[Paper Review] The Subtle Simplicity of Cosmological Correlators

Chandramouli Chowdhury, Arthur Lipstein+3 more|arXiv (Cornell University)|Dec 21, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates in-in cosmological correlators in four-dimensional de Sitter space for conformally coupled φ⁴ theory, showing that despite the complexity of de Sitter spacetime and loop regularization, these correlators are structurally simpler than wavefunction coefficients due to nontrivial cancellations from shadow fields. Up to two loops, their loop integrands reduce to flat space Feynman integrals and obey a novel recursion relation, yielding results with the same transcendentality as flat space amplitudes.

ABSTRACT

We investigate cosmological correlators for conformally coupled $ϕ^4$ theory in four-dimensional de Sitter space. These extit{in-in} correlators differ from scattering amplitudes for massless particles in flat space due to the spacelike structure of future infinity in de Sitter. They also require a regularization which preserves de Sitter-invariance, which makes the flat space limit subtle to define at loop-level. Nevertheless we find that up to two loops, the extit{in-in} correlators are structurally simpler than the wave function and have the same transcendentality as flat space amplitudes. Moreover, we show that their loop integrands can be recast in terms of flat space integrands and can be derived from a novel recursion relation.

Motivation & Objective

• To understand the analytic structure of in-in cosmological correlators in de Sitter space, which are more directly observable than wavefunction coefficients.
• To address the challenge of defining a flat space limit in de Sitter due to spacelike future infinity and de Sitter-invariant regularization.
• To investigate whether loop corrections to in-in correlators are simpler than those for wavefunction coefficients, despite the nontrivial geometry.
• To derive a novel recursion relation for in-in correlators analogous to those used for wavefunctions in de Sitter space.
• To establish a connection between in-in correlator integrands and standard flat space Feynman integrals via shadow field contributions.

Proposed method

• Use an effective action with shadow fields to compute in-in correlators in de Sitter space, preserving de Sitter invariance.
• Apply a radial cutoff regularization that maintains de Sitter symmetry and allows consistent loop computations.
• Decompose loop integrals into radial and boundary momentum components, with the boundary loop momentum governed by a three-dimensional momentum space.
• Derive loop integrands in terms of standard four-dimensional flat space Feynman integrals, with modifications due to the boundary structure.
• Construct a recursion relation for in-in correlators analogous to the one for wavefunctions, using the same diagrammatic structure but with modified propagators from shadow fields.
• Map the resulting integrands to flat space-like structures, enabling direct comparison with scattering amplitudes.

Experimental results

Research questions

• RQ1 Are in-in cosmological correlators in de Sitter space structurally simpler than wavefunction coefficients, despite the nontrivial geometry and regularization?
• RQ2 Can loop integrands of in-in correlators be recast in terms of standard flat space Feynman integrals?
• RQ3 Does the inclusion of shadow fields lead to cancellations that restore translational invariance and simplify the analytic structure?
• RQ4 Can a recursion relation for in-in correlators be derived that mirrors the one used for wavefunctions in de Sitter space?
• RQ5 Do in-in correlators up to two loops have the same transcendentality as flat space scattering amplitudes?

Key findings

• Up to two loops, in-in correlators in de Sitter space for φ⁴ theory are structurally simpler than wavefunction coefficients due to nontrivial cancellations from shadow field contributions.
• The loop integrands of in-in correlators can be expressed in terms of standard four-dimensional flat space Feynman integrals, with the radial and boundary loop momenta separated.
• The analytic structure of in-in correlators after loop integration matches that of flat space scattering amplitudes, including the same transcendentality.
• A novel recursion relation for in-in correlators is derived, analogous to the one for wavefunctions, with the same diagrammatic structure but modified by shadow field propagators.
• The shadow field contributions partially restore translational invariance, reducing complexity and making in-in correlators closer in structure to flat space amplitudes.
• The result implies that in-in correlators are more amenable to amplitude-theoretic techniques than previously assumed, despite the curved spacetime context.