Inflation and conformal invariance: the perspective from radial quantization

Abstract

According to the dS/CFT correspondence, correlators of fields generated during a primordial de Sitter phase are constrained by three-dimensional conformal invariance. Using the properties of radially quantized conformal field theories and the operator-state correspondence, we glean information on some points. The Higuchi bound on the masses of spin-s states in de Sitter is a direct consequence of reflection positivity in radially quantized CFT 3 and the fact that scaling dimensions of operators are energies of states. The partial massless states appearing in de Sitter correspond from the boundary CFT 3 perspective to boundary states with highest weight for the conformal group. We discuss inflationary consistency relations and the role of asymptotic symmetries which transform asymptotic vacua to new physically inequivalent vacua by generating long perturbation modes. We show that on the CFT 3 side, asymptotic symmetries have a nice quantum mechanics interpretation. For instance, acting with the asymptotic dilation symmetry corresponds to evolving states forward (or backward) in "time" and the charge generating the asymptotic symmetry transformation is the Hamiltonian itself. Finally, we investigate the symmetries of anisotropic inflation and show that correlators of four-dimensional free scalar fields can be reproduced in the dual picture by considering an isotropic three-dimensional boundary enjoying dilation symmetry, but with a nonvanishing vacuum expectation value of the boundary stress-energy momentum tensor.

The Hunt for Primordial Interactions in the Large-Scale Structures of the Universe

“…Here we want to stress that we are not only restricting to scalar fields: indeed a tower of high-spin states can arise in string theory constructions [81,82]. While the effect of massive scalar fields have been thoroughly investigated in the context of quasi-single field inflation [12,54,[83][84][85][86][87][88][89][90][91][92], higher-spin particles studies arose more recently [87,88,91,[93][94][95][96][97].…”

“…For these values, the system acquires an additional gauge invariance and the corresponding fields are called partially massless fields [101]. Partially massless fields produce sizeable tensor-scalar-scalar bispectra and the scalar trispectra [91,93,95]. In the case of study here, i.e.…”

Imprints of spinning particles on primordial cosmological perturbations

“…This inequality can be inferred from the dS/CFT 3 correspondence [4,11,12] and implies that higherspin super-Hubble two-point correlators A i 1 ···is A i 1 ···is decay as (−τ ) 2∆ with ∆ > 1, as one can deduce from the relation (1.1). Higher-spin fields are therefore short-lived and their impact on cosmological observables is rather suppressed.…”

Correlation functions of sourced gravitational waves in inflationary scalar vector models. A symmetry based approach

“…The relation between the de Sitter space and the conformal field theory have been widely used in cosmology. In particular, a powerful application of this relationship is to use the isomorphism between the de Sitter group in four dimensions and the conformal group in three dimensions to fix the form of the primordial correlation functions [1][2][3][4][5][6][7][8][9][10][11][12][13] 1 . The key idea of this method comes from the fact that, during the inflationary expansion, deep in the super horizon regime, the fields behave (approximately) like conformal fields.…”