Non-linear Realizations of Conformal Symmetry and Effective Field Theory for the Pseudo-Conformal Universe

TL;DR

This paper develops a comprehensive effective field theory framework for the pseudo-conformal universe scenario, capturing its symmetry-breaking pattern and low-energy dynamics, and computes relevant correlation functions.

Contribution

It applies coset techniques and geometric invariants to derive the most general effective Lagrangian for pseudo-conformal models, unifying various realizations.

Findings

Derived the general effective Lagrangian for pseudo-conformal scenarios.

Computed two-point functions for Goldstone and weight-0 fields.

Analyzed three-point functions involving these fields.

Abstract

The pseudo-conformal scenario is an alternative to inflation in which the early universe is described by an approximate conformal field theory on flat, Minkowski space. Some fields acquire a time-dependent expectation value, which breaks the flat space so(4,2) conformal algebra to its so(4,1) de Sitter subalgebra. As a result, weight-0 fields acquire a scale invariant spectrum of perturbations. The scenario is very general, and its essential features are determined by the symmetry breaking pattern, irrespective of the details of the underlying microphysics. In this paper, we apply the well-known coset technique to derive the most general effective lagrangian describing the Goldstone field and matter fields, consistent with the assumed symmetries. The resulting action captures the low energy dynamics of any pseudo-conformal realization, including the U(1)-invariant quartic model and the Galilean Genesis scenario. We also derive this lagrangian using an alternative method of curvature invariants, consisting of writing down geometric scalars in terms of the conformal mode. Using this general effective action, we compute the two-point function for the Goldstone and a fiducial weight-0 field, as well as some sample three-point functions involving these fields.