Program Results

Introduction to the event

Prof. Baumann recently developed the “Cosmological Bootstrap,” a new framework for computing and classifying inflationary correlations [1]. Adopting a perspective familiar from the study of scattering amplitudes, Baumann and collaborators showed that these correlations can be determined by consistency conditions alone (such as symmetries, locality and unitarity), avoiding the crippling complexity of standard inflationary perturbation theory. As a Yushan scholar, Prof. Baumann significantly extended this work [2,3,4,5].

He showed that the structure of cosmological correlators is controlled by their singularities, which in turn are fixed in terms of flat-space scattering amplitudes [2]. Scattering amplitudes are therefore shown to be the fundamental building blocks of cosmological correlators. The recent work explains how complex correlators can be reconstructed just by knowing their singular limits and imposing additional consistency requirements (like de Sitter symmetries and perturbative unitarity).

Recently, Prof. Baumann and collaborators also studied the correlators of conformally coupled scalars in a general expanding spacetime [3,4]. These correlators have an integral representation in kinematic space, with the integrand being the product of the corresponding flat-space correlators and “twist factors” that depend on the cosmological evolution. The same type of twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are members of a larger set of master integrals which can be analyzed using ideas from “twisted cohomology.” Baumann derived a set of first-order coupled differential equations for the finite-dimensional integral basis. These differential equations provide a new way to understand the analytic structure of cosmological correlators and to derive new insights into the space of functions allowed by consistent cosmological time evolution.

Massless spinning correlators in cosmology are extremely complicated. The reason for the unreasonable complexity of these correlators lies in the use of inconvenient kinematic variables. For example, in de Sitter space, consistency with unitarity and the background isometries imply that the correlators must be conformally covariant and conserved. However, the commonly used kinematic variables for correlators do not make all these properties manifest. In [5], we introduced twistor space as a powerful way to satisfy all kinematic constraints. We showed that conformal correlators of conserved currents can be written as twistor integrals, where the conservation condition translates into holomorphicity of the integrand. The functional form of the twistor-space correlators is very simple and easily bootstrapped. For the case of three-point functions, we verified explicitly that this reproduces known results in embedding space. We also performed a half-Fourier transform of the twistor-space correlators to obtain their counterparts in momentum space. We therefore showed that twistors provide a promising new avenue to study conformal correlation functions that exposes their hidden simplicity.

In upcoming work, Baumann, Joyce and Lee will present a “double copy” prescription for correlators in (A)dS [6]. This solves a long-standing problem in the field.

Baumann also proposed a new method to measure primordial correlations (such as those computed by the bootstrap method) in cosmological observations of the large-scale structure of the universe [7]. 

The cosmological bootstrap program is now being pursued by many different groups and progress  is happening fast. Together with other leading researchers, Baumann recently summarized this research direction in a Snowmass white paper [8]. Baumann has also lectured on this topic at multiple graduate schools and extensive lectures notes will be published soon [9]. 

Finally, Baumann and collaborators recently also made significant contributions to the emerging field of gravitational wave physics, by showing how future observations can become an interesting probe of particle physics beyond Standard Model [10,11]. This work provides an important bridge between work in these two areas. 

References

[1] N. Arkani-Hamed, D. Baumann, H. Lee and G. Pimentel, The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities,  JHEP 04, 105 (2020).

[2] D. Baumann, W.-M. Chen, C. Duaso Pueyo, A. Joyce, H. Lee and G. Pimentel, Linking the Singularities of Cosmological Correlators, JHEP 09, 010 (2022).

[3] N. Arkani-Hamed, D. Baumann, A. Hillman, A. Joyce, H. Lee and G. Pimentel, Differential Equations for Cosmological Correlators, [arXiv:2312.05303 [hep-th]].

[4] N. Arkani-Hamed, D. Baumann, A. Hillman, A. Joyce, H. Lee and G. Pimentel, Kinematic Flow and the Emergence of TIme, [arXiv:2312.05300 [hep-th]].

[5] D. Baumann, G. Mathys, G. Pimentel and F. Rost, A New Twist on Spinning (A)dS Correlators, [arXiv:2408.02727 [hep-th]].

[6] D. Baumann, A. Joyce and H. Lee, A Differential Double Copy for (A)dS Correlators, [to appear].

[7] D. Baumann and D. Green, The Power of Locality: Primordial Non-Gaussianity at the Map Level, JCAP 08, no.08, 061 (2022).

[8] D. Baumann, D. Green, A. Joyce, E. Pajer, G. Pimentel, C. Sleight and M. Taronna, Snowmass White Paper: The Cosmological Bootstrap, [arXiv:2203.08121 [hep-th]].

[9] D. Baumann and A. Joyce, Lectures on Cosmological Correlations, [to appear].

[10] D. Baumann, G. Bertone, J. Stout and G.M. Tomaselli, Ionization of Gravitational Atoms, Phys. Rev. D 105, no.11, 115036 (2022).

[11] D. Baumann, G. Bertone, J. Stout and G.M. Tomaselli, Sharp Signals of Boson Clouds in Black Hole Binary Inspirals, Phys. Rev. Lett. 128, no.22, 221102 (2022).