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

Nuclear Physics B (Impact Factor: 3.93). 05/2012; 864(3). DOI: 10.1016/j.nuclphysb.2012.07.004
Source: arXiv


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.

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    • "Although α in the squeezed limit was given in [62] [63] in terms of OPE coefficients. "
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    ABSTRACT: We calculate the squeezed limit of the bispectrum produced by inflation with multiple light fields. To achieve this we allow for different horizon exit times for each mode and calculate the intrinsic field-space three-point function in the squeezed limit using soft-limit techniques. We then use the $\delta N$ formalism from the time the last mode exits the horizon to calculate the bispectrum of the primordial curvature perturbation. We apply our results to calculate the spectral index of the halo bias, $n_{\delta b}$, an important observational probe of the squeezed limit of the primordial bispectrum and compare our results with previous formulae. We give an example of a curvaton model with $n_{\delta b} \sim {\cal O}(n_s-1)$ for which we find a 20% correction to observable parameters for squeezings relevant to future experiments. For completeness, we also calculate the squeezed limit of three-point correlation functions involving gravitons for multiple field models.
    Full-text · Article · Jul 2015 · Journal of Cosmology and Astroparticle Physics
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    • "There are many other references also of relevance. The use of conformal symmetry to constrain inflationary correlation functions has also been discussed in [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]. Approaches where the conformal symmetries are often thought of as being non-linearly realized include [19–38]. "
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    ABSTRACT: We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.
    Full-text · Article · Jul 2015 · Journal of High Energy Physics
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    • "In this case the consistency relation is a consequence of the spatial dilation which is non-linearly realized by the curvature perturbations ζ. More recently, inflationary consistency relations derived for other non-linearly realized symmetries have been derived [15] [16] [17] [18] [19] [20]. "
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    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 $.
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