Snowmass White Paper: The Cosmological Bootstrap

TL;DR

The cosmological bootstrap aims to reconstruct primordial fluctuations directly from fundamental principles—unitarity, locality, and symmetry—rather than evolving bulk dynamics. By exploiting de Sitter and quasi-de Sitter symmetries, boundary wavefunctions, and their singularities, the framework bootstrap's tree-level correlators, including boostless cases, and draws deep connections to AdS holography via double Wick rotations. Nonperturbative implications are explored through Källén–Lehmann-type representations and conformal partial waves, suggesting positivity constraints and potential nonperturbative bootstrap structures for cosmology. The program aspires to a holographic-like, diagram-free understanding of inflationary observables, guiding future observational strategies and theoretical development toward loops, nonperturbative formulations, and a fuller AdS/dS mapping.

Abstract

This white paper summarizes recent progress in the cosmological bootstrap, an approach to the study of the statistics of primordial fluctuations from consistency with unitarity, locality and symmetry assumptions. We review the key ideas of the bootstrap method, with an eye towards future directions and ambitions of the program. Focusing on recent progress involving de Sitter and quasi-de Sitter backgrounds, we highlight the role of singularities and unitarity in constraining the form of the correlators. We also discuss nonperturbative formulations of the bootstrap, connections to anti-de Sitter space, and potential implications for holography.

Figures (7)

• Figure 1: The pattern of correlations measured after inflation traces the dynamics and retains a memory of the physics during inflation. Because fluctuations of different wavelength freeze out at different times, the scale/shape dependence of late-time correlations encodes the time-dependant inflationary physics in a purely static object. An aspect of this remarkable connection is that we can learn about the particle content present during inflation by measuring subtle correlations imprinted in correlations on the reheating surface.
• Figure 2: Schematic of the singularities of the cosmological wavefunction. The wavefunction has singularities when (partial) energies are conserved. The coefficients of these singularities can be written in terms of scattering amplitudes and lower-point wavefunctions. Even though these singularities lie at analytically continued momentum configurations, they nevertheless partially control the behavior of the wavefunction for physical kinematics. Extending away from these singularities to general momentum configurations is a boundary version of the challenge of time evolution in the bulk.
• Figure 3: The inflationary three-point function due to the exchange of a massive spinning particle inherits the analytic structure of the four-point function of conformally coupled scalars exchanging a massive scalar. To obtain the inflationary correlator, we apply a spin-raising operator ${\cal S}$ (changing the spin of the exchanged particle) and a weight-shifting operator ${\cal W}$ (converting the external particles from conformally coupled to massless). Finally, taking one of the legs to be soft gives the inflationary three-point function in the slow-roll limit.
• Figure 4: Graphical summary of the cosmological cutting rules for wavefunction coefficients Melville:2021lst. The discontinuity of a given diagram in perturbation theory with all internal energy kept fixed is equal to the product of the discontinuities of all disconnected diagrams obtained by summing over all possible ways to cut one or more internal legs and substituting them with a pair of external legs. For each cut leg, one should multiply by the associated power spectrum and integrate over the cut momentum.
• Figure 5: Penrose diagrams showing the asymptotic boundaries of AdS ( left) and dS ( right). An important difference between the two cases is that the boundary in AdS is timelike, so that there is a boundary notion of causality and unitarity. On the other hand, the boundary of dS is spacelike, so the only natural notions of this kind are the ones inherited from the bulk spacetime, casting into relief the challenge of holography in this space.