Amplitudes Meet Cosmology

Date & Time


  • Nima Arkani-Hamed, Institute for Advanced Study
  • Daniel Baumann, University of Amsterdam
  • John Joseph Carrasco, Northwestern University and The Institute for Theoretical Physics (IPhT, CEA-Saclay)
  • Daniel Green, University of California, San Diego

Cosmology is both source and arbiter of some of the biggest questions in physics, such as the origin and fate of space and time, as well as the nature and evolution of everything within it. Precise observations of the cosmic microwave background and the large-scale structure of the universe have recently brought these questions into sharp focus. Although there is growing evidence that the primordial fluctuations originated from quantum fluctuations during a period of inflation, the physics of inflation remains a mystery.

Moreover, while there have been significant theoretical advances in our understanding of cosmological correlation functions, it remains challenging to isolate fundamental physics from these correlators. In particular, we don’t know the precise rules that cosmological correlators have to obey, so that, naively, it might seem that anything goes.

This is to be contrasted with the observation that the laws of physics are a nearly inevitable consequence of quantum mechanics and special relativity. Nowhere is this seen more clearly than in the invariant observables associated with scattering amplitudes in asymptotically flat space. If cosmology is a source of ultimate questions, scattering theory can be thought of as a source of ultimate answers. Demanding only the minimal criteria of self-consistency, scattering theory has recently discovered a variety of often radically simpler ways to frame, extract, and unify predictions from physical theories. Generalizing from the relative security of flat spacetime to confront cosmological challenges provides a spectacular opportunity to stretch the applicability and reach of the S-matrix framework’s greatest ambitions.

The Simons Symposium on Amplitudes meet Cosmology brought experts from the cosmology and scattering amplitudes communities together, at this critical time, to share their key insights and challenges, in order to synthesize their complementary perspectives. Through a series of organized discussions, the goal of the symposium was to identify a set of precise questions against which shared progress can be measured jointly in both communities. For example, we discussed what progress will mean in the inflationary context and how this might shape collaborations at the boundaries of both fields.


  • Meeting reportplus--large

    Overview and New Developments

    Recent breakthroughs in the field of scattering amplitudes have revealed that fundamental laws of physics are a nearly inevitable consequence of quantum mechanics and special relativity. In particular, simple self-consistency requirements (e.g., Lorentz symmetry, locality and causality) limit the types of particles and interactions to essentially only those observed in nature. This is to be contrasted with the situation in cosmology where even the basics rules for consistent cosmological correlators remain poorly understood. The Simons Symposium on Amplitudes Meet Cosmology brought together 23 leading researchers from the cosmology and scattering communities to synthesize these distinct but complementary perspectives.

    Nima Arkani-Hamed opened the symposium with a pedagogical introduction to the commonalities between the analytic structure of amplitudes and cosmological correlators. He highlighted the state of the art in the field of scattering amplitudes, pointing out opportunities for similar advances in the study of cosmological correlators. This was followed by Yu-tin Huang’s review talk describing the methods and goals of the modern amplitudes program. On the cosmology side, Matias Zaldarriaga reviewed the central goals and challenges of the subject while providing an overview of current observational constraints. This set the stage for the more detailed discussions at the intersection of the two fields, which took place during the symposium.

    One of the central questions confronted was the degree to which cosmological correlators can be determined from consistency requirements alone, as in the bootstrap program for scattering amplitudes. Daniel Baumann shared the status of the ‘cosmological bootstrap,’ a new approach to determine the form of cosmological correlators from symmetries and singularities. Paolo Benincasa showed how correlators can be constructed by imposing the correct behavior of the leading singularities in terms of amplitude data alone — a spectacular result in support of the idea that progress in amplitudes could directly transfer to progress in understanding de Sitter correlators. These talks and subsequent discussions established intimate links between the two fields.

    A major goal of the ‘bootstrap’ approach is to understand the space of amplitudes and cosmological correlators arising from consistent high-energy theories. Kurt Hinterbichler and Rachel Rosen led a lively discussion on the interplay of causality, positivity and analyticity constraints in effective field theories (including gravitational theories). Sasha Zhiboedov presented new causality constraints arising from the eikonal limit of scattering amplitudes and the commutativity of shock waves. These constraints are currently only defined rigorously in anti-de Sitter space (AdS), where a dual-CFT defines the UV completion of gravity. Liam McAllister gave an overview of the status of UV-complete cosmological space-times and constraints derived from the weak gravity conjecture. Tom Hartman illustrated how AdS/CFT can be used to understand the structure of gravitational theories relevant to cosmology. He showed that the analytic properties of scattering amplitudes defined on the boundary of the AdS space-time lead to interesting constraints on bulk interactions. Making these arguments precise in flat space and in de Sitter space remains an important open problem.

    In both fields, soft limits play an important role both in constraining the form of observables and in encoding information about the spectrum of particles and their interactions. The intimate relation between the soft behavior of amplitudes and correlators is, however, often clouded by a difference in language used by the two communities. To overcome this language barrier, Enrico Pajer led a discussion on the relation between soft theorems in amplitudes and in cosmology. A number of similar results have been found in each community and a promising direction for future research is to connect these parallel, but clearly related, lines of investigation.

    One of the main advances in the field of scattering amplitudes has been the efficient treatment of loop corrections. Radu Roiban explained how many modern on-shell techniques for amplitude generalize to correlators. J.J. Carrasco and Jacob Bourjaily led a fruitful discussion on importing these techniques to the cosmological context. In particular, new insights may have direct impact in the perturbation theory describing dark matter and galaxies in the late universe. Another important development has been the realization that gravity amplitudes can be written as the square of gauge theory amplitudes, with similar relations linking a wide web of theories. Henrik Johansson and Donal O’Connell gave a pedagogical introduction to the color-kinematics duality and double-copy construction, illustrating its use in black hole physics. This was followed up by Rafael Porto and Yu-tin Huang in a discussion on the application of these ideas to high-precision calculations of the gravitational wave signals from black hole binaries. Lionel Mason introduced a generalization of the double-copy construction to non-flat space-time, and the group discussed how the double-copy might meet the cosmological context, such as the possible characterization of graviton correlators in de Sitter space by looking at gluon correlators on a nontrivial gauge background. The final day of the symposium began with Mina Arvanitaki and Dick Bond reviewing upcoming experimental programs in particle physics and cosmology. This was followed by two extended discussions on the future prospects of the Amplitudes Meet Cosmology program. Representing the amplitudes community, Lance Dixon summarized the most important directions identified in the workshop and led a discussion on promising paths forward in developing this new interdisciplinary research program. Daniel Green then presented the main challenges in the field of cosmology and discussed what techniques might prove useful to achieve some of the goals set at the beginning of the symposium.

    Future Directions and Collaborations

    A number of promising directions for future work were identified during the meeting and possible joint collaborations emerged. Many of the participants discussed the prospects for the bootstrapping of cosmological correlators. Concrete plans were made for studying the structure of correlations of massless spinning particles. In flat space, the corresponding amplitudes are highly constrained. It will be interesting to establish the cosmological analogs of these results.

    In recent years, a number of nontrivial constraints have been derived on the ultraviolet consistency of gravitational theories. So far, however, these results have only been established rigorously in anti-de Sitter space, and only conjectured ‘quasi-bounds’ exist in de Sitter space. An important direction for future progress is therefore to develop new methods to formulate UV consistency constraints in de Sitter space and in inflationary backgrounds. The group discussed how such results might be obtained in the future.

    Future Meetings and Dissemination

    To propagate the successes of the symposium, plans have been made to organize additional workshops and summer schools. The objective of these events is to invite the wider community into the new research opportunities developed at the symposium. In late May, an International School on Amplitudes and Cosmology is being held in Southern Italy ( with many of our participants lecturing. In October 2019, a three-day workshop will be held at Northwestern University, engaging early career scientists, especially postdocs, interested in research at the intersection of amplitudes and cosmology. In the summer of 2020, a graduate school will be organized at the University of Amsterdam.

  • Agenda & Slidesplus--large


    10:00 - 11:00 AMNima Arkani-Hamed | Amplitudes Meet Cosmology (O)*
    11:30 - 12:30 PMNima Arkani-Hamed | Amplitudes Meet Cosmology (O)
    5:00 - 6:00 PMMatias Zaldarriaga | Cosmology Goals (O)
    6:15 - 7:15 PMYu-tin Huang | Amplitudes Goals (O)
    View Slides (PDF)


    10:00 - 11:00 AMDaniel Baumann | Bootstrapping Inflationary Correlators (O)
    View Slides (PDF)
    11:30 - 12:30 PMRadu Roiban | From Amplitudes to Correlators (O)
    View Slides (PDF)
    5:00 - 6:00 PMJacob Bourjaily & John-Joseph Carrasco | Loops in Amplitudes and Cosmology (D)
    6:15 - 7:15 PMEnrico Pajer | IR Structure in Cosmology and Amplitudes (D)
    View Slides (PDF)


    9:45 - 2:00 PMGuided Hike to Partnach Gorge
    5:00 - 6:00 PMPaolo Benincasa & Lionel Mason | Amplitudes Beyond Flat Space (O)
    View Slides (PDF)
    View Slides (PDF)
    6:15 - 7:15 PM Alexander Zhiboedov | Causality Constraints and Gravity (O)


    10:00 - 11:00 AMTom Hartman | Insights from the Conformal Bootstrap (O)
    11:30 - 12:30 PMHenrik Johansson & Donal O'Connell | Opportunities of the Double Copy (O)
    5:00 - 6:00 PMKurt Hinterbichler & Rachel Rosen | Sum Rules and Positivity (D)
    6:15 - 7:15 PMYu-tin Huang & Rafael Porto | Amplitudes Meet Classical Gravity (D)


    10:00 - 11:00 AMLiam McAllister | Challenges in De Sitter (O)
    11:30 - 12:30 PMMina Arvanitaki & Dick Bond | Future Observations (O)
    View Slides (PDF)
    View Slides (PDF)
    5:00 - 6:00 PMLance Dixon | Next Steps: Amplitudes (D)
    6:15 - 7:15 PMDaniel Green | Next Steps: Cosmology (D)


  • Participantsplus--large
    Nima Arkani-HamedInstitute for Advanced Study
    Mina ArvanitakiPerimeter Institute
    Daniel BaumannUniversity of Amsterdam
    Paolo BenincasaNiels Bohr Institute
    Dick BondCITA
    Jacob BourjailyNiels Bohr Institute
    John-Joseph CarrascoNorthwestern University and The Institute for Theoretical Physics
    Lance DixonSLAC
    Daniel GreenUniversity of California, San Diego
    Tom Hartman Cornell University
    Kurt HinterbichlerCase Western Reserve University
    Yu-tin HuangNational Taiwan University
    Henrik JohanssonUppsala & Nordita
    Lionel MasonOxford University
    Liam McAllisterCornell University
    Donal O’ConnellUniversity of Edinburgh
    Enrico PajerUniversity of Cambridge
    Rafael PortoDeutsches Elektronen-Synchrotron (DESY)
    Radu RoibanPenn State University
    Rachel RosenColumbia University
    Matias ZaldarriagaInstitute for Advanced Study
    Alexander ZhiboedovCERN
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