The Cosmological δ-shift
Abstract
We consider the extension of the δ-shift connecting Tr(ϕ3) and pion amplitudes to observables in cosmology. We start in flat-space and explain how one can extract the pion wavefunction and correlators from those of Tr(ϕ3) theory, via a simple kinematic deformation. As opposed to the amplitude, the δ-shift for the wavefunction is no longer a linear deformation on the kinematics since the wavefunction depends on magnitudes rather than the squares of momenta. We "linearize" this deformation by using the frequency representation - allowing us to recast the contribution from any graph as a sum over residues. We then show how this construction extends to de Sitter, and find that, remarkably, in the frequency representation, the pion de Sitter wavefunction and correlators can be formulated in precisely the same way as in flat-space. Amongst other things, this unified formulation reveals a simple universal soft-limit for flat-space and de Sitter, where, in the soft-limit, the wavefunction turns into a sum of wavefunctions in a mixed theory of pions and scalars.
Related
- Cosmological extra dimensions can mimic dark matter II. Growth of cosmological structures
- Analytical Cosmological Collider at Strong Mixing in Laplace Space
- Electric Penrose process in spherically symmetric regular black holes with and without a cosmological constant
- Rates of tidal disruption events from constrained cosmological simulations of the local Universe: population properties and implications for transient surveys
- Unification of polynomial and exponential cosmological attractors
BibTeX
@misc{figueiredo2026cosmological,
title = {{The Cosmological $δ$-shift}},
author = {Carolina Figueiredo and Jiajie Mei and Yuyu Mo and Francisco Vazão},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08904},
eprint = {2610.08904},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08904},
}
RIS
TY - UNPB
TI - The Cosmological δ-shift
AU - Carolina Figueiredo
AU - Jiajie Mei
AU - Yuyu Mo
AU - Francisco Vazão
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.08904
UR - https://arxiv.org/abs/2610.08904
AB - We consider the extension of the δ-shift connecting Tr(ϕ^3) and pion amplitudes to observables in cosmology. We start in flat-space and explain how one can extract the pion wavefunction and correlators from those of Tr(ϕ^3) theory, via a simple kinematic deformation. As opposed to the amplitude, the δ-shift for the wavefunction is no longer a linear deformation on the kinematics since the wavefunction depends on magnitudes rather than the squares of momenta. We "linearize" this deformation by using the frequency representation - allowing us to recast the contribution from any graph as a sum over residues. We then show how this construction extends to de Sitter, and find that, remarkably, in the frequency representation, the pion de Sitter wavefunction and correlators can be formulated in precisely the same way as in flat-space. Amongst other things, this unified formulation reveals a simple universal soft-limit for flat-space and de Sitter, where, in the soft-limit, the wavefunction turns into a sum of wavefunctions in a mixed theory of pions and scalars.
ER -