Amplitudes Meet Cosmology (2024)

Overview

The Simons Symposium “Amplitudes Meets Cosmology” has been a focal point for dramatic progress at the intersection of these two fields. The prior meetings in 2019 and 2022 helped establish new connections between researchers and opened new lines of inquiry that were neither squarely in one field or the other. The meeting in 2024 brought together 22 researchers, some working along these newly established lines, and new participants representing more potential directions combining these communities, to discuss the big open problems and opportunities that cross these boundaries.

The meeting opened with “Hopes and Dreams” talks by Austin Joyce and Lance Dixon representing the aspirations of the cosmology and amplitude communities respectively. Joyce explained the motivations for cosmologists to understand the origins of the universe and how existing results in the study of scattering amplitudes suggest deeper hidden structures in cosmology. Dixon described the value of combining perturbative and non-perturbative information in the quest to understand deeper structures in these theories. These talks were followed by reviews on the state of progress in both fields since the last meeting by Scott Melville and Mariana Carrillo Gonzalez.

A common point of discussion in the meeting was the interplay between perturbative methods and non-perturbative questions. Eva Silverstein led a discussion about the challenges and opportunities in understanding rare fluctuations, which are beyond the scope of more conventional summary statistic calculations but can be understood in some models by resumming perturbative results. Dio Anninos led a discussion on the state of holography and the value of understanding cosmology from a local perspective (static patch). Jaroslav Trnka then presented a review of positive geometry and methods to define amplitudes from a single geometric object. Hayden Lee and Henrik Johansson then led a discussion on the state of the double copy in cosmology and amplitudes, respectively. The double copy is a hidden structure that relates gravitational theories to the square of non-gravitational theories. Since the last meeting, there have been significant discoveries of double copy structure in cosmological observables, an exciting direction of research that has emerged from these meetings.

One of the topics of significant interest in this symposium is the implications of higher-order calculations to astrophysical and cosmological data. Higher-order quantum and nonlinear corrections are perturbatively represented as loop corrections. We heard from Tim Cohen about conceptual and calculational progress in regulating loop integrals in de Sitter, and from Johannes Henn a very accessible review of current and novel approaches developed in the amplitudes and particle physics community to approach evaluating loop integrals. Mikhail Solon gave a review of recent progress on the use of scattering amplitude calculations for determining properties of the black hole inspiral process and gravitational wave signal relevant to LIGO and other future gravitational wave observatories. Julio Parra Martinez then led a discussion on the lessons learned from the highly successful application to gravitational waves and how that might inform directions for future progress in cosmology. Matt Lewandowski provided an overview on the use of maps of galaxies to inform our understanding of inflation and how those analyses depend on state-of-the-art loop calculations. Tongyan Lin discussed the state of sub-GeV dark matter detection and how it requires knowledge of higher multiplicity dark matter phonon scatter calculations. Finally, Soubhik Kumar discussed recent progress in understanding how interactions between multiple particles during inflation manifest themselves in new observational signatures in cosmic data. These discussions collectively helped articulate how theory determines our observational capabilities, and the potential role for amplitude techniques in both higher precision calculations and revealing new directions in the space of interesting signals.

A unifying perspective on both flat space and cosmological predictions is the relationship between boundary symmetries and soft behavior, a point brought home by Silvia Nagy both in discussion of flat and de Sitter space, with concrete steps towards describing self-dual gauge and gravity theories in de Sitter perturbing towards the full theory. Finally, a spectacular exemplar of the power of bootstrap methods in curved space time was demonstrated by Fernando Alday in the construction of four-point closed and open string amplitudes (Virasoro-Shapiro and Veneziano) to higher order in curvature corrections in AdS.

We closed the symposia with an animated discussion led by Clifford Cheung on the path forward to concrete progress in achieving the hopes and dreams identified through the week, identifying a number of sharp targets both formally in dS and near term in large-scale structure.

Future Directions and Collaborations

A lot of progress has been made since the first Amplitudes meets Cosmology symposium. Many of the powerful tools that have been essential for flat space scattering, such as unitarity, factorization, double copy and bootstrap have all found cosmological analogues. These have already proven to be very powerful tools for understanding the space of tree-level cosmological correlators. Moreover, there has been significant progress in understanding structures at loop level, including windows into all orders or non-perturbative results such as positivity and sum rules. One future direction of particular interest is to translate these insights from the purely theoretical domain to an observational one. Higher-order calculations would be of immediate benefit to large-scale structure analyses. However, there is a long transition in cosmology of theoretical structures transforming how we interpret and analyze cosmic observations.

Future Meetings and Disseminations

Since the first Amplitudes meets Cosmology symposium in 2019, one of our central tools for disseminating progress has been through additional workshops and meetings that engage the large communities. The coming few years will be no exception. In 2024, Baumann will be hosting two meetings in Taiwan, “Cosmological Correlators” and “QCD Meets Gravity.” Baumann, Green and Carrasco are also looking to host a meeting targeted at early career researchers in 2025, like the very successful meeting held at Northwestern in 2019. In 2026, Green and Baumann (with Pimentel and Joyce) will be organizing a IHES summer school on Cosmological Correlators. The impact of our earlier satellite meetings was noteworthy at the final Amplitudes meets Cosmology symposium, as a number of participants had become active in this area after attending one of these workshops.