The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds

Abstract

A key insight of the bootstrap approach to cosmological correlations is the fact that all correlators of slow-roll inflation can be reduced to a unique building block-the four-point function of conformally coupled scalars, arising from the exchange of a massive scalar. Correlators corresponding to the exchange of particles with spin are then obtained by applying a spin-raising operator to the scalar-exchange solution. Similarly, the correlators of massless external fields can be derived by acting with a suitable weight-raising operator. In this paper, we present a systematic and highly streamlined derivation of these operators (and their generalizations) using tools of conformal field theory. Our results greatly simplify the theoretical foundations of the cosmological bootstrap program.

Primordial Gravitational Waves from Galaxy Intrinsic Alignments

“…Primordial tensor non-Gaussianities have been object of several studies and provide an interesting window to interactions taking place during inflation at very high energies [62,68,[74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]. The galaxy shape field bispectrum g g g or cross-correlations of shape and density such as g g δ and g δ δ contain the direct information on tensor non-Gaussianities h h h and the respective cross-correlations with the scalar perturbation h h ζ and h ζ ζ through the modelling of how g ij responds to tensor perturbations we explained in Section 3.…”

Momentum space CFT correlators for Hamiltonian truncation

“…Indeed, momentum space is the natural arena for many types of observables. Example contexts include cosmology [16][17][18][19][20][21][22][23][24][25][26], 'conformal collider' physics [27][28][29][30][31], anomalies [32][33][34][35], and quantum critical transport [36][37][38][39][40][41]. Momentum space is also useful for computing conformal blocks and the conformal bootstrap [42][43][44][45].…”

Chaos and complementarity in de Sitter space

“…Related to this, we also noted that the purely single-sided correlator that displays maximal chaos can be interpreted as an inflationary correlator by moving all operators to the future boundary. It might therefore be possible to use the recent developments in the cosmological bootstrap [56][57][58][59] to directly write down the OTOC for arbitrary masses. If it can then be confirmed that the OTOC also displays maximal chaos for very light fields (such as the inflaton), one can study the implications of maximal chaos on inflation.…”