High Energy Physics Signatures from Inflation and Conformal Symmetry of de Sitter
Alex Kehagias, Antonio Riotto
TL;DR
The paper investigates how heavy fields during inflation affect light-field correlators using the dS/CFT correspondence. It shows that heavy states with $m>H$ induce power-law corrections of ${\cal O}(H^2/m^2)$ in two- and four-point functions, in addition to Boltzmann suppression captured by loops. The leading heavy-state effect on the four-point function is a power-law suppressed contribution from massive scalar exchange, and the conformal structure of correlators is preserved. These results provide a robust, UV-sensitive imprint on inflationary observables that could, in principle, inform searches for high-energy physics in cosmological data.
Abstract
During inflation, the geometry of spacetime is described by a (quasi-)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group SO(1, 4) which acts like a conformal group on R^3: when the fluctuations are on super-Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three-dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides the Boltzmann suppression expected from the thermal properties of de Sitter space, the generic effect of heavy fields in the inflationary correlators of the light fields is to introduce power-law suppressed corrections of the form O(H^2/m^2). This can be seen, for instance, at the level of the four-point correlator for which we provide the correction due to a massive scalar field exchange.