The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization

Abstract

We extend the cosmological bootstrap to correlators involving massless particles with spin. In de Sitter space, these correlators are constrained both by symmetries and by locality. In particular, the de Sitter isometries become conformal symmetries on the future boundary of the spacetime, which are reflected in a set of Ward identities that the boundary correlators must satisfy. We solve these Ward identities by acting with weight-shifting operators on scalar seed solutions. Using this weight-shifting approach, we derive three-and four-point correlators of massless spin-1 and spin-2 fields with conformally coupled scalars. Four-point functions arising from tree-level exchange are singular in particular kinematic configurations, and the coefficients of these singularities satisfy certain factorization properties. We show that in many cases these factorization limits fix the structure of the correlators uniquely, without having to solve the conformal Ward identities. The additional constraint of locality for massless spinning particles manifests itself as current conservation on the boundary. We find that the four-point functions only satisfy current conservation if the s, t, and u-channels are related to each other, leading to nontrivial constraints on the couplings between the conserved currents and other operators in the theory. For spin-1 currents this implies charge conservation, while for spin-2 currents we recover the equivalence principle from a purely boundary perspective. For multiple spin-1 fields, we recover the structure of Yang-Mills theory. Finally, we apply our methods to slow-roll inflation and derive a few phenomenologically relevant scalar-tensor three-point functions.

Towards the non-perturbative cosmological bootstrap

“…• The consequences of perturbative unitarity are currently being investigated in a program known as the cosmological bootstrap [5,10,6,7]. Is it possible to make contact between our work and the perturbative cosmological bootstrap?…”

“…It is interesting to understand the behaviour of quantum fields in such a background spacetime. Most studies so far focus on a perturbative treatment of interactions [3][4][5][6][7][8][9][10]. In this paper, we take the first steps towards a non-perturbative formulation of Quantum Field Theory (QFT) on a dS background.…”

“…The minus sign in the second term of (3.21) arises from the fact that the contour is taken in the clockwise direction 10. There are two types of subleading terms.…”

Cosmological Scattering Equations at Tree-level and One-loop

“…The relation between scattering amplitudes and conformal correlators opens up the the possibilty of importing amplitude methods to the study of cosmology. Recent progress along these lines includes geometric approaches [51,52], reconstruction from symmetries and factorisation [53][54][55][56][57][58][59], unitarity methods [60][61][62][63][64], color/kinematics duality [66][67][68][69], and the double copy [70][71][72][73]. There has also been recent progress in the nonperturbative calculation of non-gravitational correlators in rigid dS background [74,75].…”

Precision Calculation of Inflation Correlators at One Loop

“…The recent progress [41][42][43] in the analytical computation of tree-level diagrams is essentially achieved by fully exploiting the symmetry of the inflation background, which can sometimes be approximated by de Sitter (dS) space. Due to the enlarged symmetry of dS relative to a general slow-roll background, it is possible to transform a flat-space correlator into the corresponding object in dS via dS time translation and boosts, a process called "cosmological bootstrap".…”