Conformal consistency relations for single-field inflation
By P. Creminelli, J. Noreña, M. Simonovi'c. 2012
238 citations recorded by the source corpus.
We generalize the single-field consistency relations to capture not only the leading term in the squeezed limit — going as 1/q3, where q is the small wavevector — but also the subleading one, going as 1/q2. This term, for an (n+1)-point function, is fixed in terms of the variation of the n-point function under a special conformal transformation; this parallels the fact that the 1/q3 term is related with the scale dependence of the n-point function. For the squeezed limit of the 3-point function, this conformal consistency relation implies that there are no terms going as 1/q2. We verify that the squeezed limit of the 4-point function is related to the conformal variation of the 3-point function both in the case of canonical slow-roll inflation and in models with reduced speed of sound. In the second case the conformal consistency conditions capture, at the level of observables, the relation among operators induced by the non-linear realization of Lorentz invariance in the Lagrangian. These results mean that, in any single-field model, primordial correlation functions of ζ are endowed with an SO(4,1) symmetry, with dilations and special conformal transformations non-linearly realized by ζ. We also verify the conformal consistency relations for any n-point function in models with a modulation of the inflaton potential, where the scale dependence is not negligible. Finally, we generalize (some of) the consistency relations involving tensors and soft internal momenta.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/4c4e77316b0ddefe2dc399ce5a6639d6835135a9
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Citations in the corpus
- 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].”
- An infinite set of Ward identities for adiabatic modes in cosmology (2013, methodology): “In the absence of tensors, for instance, it has been argued recently that conformal transformations on spatial slices are residual symmetries of the scalar sector [47, 48].”
- Building a boostless bootstrap for the bispectrum (2020, background): “Within single-clock inflation and without any further assumptions about the particle content, a given correlator is a correlator of ζ (in some cosmological model) if and only if it obeys all the soft theorems [37, 34, 33, 35] that generalize Maldacena’s consistency relation [38].”
- Non-Gaussianity as a particle detector (2016, background): “As in the case of the scalar bispectrum, the leading coefficients are determined by the singlefield consistency relation [12] (see also [41, 43]).”
- The bispectrum in the Effective Field Theory of Large Scale Structure (2014, unknown): “first studied in [39].”
- On soft limits of inflationary correlation functions (2012, methodology): “As explained nicely in recent work by Creminelli, Noreña, and Simonović [12] and Hinterbichler, Hui and Khoury [11], the symmetries in eqs.”
- Single-field consistency relations of large scale structure part II: resummation and redshift space (2013, methodology): “[26] we work in Newtonian gauge (see [16] for an analogous calculation in ζ-gauge).”
- Conformal Symmetries of Adiabatic Modes in Cosmology (2012, methodology): “This relation has been derived using the background-wave method in a recent paper by Creminelli, Noreña and Simonović [19] (who have kindly shared with us their preprint ahead of submission).”
- Implications of conformal invariance in momentum space (2013, methodology): “In momentum space, the Ward identities for scalar operators have been partially analysed in [20, 21], and we will use these results here before generalising them in the following sections.”
- Symmetries and loops in inflation (2012, background): “8) implies that g1(k) = 0, which ensures that first subleading term is suppressed by q2/k2 [12].”