De Sitter correlators in conformally coupled φ³ theory admit a time-integral representation built from flat-space correlators, revealing intrinsic simplifications including vanishing of odd conjugate-momentum graphs and a smaller symbol alphabet than the corresponding wavefunction coefficients.
A Compact Story of Positivity in de Sitter
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abstract
Recent developments have yielded significant progress towards systematically understanding loop corrections to de Sitter (dS) correlators. In close analogy with physics in Anti-de Sitter (AdS), large logarithms can result from loops that can be interpreted as corrections to the dimensions of operators. In contrast with AdS, these dimensions are not manifestly real. This implies that the theoretical constraints on the associated correlators are less transparent, particularly in the presence of light scalars. In this paper, we revisit these issues by performing and comparing calculations using the spectral representation approach and the Soft de Sitter Effective Theory (SdSET). We review the general arguments that yield positivity constraints on dS correlators from both perspectives. Our particular focus will be on vertex operators for compact scalar fields, since this case introduces novel complications. We will explain how to resolve apparent disagreements between different techniques for calculating the anomalous dimensions for principal series fields coupled to these vertex operators. Along the way, we will offer new proofs of positivity of the anomalous dimensions, and explain why renormalization group flow associated with these anomalous dimensions in SdSET is the same as resumming bubble diagrams in the spectral representation.
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Compactified 5D unparticle theories generate gapped excitations whose exchange in inflationary correlators yields oscillations modulated by anomalous dimensions and possible interference patterns under brane-localized interactions.
Standard SdSET power counting fails for classically conformal φ⁴; leading superhorizon modes must be read from the two-loop anomalous dimension of the two-point function.
Quantization of axions on dS_D yields Hilbert space H = L^2(S^1) ⊗ F with zero-mode U(1) charge, producing non-dS-invariant charged sectors and Hadamard Wightman functions that become asymptotically invariant.
Unified tree-level bispectrum shapes for cosmological collider processes are computed and searched in Planck data, yielding no detection but a weak hint for chemical potential extensions at ω - M ≃ 3H.
citing papers explorer
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On the simplicity of de Sitter correlators
De Sitter correlators in conformally coupled φ³ theory admit a time-integral representation built from flat-space correlators, revealing intrinsic simplifications including vanishing of odd conjugate-momentum graphs and a smaller symbol alphabet than the corresponding wavefunction coefficients.
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Strongly Coupled Sectors in Inflation: Gapped Theories of Unparticles
Compactified 5D unparticle theories generate gapped excitations whose exchange in inflationary correlators yields oscillations modulated by anomalous dimensions and possible interference patterns under brane-localized interactions.
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Classical conformal invariance and superhorizon dynamics in de Sitter
Standard SdSET power counting fails for classically conformal φ⁴; leading superhorizon modes must be read from the two-loop anomalous dimension of the two-point function.
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Axions on de Sitter space
Quantization of axions on dS_D yields Hilbert space H = L^2(S^1) ⊗ F with zero-mode U(1) charge, producing non-dS-invariant charged sectors and Hadamard Wightman functions that become asymptotically invariant.
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Scalars at the Cosmological Collider: Full Shapes of Tree Diagrams and Bispectrum Searches using Planck Data
Unified tree-level bispectrum shapes for cosmological collider processes are computed and searched in Planck data, yielding no detection but a weak hint for chemical potential extensions at ω - M ≃ 3H.