Article

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

(Impact Factor: 3.95). 05/2012; 864(3). DOI: 10.1016/j.nuclphysb.2012.07.004
Source: arXiv

ABSTRACT 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 $f_{\rm NL}$ of the bispectrum in the squeezed limit and $\tau_{\rm NL}$ 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.

0 Followers
·
81 Views
• Source
##### Article: A Consistency Relation for the Observed Galaxy Bispectrum and the Local non-Gaussianity from Relativistic Corrections
[Hide abstract]
ABSTRACT: We obtain a consistency relation for the observed three-point correlator of galaxies. It includes relativistic effects and it is valid in the squeezed limit. Furthermore, the consistency relation is non-perturbative and can be used at arbitrarily small scales for the short modes. Our results are also useful to compute the non-linear relativistic corrections which induce a signal in the observations that might be misinterpreted as primordial non-Gaussianity with a local shape. We estimate the effective local non-Gaussianity parameter from the relativistic corrections. The exact value depends on the redshift and the magnification bias. At redshift of $z = 1$, in the absence of magnification bias, we get $\,\, f^{\rm GR}_{\rm NL} \simeq - 3.7$.
• Source
##### Article: A Consistency Relation for the Observed Galaxy Bispectrum and the Local non-Gaussianity from Relativistic Corrections
[Hide abstract]
ABSTRACT: We obtain a consistency relation for the observed three-point correlator of galaxies. It includes relativistic effects and it is valid in the squeezed limit. Furthermore, the consistency relation is non-perturbative and can be used at arbitrarily small scales for the short modes. Our results are also useful to compute the non-linear relativistic corrections which induce a signal in the observations that might be misinterpreted as primordial non-Gaussianity with a local shape. We estimate the effective local non-Gaussianity parameter from the relativistic corrections. The exact value depends on the redshift and the magnification bias. At redshift of z=1, in the absence of magnification bias, we get fGRNL≃−3.7.
• Source
##### Article: Soft limits in holographic cosmology
[Hide abstract]
ABSTRACT: We study the soft limits of cosmological correlators from a holographic perspective, showing how the inflationary consistency relations arise from the diffeomorphism invariance of the dual quantum field theory. Starting from the corresponding Ward identity, by taking moments we derive the leading and subleading behaviour of the stress tensor 3-point function in the limit as one momentum vanishes. These results are non-perturbative and valid in quantum field theories of a very general nature. Exploiting the known mapping of correlators in the dual quantum field theory to those of the cosmology, we then obtain the leading and subleading soft behaviour of all cosmological 3-point correlators of curvature perturbations and gravitons. Our results thus provide a holographic derivation of all leading and subleading consistency relations for cosmological 3-point functions, and our method is easily generalised. We verify our results explicitly for slow-roll inflation and for strongly coupled holographic cosmologies with a perturbative dual description.