The Inflationary Wavefunction from Analyticity and Factorization. (arXiv:2107.10266v3 [hep-th] UPDATED)
<a href="http://arxiv.org/find/hep-th/1/au:+Meltzer_D/0/1/0/all/0/1">David Meltzer</a>
We study the analytic properties of tree-level wavefunction coefficients in
quasi-de Sitter space. We focus on theories which spontaneously break dS boost
symmetries and can produce significant non-Gaussianities. The corresponding
inflationary correlators are (approximately) scale invariant, but are not
invariant under the full conformal group. We derive cutting rules and
dispersion formulas for the late-time wavefunction coefficients by using
factorization and analyticity properties of the dS bulk-to-bulk propagator.
This gives a unitarity method which is valid at tree-level for general
$n$-point functions and for fields of arbitrary mass. Using the cutting rules
and dispersion formulas, we are able to compute $n$-point functions by gluing
together lower-point functions. As an application, we study general four-point,
scalar exchange diagrams in the EFT of inflation. We show that exchange
diagrams constructed from boost-breaking interactions can be written as a
finite sum over residues. Finally, we explain how the dS identities used in
this work are related by analytic continuation to analogous identities in
Anti-de Sitter space.
We study the analytic properties of tree-level wavefunction coefficients in
quasi-de Sitter space. We focus on theories which spontaneously break dS boost
symmetries and can produce significant non-Gaussianities. The corresponding
inflationary correlators are (approximately) scale invariant, but are not
invariant under the full conformal group. We derive cutting rules and
dispersion formulas for the late-time wavefunction coefficients by using
factorization and analyticity properties of the dS bulk-to-bulk propagator.
This gives a unitarity method which is valid at tree-level for general
$n$-point functions and for fields of arbitrary mass. Using the cutting rules
and dispersion formulas, we are able to compute $n$-point functions by gluing
together lower-point functions. As an application, we study general four-point,
scalar exchange diagrams in the EFT of inflation. We show that exchange
diagrams constructed from boost-breaking interactions can be written as a
finite sum over residues. Finally, we explain how the dS identities used in
this work are related by analytic continuation to analogous identities in
Anti-de Sitter space.
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