying the process considerably. This advancement not only clarifies the theoretical framework for understanding early universe cosmology, but also opens new avenues for exploring relationships between different physical theories through the concept of colour/kinematics duality and the double copy.

Cosmological Correlators and AdS/CFT Correspondence

This body of work explores a comprehensive range of research concerning cosmology, quantum field theory, and the AdS/CFT correspondence, a theoretical framework linking gravity in Anti-de Sitter space to conformal field theories on its boundary. Investigations focus on calculating and interpreting cosmological correlators, which describe relationships between quantum fields in the early universe and provide observable signatures in the Cosmic Microwave Background and large-scale structure. The research leverages the holographic principle to study strongly coupled quantum systems and cosmology, with a particular emphasis on non-Gaussianity, deviations from Gaussian statistics in primordial fluctuations that serve as crucial tests of inflationary models. Scientists are developing techniques to address the complexities of quantum fields in an expanding universe, ensuring consistency with fundamental principles like locality and unitarity. The Schwinger-Keldysh formalism, a method for handling out-of-time-order correlators, plays a central role, alongside the double copy method for constructing gravity theories from gauge theories and bootstrap methods for constraining correlator forms. This research demonstrates an active and interdisciplinary field, drawing from cosmology, quantum field theory, string theory, and mathematical physics.

In-In Correlators via Manifestly Local Shadow Action

Scientists have developed a new method for calculating in-in correlators, essential quantities in cosmology, for spinning fields, photons, gluons, and gravitons, interacting with scalar fields in de Sitter space. This approach avoids the traditional process of eliminating unphysical modes, instead retaining all degrees of freedom and employing a carefully designed gauge-fixing procedure. This results in a manifestly local action, significantly simplifying calculations compared to existing methods. By performing the in-in path integral with this local action, researchers mapped these calculations to Euclidean Anti-de Sitter space, allowing them to leverage familiar techniques from scattering amplitude calculations.

The team demonstrated the efficacy of this approach at both tree-level and loop-level, revealing a direct correspondence between Feynman diagrams contributing to in-in correlators and those found in flat space scattering amplitudes. Furthermore, they derived a set of “dressing rules” for translating flat space Feynman diagrams into de Sitter space in-in correlators, distinguishing between transverse-traceless and longitudinal modes. These rules were then used to investigate colour/kinematics duality and the double copy, revealing that kinematic numerators obey a Jacobi relation analogous to those in flat space. This innovative methodology provides a powerful new tool for exploring the connections between cosmology and scattering amplitudes.

In-In Correlators in de Sitter Space Derived

Scientists have developed a novel approach to calculating in-in correlators, fundamental observables in cosmology, for theories involving scalars, gluons, and gravitons in four-dimensional de Sitter space. This work revisits the Schwinger-Keldysh formalism and introduces a new treatment of boundary gauge-fixing within the underlying path integral, ultimately deriving effective actions in Euclidean Anti-de Sitter space. These actions allow for the calculation of in-in correlators through Feynman rules, generalizing a recently obtained shadow formalism initially developed for scalar theories. Researchers demonstrated a mapping between calculations in de Sitter space and computations of Witten diagrams in Euclidean Anti-de Sitter space, effectively doubling the number of bulk fields.

This simplification allows for the calculation of in-in correlators as a sum over flat space Feynman diagrams, dressed with theory-dependent auxiliary propagators attached to interaction vertices. For a tree-level four-point correlator, the residue of the total energy pole is equivalent to the flat space amplitude. The team derived dressing rules for conformally coupled φ4 theory and are extending these ideas to theories with photons, gluons, and gravitons.

In-In Correlators Mapped to Anti-de Sitter Space

Scientists have developed a new method for calculating in-in correlators, essential quantities in cosmology, for spinning fields, photons, gluons, and gravitons, interacting with scalar fields in de Sitter space. This approach avoids the complexities of eliminating unphysical modes, instead retaining them throughout the process and employing careful gauge-fixing techniques. This results in a manifestly local action, simplifying calculations compared to existing methods. By mapping these in-in correlators to calculations within Euclidean Anti-de Sitter space, researchers can leverage familiar techniques from scattering amplitude calculations.

The team demonstrated this approach at both tree-level and one-loop order, showcasing its relative simplicity and efficiency. Furthermore, they initiated an exploration of colour/kinematics duality and the double copy for these in-in correlators, utilising dressing rules to translate flat space Feynman diagrams into the de Sitter space framework. While current calculations are limited to perturbative orders, the team acknowledges the potential for extending the method to higher loops and exploring connections between their approach and non-local formulations, offering avenues for future research. This work provides a new tool for cosmological calculations and opens possibilities for applying techniques from particle physics to better understand the early universe.