Operator Product Expansion of Inflationary Correlators and Conformal Symmetry of de Sitter

By A. Kehagias, A. Riotto. 2012

150 citations recorded by the source corpus.

We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special conformally invariant. We exploit the operator product expansion technique of conformal field theories to study the inflationary correlators enjoying the symmetries present during the de Sitter epoch. The operator product expansion is particularly powerful in characterizing inflationary correlation functions in two observationally interesting limits, the squeezed limit of the three-point correlator and the collapsed limit of the four-point correlator. Despite the fact that the shape of the four-point correlators is not fixed by the symmetries of de Sitter, its exact shape can be found in the collapsed limit making use of the operator product expansion. By employing the fact that conformal invariance imposes the two-point cross-correlations of the light fields to vanish unless the fields have the same conformal weights, we are able to show that the Suyama–Yamaguchi inequality relating the coefficients fNLfNL of the bispectrum in the squeezed limit and τNLτNL of the trispectrum in the collapsed limit also holds when the light fields are intrinsically non-Gaussian. In fact, we show that the inequality is valid irrespectively of the conformal symmetry, being just a consequence of fundamental physical principles, such as the short-distance expansion of operator products. The observation of a strong violation of the inequality will then have profound implications for inflationary models as it will imply either that multifield inflation cannot be responsible for generating the observed fluctuations independently of the details of the model or that some new non-trivial degrees of freedom play a role during inflation.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f71f393f648991ecdaf6d25c747d3ad5b5186d1e

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In Astronomy and Astrophysics

1. E. Pajer
2. D. Baumann
3. D. Green
4. Valentin Assassi
5. A. Joyce
6. G. L. Pimentel
7. J. Khoury
8. Hayden Lee

In Nuclear and High Energy Physics

1. E. Pajer
2. D. Baumann
3. D. Green
4. A. Joyce
5. Valentin Assassi
6. Adam Bzowski
7. G. L. Pimentel
8. Hayden Lee

Citations in the corpus

• Implications of conformal invariance in momentum space (2013, methodology): “Our original motivation for analysing this question was the requirement for these results in our work on holographic cosmology [14–18], and similar applications of the conformal/de Sitter symmetry in cosmology have been discussed in [19–25].”
• Symmetries and loops in inflation (2012, methodology): “(4.3) 8The utility of OPEs to describe soft limits of inflationary correlation functions has recently been emphasized by Kehagias and Riotto [41].”
• An infinite set of Ward identities for adiabatic modes in cosmology (2013, background): “The conformal symmetries are restored (and linearly realized on the fields) in the limit that the background becomes exact de Sitter space [49–56].”
• Building a boostless bootstrap for the bispectrum (2020, result): “A similar result was found in [7] for the bispectrum of a spectator scalar (see also [8]).”
• On soft limits of inflationary correlation functions (2012, background): “The symmetries are still explicit for fields that don’t couple to the inflaton, such as tensor metric fluctuations [42] or scalar spectator fields [43, 44].”
• Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies (2015, background): “The initial motivation for this work was the need for momentum-space CFT correlators in the context of holographic cosmology [8–12]; similar applications of conformal/de Sitter symmetry in cosmology have been discussed in [13–21].”
• The cosmological bootstrap: weight-shifting operators and scalar seeds (2019, background): “In particular, the cosmological bootstrap exploits the approximate de Sitter symmetries—which act as conformal transformations on the boundary [8–12]—along with consistency requirements on the singularity structure of correlation functions to reconstruct the output of bulk time evolution without eve”