Amplitudes Meet Cosmology (2022)

Date & Time

Daniel Baumann, University of Amsterdam
John Joseph Carrasco, Institute for Theoretical Physics
Daniel Green, University of California, San Diego

Cosmology is both the 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.

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 2022 Simons symposium brought together leading researchers in scattering amplitudes, cosmology, and quantum field theory. Key discussions included recent progress in the cosmological bootstrap, the understanding of infrared effects in cosmology, new perspectives from the celestial sphere, and lessons learned from bootstrapping in AdS/CFT. A concrete goal of this meeting was to leverage knowledge from across these communities towards insights applicable beyond the tree-level approximation.

Previous Meeting:

  • Meeting Reportplus--large


    The past three years have seen remarkable progress in the study of cosmological correlators and its connection to the physics of scattering amplitude. Spurred in part by the first “Amplitudes Meet Cosmology” Simons Symposium in 2019, there has been a lively exchange of ideas between the two communities. The second “Amplitudes Meet Cosmology” symposium brought together 20 leading researchers to take stock of this exciting progress, to forge new collaborations and to identify promising directions for future research.

    The meeting opened with review talks by Daniel Baumann and Jaroslav Trnka introducing the topics of “Cosmology” and “Scattering Amplitudes,” respectively. Baumann described the big-picture goals of the cosmology community and how they will be informed by a deeper understanding of the predictions of inflation. Trnka gave a broad overview of the types of questions that have been successfully addressed by the amplitudes community, with an eye towards related questions in the cosmological context. These review talks were followed by a lively discussion of the physics of de Sitter (dS) space led by Dionysios Anninos. Most of our understanding of dS physics is rooted in perturbation theory, and Anninos presented some preliminary ideas for gaining more nonperturbative insights, especially in lower-dimensional toy models.

    A major topic of the meeting was the “Cosmological Bootstrap,” a relatively new approach to determine cosmological correlators from basic self-consistency requirements. Austin Joyce gave an overview of the bootstrap approach, highlighting the numerous accomplishments made by a variety of researchers over the past few years. Charlotte Sleight and Massimo Taronna discussed progress in relating insights from AdS/CFT to dS space. In particular, they introduced a specific analytic continuation to map results for Witten diagrams in AdS to in-in correlators in dS. Finally, Enrico Pajer led a discussion on near-term opportunities and open questions of the cosmological bootstrap program.

    The talks on the cosmological bootstrap were complemented by discussions of recent progress in the field of scattering amplitudes and their possible relevance for cosmology. Andrea Puhm reviewed the study “Celestial Amplitudes” and its relation to flat-space holography. David Skinner presented the “Twistor Space” formulation for scattering amplitudes and showed how it can be adapted to study cosmological correlators. He made a promising proposal for using twistors to derive the dS equivalent of the famous Park-Taylor formula for amplitudes.

    The true prize of the modern amplitude program has been the litany of newly discovered structures, long hidden in plain sight in theories more than a century old. For example, “double copy” relations have been found between seemingly distinct theories like in the famous relation between amplitudes in Yang-Mills theory and in gravity. Similar structures still remain to be discovered in the cosmological context and especially double copy relations do not yet exist for cosmological correlators. Arthur Lipstein, Silvia Nagy and Mariana Carrillo-González presented recent work on the cosmological double copy, distinguishing between double-copying predictions already in curved-space and generating the curved space through a double-copy procedure itself. They led an engaged discussion highlighting both the limitations of current approaches and current progress in a number of directions, as well as identifying new strategies and ideas towards future progress.

    The last few years have seen significant progress in deriving rigorous “positivity constraints” on gravitational theories in flat space, relating IR couplings of effective theories to their UV completion. A significant ambition of theoretical cosmology is to derive similar constraints on effective theories in cosmological spacetimes. A full day of the symposium was devoted to a discussion of this important open problem. Andrew Tolley opened the day with a talk that covered a comprehensive review of positivity constraints for flat-space amplitudes. He carefully laid out the technical assumptions that go into the derivation of the positivity bound and highlighted which parts of the argument fail in the cosmological context and therefore need to be revisited. Grant Remmen then gave a talk relating S-matrix positivity bounds to the weak gravity conjecture and entropy arguments. Gary Shiu presented connections of positivity bounds to the swampland program. Julio Parra-Martinez critically evaluated how current approaches using unitarity and causality to derive dispersion relations need to be adapted before they can be applied in the cosmological context.

    The final day opened with two research talks on effective field theory in inflation and dS. Chia-Hsien Shen derived the equivalent of the Adler zero for the effective theory of inflation. Daniel Green reviewed recent progress in the understanding of loop corrections in dS and inflation. Finally, the meeting ended with an extended discussion session led by Donal O’Connell. After summarizing many of the key results presented during the symposium, the participants identified critical (and sometimes subtle) open questions and shared promising future directions.

    Future Directions and Collaborations

    A number of promising directions for future work were clarified during the meeting and possible joint collaborations emerged. Tree-level correlators are now much better understood than they were at the first “Amplitudes Meet Cosmology” symposium. The challenge now has become to understand the analytic structure of correlators at loop level. The participants discussed concrete ideas for how this problem can be attacked. Recent progress on dispersion relations for gravitational theories in flat space also suggest that the time is ripe to apply these new insights to theories in curved spacetimes. The complementary expertise of the participants was very useful in formulating the key challenges of this new research direction. Finally, a concerted effort is now being made to identify unifying structures (like the double copy) for cosmological correlators.

    Future Meetings and Disseminations

    To continue to propagate the successes of the symposium, plans are being made to organize additional workshops and summer schools. In the near term, the organizers are planning another follow-up meeting for promising early career researchers interested in this program, following the success of a similar workshop at Northwestern in 2019. We currently expect to host the meeting at the University of California, San Diego, in the fall of 2022.

    Some of the major topics discussed at this meeting have been summarized in reviews led by the organizers. Six of the participants of the meeting, including Baumann and Green were authors of a Snowmass report on the Cosmological Bootstrap ( Carrasco, Carrillo-González and O’Connell were authors of another Snowmass report on the double copy, including applications to cosmology ( Baumann and Joyce are working on lecture notes covering the theory of “Cosmological Correlations” at the level of beginning graduate students. Finally, Green will author a chapter in the upcoming book Handbook of Quantum Gravity reviewing the topic of “Effective Field Theory in de Sitter Space.”

  • Agenda & Slidesplus--large


    10:00 - 11:00 AMDaniel Baumann | Cosmology Introduction
    View Slides (PDF)
    11:30 - 12:30 PMJaroslave Trnka | Amplitudes Introduction
    5:00 - 6:00 PMDionysios Anninos | de Sitter Musings
    6:15 - 7:15 PMAustin Joyce | An Invitation to the Cosmological Bootstrap
    View Slides (PDF)


    10:00 - 11:00 AMDavid Skinner | Twistors, Ambitwistors and Cosmological Correlators
    11:30 - 12:30 PMAndrea Puhm | Tales from the Celestial Sphere
    5:00 - 5:30 PMCharlotte Sleight | From dS to AdS, and back
    5:30 - 6:00 PMMassimo Taronna | From dS to AdS, and back, continued
    6:15 - 7:15 PMEnrico Pajer | What's next for the cosmological bootstrap?


    5:00 - 6:00 PMArthur Lipstein | Towards a de Sitter double copy
    View Slides (PDF)
    6:15 - 6:45 PMSylvia Nagy | Double Copy and Cosmology
    View Slides (PDF)
    6:45 - 7:15 PMMariana Carrillo-González | Double Copy and Cosmology beyond dS
    View Slides (PDF)


    10:00 - 11:00 AMAndrew Tolley | UV Constraints on IR Physics
    11:30 - 12:00 PMGrant Remmen | Positivity, Entropy, and Weak Gravity
    View Slides (PDF)
    12:00 - 12:30 PMGary Shiu | Amplitudes meet the Swampland
    5:00 - 6:00 PMJulio Parra-Martinez | Unitarity, causality, dispersion relations, and all that...
    View Slides (PDF)


    10:00 - 11:00 AMChia-Hsien Shen | Inflationary Adler Conditions
    11:30 - 12:30 PMDan Green | IR Behavior in de Sitter
    View Slides (PDF)
    5:00 - 6:00 PMDonal O'Connell | Final Discussion
    6:15 - 7:15 PMFinal Discussion, Continued
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