Researchers are increasingly finding connections between the well-understood world of particle physics and the complexities of cosmology. Chandramouli Chowdhury, Sadra Jazayeri, and Arthur Lipstein, alongside Joe Marshall, Jiajie Mei, and Ivo Sachs, from institutions including the University of Southampton, Imperial College, Durham University, and the University of Amsterdam, demonstrate a novel method for calculating cosmological correlators, fundamental quantities describing the evolution of the universe. Their work reveals that these correlators share a surprising mathematical relationship with scattering amplitudes, traditionally used to describe particle interactions, and can be systematically reconstructed using techniques borrowed from flat-space physics. This approach, detailed in their paper, offers a powerful new framework for understanding cosmological observables and potentially extracting meaningful data from the early universe.
Cosmological correlators and flat-space amplitudes share a surprising mathematical equivalence, hinting at a deeper connection between them
Scientists have uncovered a surprising link between cosmological correlators in de Sitter space and the well-established mathematics of scattering amplitudes in flat space. Recent theoretical work demonstrates that these cosmological correlators, fundamental observables in the study of the early universe, possess a mathematical structure remarkably similar to their flat-space counterparts.
This simplification is achieved through a set of “cosmological dressing rules” which effectively translate flat-space Feynman diagrams into cosmological correlators by attaching auxiliary propagators to interaction vertices. The research reveals that discontinuities of cosmological correlators, calculated with respect to internal energy variables, can be directly obtained by applying these auxiliary propagators to unitarity cuts of flat space Feynman diagrams.
Furthermore, discontinuities with respect to external energy variables are obtained by cutting the auxiliary propagators themselves, leading to highly non-trivial constraints on cosmological correlators expressed as simple sum rules. These findings are illustrated through calculations at both tree-level and one-loop order for conformally coupled scalar theories, although the principles are broadly applicable.
This work introduces a powerful new approach to reconstructing cosmological correlators from their discontinuities using dispersion relations, enabling systematic computation from data originating in flat space. The ability to map discontinuities of cosmological observables to flat-space scattering amplitudes is conceptually significant and offers practical benefits.
The derived sum rules provide constraints for bootstrapping correlators, potentially aiding in the development of more accurate cosmological models. Researchers demonstrate how to reconstruct complete cosmological correlators from these discontinuities, offering a novel computational pathway. This reconstruction relies on dispersion relations, effectively building cosmological observables from data initially calculated in the simpler flat-space framework.
This study provides a new machinery for computing cosmological correlators, validated through examples involving conformally coupled scalar theories, with broader applicability explored in ongoing work. The investigation builds upon earlier efforts to relate in-in correlators to a shadow formalism in Euclidean Anti-de Sitter space and extends these developments to include spinning theories. By leveraging the established tools of scattering amplitudes, this research offers a promising avenue for advancing our understanding of the early universe and interpreting data from upcoming cosmic microwave background and large-scale structure surveys.
Computation of cosmological correlator discontinuities via flat-space unitarity and auxiliary propagators reveals important constraints on effective field theory parameters
A detailed analysis of cosmological correlators commenced with the computation of discontinuities using unitarity cuts of flat space Feynman diagrams. Researchers applied auxiliary propagators to these diagrams, effectively uplifting them to represent in-in correlators within de Sitter space. This methodology leverages the established connection between cosmological correlators and flat-space scattering amplitudes, simplifying calculations and revealing underlying mathematical structures.
The study focused on conformally coupled scalar theories, although the principles extend to more general cases. Specifically, the work examined discontinuities related to both internal and external energy variables. Discontinuities with respect to internal energies were directly mapped onto discontinuities of flat-space Feynman diagrams via the cosmological dressing rules.
This allowed for the computation of cosmological correlator discontinuities by simply applying auxiliary propagators to unitarity cuts of flat-space diagrams. Conversely, cutting auxiliary propagators attached to Feynman diagrams yielded discontinuities corresponding to external energies. This innovative approach revealed highly non-trivial constraints on cosmological correlators, manifesting as simple sum rules not present in wavefunction coefficients.
Furthermore, the research demonstrated the reconstruction of cosmological correlators from their discontinuities using dispersion relations. Calculations were performed at both tree-level and 1-loop order to validate the method and illustrate its applicability. The precision of these calculations is crucial given the anticipated accuracy of upcoming cosmic microwave background and large-scale structure surveys, which aim to measure cosmological correlators with unprecedented detail. This technique provides a powerful new framework for systematically reconstructing cosmological observables from data originating in flat space.
Cosmological correlator reconstruction via flat-space unitarity and auxiliary propagators offers a powerful new approach to perturbation theory
Researchers demonstrate a novel approach to reconstructing cosmological correlators from flat-space data using auxiliary propagators and dispersion relations. Discontinuities of cosmological correlators, with respect to internal energy variables, are obtained by applying auxiliary propagators to unitarity cuts of flat space Feynman diagrams.
Furthermore, discontinuities concerning external energy variables result from cutting auxiliary propagators attached to Feynman diagrams, establishing highly non-trivial constraints on cosmological correlators in the form of simple sum rules. The work focuses on conformally coupled scalar theories, specifically those with masses of 2, and explores interactions involving φ4 and φ3 terms in four-dimensional de Sitter space.
Auxiliary propagators, defined as xext ptot = xext p2tot − x2ext + iε, are employed to dress flat-space Feynman diagrams, effectively uplifting them to de Sitter space. These propagators connect interaction vertices, with the energy flowing through them equal to the sum of energies of internal lines attached to that vertex.
Dressed diagrams, representing in-in correlators, take the general form Cn({x}, {y}) = Z ∞ −∞ v Y i=1 dpiδ(P j pj) p2 i −x2 i + iεAn({p}; {y}), where An is a flat space Feynman diagram dependent on Lorentz-invariant combinations of momenta and y variables. The integration over independent energies running through auxiliary propagators yields the final cosmological correlator, with an overall factor of ηn 0 (k1 · · · kn)−1 δ3 Pn i=1 ki often omitted for simplicity. For conformally coupled φ3 theory, two types of auxiliary propagators are utilized, with specific restrictions on their occurrences within any given diagram.
Constructing de Sitter correlators via modified flat space amplitudes requires careful consideration of boundary conditions
Recent advances reveal a surprising connection between cosmological correlators in de Sitter space and the well-established mathematical framework of scattering amplitudes in flat space. These correlators, which describe the relationships between fields in the expanding universe, share a simplicity previously unexpected, allowing for a novel approach to their calculation.
Researchers have demonstrated that these cosmological correlators can be constructed by modifying standard flat-space Feynman diagrams with auxiliary propagators, effectively “dressing” them for the curved spacetime of de Sitter space. Specifically, the work establishes a method for obtaining discontinuities of cosmological correlators by applying these auxiliary propagators to unitarity cuts of flat space diagrams.
Furthermore, discontinuities related to external energy variables are obtained by cutting the auxiliary propagators themselves. This process yields simple sum rules that constrain the possible forms of cosmological correlators, offering a powerful tool for theoretical calculations. The approach was successfully illustrated using calculations at tree-level and one-loop for conformally coupled scalar theories, though the underlying principles are broadly applicable.
This research provides a systematic way to reconstruct cosmological observables from data originating in flat space, potentially streamlining calculations and offering new insights into the early universe. The authors acknowledge that their results overlap with those of several recently published works, highlighting the active nature of this research area. Future work will likely focus on extending these techniques to more complex theories and exploring the implications for understanding cosmological phenomena, potentially refining the reconstruction of correlators using dispersion relations and further investigating the relationship to microcausality.