Cosmological Wavefunctions as Amplitudes: Dual Shuffle Factorization and Uniqueness from New Hidden Zeros

TL;DR

This paper reveals a new zero-based factorization structure in cosmological wavefunctions, unifying and extending known amplitude properties, and demonstrates that these zeros uniquely determine wavefunctions at tree level.

Contribution

It introduces a dual shuffle factorization principle based on hidden zeros, establishing a connection between cosmological wavefunctions and flat-space amplitudes, and proves their uniqueness without unitarity assumptions.

Findings

Uncovered new graph-based hidden zeros extending known cosmological zeros.

Established a dual factorization principle relating zeros to graph decompositions.

Proved that zeros and locality uniquely determine tree-level wavefunctions.

Abstract

We show that cosmological wavefunctions in $\phi^n$ theories naturally generalize flat-space $\mathrm{Tr}(\phi^3)$ scattering amplitudes: via a simple map from tube variables to Mandelstam invariants, each wavefunction coefficient $\psi_{\mathcal{G}}$ becomes an on-shell amplitude-like object $\mathcal{A}_G$ associated with a generating graph $G$. At tree level these objects coincide with the Cachazo-He-Yuan construction based on Cayley functions that generalizes Parke-Taylor factors. We uncover new graph-based hidden zeros that extend and unify all known cosmological zeros. Based on this zero structure, we uncover a factorization principle dual to unitarity. Instead of factorization across poles, $A\to A_L\times A_R$, a zero at $p_{a\in G_L}\!\cdot\! p_{b\in G_R}=0$ factorizes the generating graph, $G\to G_L\times G_R$, and is equivalent to the shuffle decomposition $\mathcal{A}_G=\mathcal{A}_{G_L}\unicode{x29E2}\mathcal{A}_{G_R}$. Near-zero factorization is a simple consequence of this new structure. Using dual factorization, we show that locality together with the full set of hidden zeros uniquely fixes tree-level cosmological wavefunctions without assuming unitarity. We show that these zeros are equivalent to special enhanced large-$z$ behavior under Britto-Cachazo-Feng-Witten (BCFW) shifts, extending the zeros--BCFW correspondence beyond flat-space amplitudes. We also find evidence for further extensions of the zero structure and loop-level uniqueness. Our results show that cosmology provides a natural arena for on-shell methods and even reveals new structure in flat-space amplitudes.